Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.9% → 96.6%

Time: 8.8s

Alternatives: 14

Speedup: 0.5×

• 31.7% 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: 92.9% 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: 96.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\mathsf{fma}\left(a, t + z \cdot b, \mathsf{fma}\left(y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), \mathsf{fma}\left(t, a, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 5e-57)
   (fma a (+ t (* z b)) (fma y z x))
   (fma z (fma a b y) (fma t a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 5e-57) {
		tmp = fma(a, (t + (z * b)), fma(y, z, x));
	} else {
		tmp = fma(z, fma(a, b, y), fma(t, a, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 5e-57)
		tmp = fma(a, Float64(t + Float64(z * b)), fma(y, z, x));
	else
		tmp = fma(z, fma(a, b, y), fma(t, a, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 5e-57], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(y * z + x), $MachinePrecision]), $MachinePrecision], N[(z * N[(a * b + y), $MachinePrecision] + N[(t * a + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.0000000000000002e-57

   1. Initial program 94.6%

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

      1. associate-+l+ 94.7%

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

      2. +-commutative 94.7%

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

      3. *-commutative 94.7%

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

      4. associate-*l* 97.2%

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

      5. distribute-lft-out 97.8%

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

      6. fma-def 97.8%

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

      7. +-commutative 97.8%

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

      8. fma-def 97.8%

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

   3. Simplified 97.8%

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

   if 5.0000000000000002e-57 < z

   1. Initial program 90.6%

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

      1. +-commutative 90.6%

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

      2. +-commutative 90.6%

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

      3. associate-+l+ 90.6%

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

      4. associate-+r+ 90.6%

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

      5. *-commutative 90.6%

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

      6. associate-*l* 95.9%

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

      7. *-commutative 95.9%

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

      8. distribute-lft-out 98.6%

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

      9. fma-def 100.0%

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

      10. fma-def 100.0%

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

      11. +-commutative 100.0%

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

      12. fma-def 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\mathsf{fma}\left(a, t + z \cdot b, \mathsf{fma}\left(y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), \mathsf{fma}\left(t, a, x\right)\right)\\ \end{array} \]

Alternative 2: 97.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + \left(x + z \cdot y\right)\right) + b \cdot \left(z \cdot a\right)\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, a \cdot \left(t + z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (* a t) (+ x (* z y))) (* b (* z a)))))
   (if (<= t_1 5e+306) t_1 (fma z y (* a (+ t (* z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a * t) + (x + (z * y))) + (b * (z * a));
	double tmp;
	if (t_1 <= 5e+306) {
		tmp = t_1;
	} else {
		tmp = fma(z, y, (a * (t + (z * b))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(a * t) + Float64(x + Float64(z * y))) + Float64(b * Float64(z * a)))
	tmp = 0.0
	if (t_1 <= 5e+306)
		tmp = t_1;
	else
		tmp = fma(z, y, Float64(a * Float64(t + Float64(z * b))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+306], t$95$1, N[(z * y + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $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)) < 4.99999999999999993e306

   1. Initial program 97.7%

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

   if 4.99999999999999993e306 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 76.6%

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

   2. Taylor expanded in x around 0 76.6%

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

      1. associate-+l+ 76.6%

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

      2. *-commutative 76.6%

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

      3. fma-def 86.4%

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

      4. associate-*l* 96.1%

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

      5. distribute-lft-out 98.0%

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

   4. Applied egg-rr 98.0%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a \cdot t + \left(x + z \cdot y\right)\right) + b \cdot \left(z \cdot a\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\left(a \cdot t + \left(x + z \cdot y\right)\right) + b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, a \cdot \left(t + z \cdot b\right)\right)\\ \end{array} \]

Alternative 3: 95.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(a * t), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(a * t), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(a * N[(t + N[(z * b), $MachinePrecision]), $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 96.9%

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

      1. associate-+l+ 96.9%

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

      2. associate-*l* 98.0%

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

   3. Simplified 98.0%

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

   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. associate-+l+ 0.0%

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

      2. associate-*l* 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in a around inf 88.9%

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

4. Final simplification 97.7%

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

Alternative 4: 38.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+33}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-173}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-258}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-194}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.62:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= t -4.4e+33)
     (* a t)
     (if (<= t -1.16e-31)
       x
       (if (<= t -9.5e-173)
         (* z y)
         (if (<= t -5.2e-217)
           x
           (if (<= t -3.6e-258)
             (* z y)
             (if (<= t 1.18e-238)
               t_1
               (if (<= t 1.8e-194)
                 (* z y)
                 (if (<= t 5.5e-192) t_1 (if (<= t 0.62) x (* a t))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (t <= -4.4e+33) {
		tmp = a * t;
	} else if (t <= -1.16e-31) {
		tmp = x;
	} else if (t <= -9.5e-173) {
		tmp = z * y;
	} else if (t <= -5.2e-217) {
		tmp = x;
	} else if (t <= -3.6e-258) {
		tmp = z * y;
	} else if (t <= 1.18e-238) {
		tmp = t_1;
	} else if (t <= 1.8e-194) {
		tmp = z * y;
	} else if (t <= 5.5e-192) {
		tmp = t_1;
	} else if (t <= 0.62) {
		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) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (t <= (-4.4d+33)) then
        tmp = a * t
    else if (t <= (-1.16d-31)) then
        tmp = x
    else if (t <= (-9.5d-173)) then
        tmp = z * y
    else if (t <= (-5.2d-217)) then
        tmp = x
    else if (t <= (-3.6d-258)) then
        tmp = z * y
    else if (t <= 1.18d-238) then
        tmp = t_1
    else if (t <= 1.8d-194) then
        tmp = z * y
    else if (t <= 5.5d-192) then
        tmp = t_1
    else if (t <= 0.62d0) 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 t_1 = a * (z * b);
	double tmp;
	if (t <= -4.4e+33) {
		tmp = a * t;
	} else if (t <= -1.16e-31) {
		tmp = x;
	} else if (t <= -9.5e-173) {
		tmp = z * y;
	} else if (t <= -5.2e-217) {
		tmp = x;
	} else if (t <= -3.6e-258) {
		tmp = z * y;
	} else if (t <= 1.18e-238) {
		tmp = t_1;
	} else if (t <= 1.8e-194) {
		tmp = z * y;
	} else if (t <= 5.5e-192) {
		tmp = t_1;
	} else if (t <= 0.62) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if t <= -4.4e+33:
		tmp = a * t
	elif t <= -1.16e-31:
		tmp = x
	elif t <= -9.5e-173:
		tmp = z * y
	elif t <= -5.2e-217:
		tmp = x
	elif t <= -3.6e-258:
		tmp = z * y
	elif t <= 1.18e-238:
		tmp = t_1
	elif t <= 1.8e-194:
		tmp = z * y
	elif t <= 5.5e-192:
		tmp = t_1
	elif t <= 0.62:
		tmp = x
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (t <= -4.4e+33)
		tmp = Float64(a * t);
	elseif (t <= -1.16e-31)
		tmp = x;
	elseif (t <= -9.5e-173)
		tmp = Float64(z * y);
	elseif (t <= -5.2e-217)
		tmp = x;
	elseif (t <= -3.6e-258)
		tmp = Float64(z * y);
	elseif (t <= 1.18e-238)
		tmp = t_1;
	elseif (t <= 1.8e-194)
		tmp = Float64(z * y);
	elseif (t <= 5.5e-192)
		tmp = t_1;
	elseif (t <= 0.62)
		tmp = x;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (t <= -4.4e+33)
		tmp = a * t;
	elseif (t <= -1.16e-31)
		tmp = x;
	elseif (t <= -9.5e-173)
		tmp = z * y;
	elseif (t <= -5.2e-217)
		tmp = x;
	elseif (t <= -3.6e-258)
		tmp = z * y;
	elseif (t <= 1.18e-238)
		tmp = t_1;
	elseif (t <= 1.8e-194)
		tmp = z * y;
	elseif (t <= 5.5e-192)
		tmp = t_1;
	elseif (t <= 0.62)
		tmp = x;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.4e+33], N[(a * t), $MachinePrecision], If[LessEqual[t, -1.16e-31], x, If[LessEqual[t, -9.5e-173], N[(z * y), $MachinePrecision], If[LessEqual[t, -5.2e-217], x, If[LessEqual[t, -3.6e-258], N[(z * y), $MachinePrecision], If[LessEqual[t, 1.18e-238], t$95$1, If[LessEqual[t, 1.8e-194], N[(z * y), $MachinePrecision], If[LessEqual[t, 5.5e-192], t$95$1, If[LessEqual[t, 0.62], x, N[(a * t), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.39999999999999988e33 or 0.619999999999999996 < t

   1. Initial program 94.3%

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

      1. associate-+l+ 94.3%

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

      2. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in t around inf 54.8%

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

   if -4.39999999999999988e33 < t < -1.15999999999999998e-31 or -9.49999999999999967e-173 < t < -5.19999999999999986e-217 or 5.49999999999999995e-192 < t < 0.619999999999999996

   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. associate-+l+ 93.9%

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

      2. associate-*l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in x around inf 53.4%

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

   if -1.15999999999999998e-31 < t < -9.49999999999999967e-173 or -5.19999999999999986e-217 < t < -3.59999999999999979e-258 or 1.18e-238 < t < 1.8e-194

   1. Initial program 90.7%

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

      1. associate-+l+ 90.7%

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

      2. associate-*l* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in y around inf 53.3%

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

      1. *-commutative 53.3%

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

   6. Simplified 53.3%

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

   if -3.59999999999999979e-258 < t < 1.18e-238 or 1.8e-194 < t < 5.49999999999999995e-192

   1. Initial program 93.3%

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

      1. associate-+l+ 93.3%

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

      2. +-commutative 93.3%

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

      3. *-commutative 93.3%

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

      4. associate-*l* 96.5%

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

      5. distribute-lft-out 96.5%

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

      6. fma-def 96.5%

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

      7. +-commutative 96.5%

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

      8. fma-def 96.5%

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

   3. Simplified 96.5%

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

      1. fma-udef 96.5%

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

      2. fma-udef 96.5%

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

      3. +-commutative 96.5%

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

      4. +-commutative 96.5%

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

      5. distribute-lft-in 96.5%

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

      6. *-commutative 96.5%

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

      7. associate-+r+ 96.5%

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

      8. +-commutative 96.5%

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

      9. associate-+l+ 96.5%

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

      10. associate-+r+ 96.5%

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

      11. *-commutative 96.5%

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

      12. fma-def 96.5%

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

      13. *-commutative 96.5%

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

   5. Applied egg-rr 96.5%

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

   6. Taylor expanded in b around inf 57.4%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+33}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-173}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-258}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{-238}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-194}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-192}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 0.62:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 5: 38.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+33}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-173}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-218}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-205}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;t \leq 92:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.15e+33)
   (* a t)
   (if (<= t -2.6e-31)
     x
     (if (<= t -4.2e-173)
       (* z y)
       (if (<= t -2.8e-218)
         x
         (if (<= t 2.6e-205) (* z y) (if (<= t 92.0) x (* a t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.15e+33) {
		tmp = a * t;
	} else if (t <= -2.6e-31) {
		tmp = x;
	} else if (t <= -4.2e-173) {
		tmp = z * y;
	} else if (t <= -2.8e-218) {
		tmp = x;
	} else if (t <= 2.6e-205) {
		tmp = z * y;
	} else if (t <= 92.0) {
		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 (t <= (-1.15d+33)) then
        tmp = a * t
    else if (t <= (-2.6d-31)) then
        tmp = x
    else if (t <= (-4.2d-173)) then
        tmp = z * y
    else if (t <= (-2.8d-218)) then
        tmp = x
    else if (t <= 2.6d-205) then
        tmp = z * y
    else if (t <= 92.0d0) 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 (t <= -1.15e+33) {
		tmp = a * t;
	} else if (t <= -2.6e-31) {
		tmp = x;
	} else if (t <= -4.2e-173) {
		tmp = z * y;
	} else if (t <= -2.8e-218) {
		tmp = x;
	} else if (t <= 2.6e-205) {
		tmp = z * y;
	} else if (t <= 92.0) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.15e+33:
		tmp = a * t
	elif t <= -2.6e-31:
		tmp = x
	elif t <= -4.2e-173:
		tmp = z * y
	elif t <= -2.8e-218:
		tmp = x
	elif t <= 2.6e-205:
		tmp = z * y
	elif t <= 92.0:
		tmp = x
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.15e+33)
		tmp = Float64(a * t);
	elseif (t <= -2.6e-31)
		tmp = x;
	elseif (t <= -4.2e-173)
		tmp = Float64(z * y);
	elseif (t <= -2.8e-218)
		tmp = x;
	elseif (t <= 2.6e-205)
		tmp = Float64(z * y);
	elseif (t <= 92.0)
		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 (t <= -1.15e+33)
		tmp = a * t;
	elseif (t <= -2.6e-31)
		tmp = x;
	elseif (t <= -4.2e-173)
		tmp = z * y;
	elseif (t <= -2.8e-218)
		tmp = x;
	elseif (t <= 2.6e-205)
		tmp = z * y;
	elseif (t <= 92.0)
		tmp = x;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.15e+33], N[(a * t), $MachinePrecision], If[LessEqual[t, -2.6e-31], x, If[LessEqual[t, -4.2e-173], N[(z * y), $MachinePrecision], If[LessEqual[t, -2.8e-218], x, If[LessEqual[t, 2.6e-205], N[(z * y), $MachinePrecision], If[LessEqual[t, 92.0], x, N[(a * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15000000000000005e33 or 92 < t

   1. Initial program 94.3%

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

      1. associate-+l+ 94.3%

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

      2. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in t around inf 54.8%

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

   if -1.15000000000000005e33 < t < -2.59999999999999995e-31 or -4.20000000000000003e-173 < t < -2.80000000000000009e-218 or 2.5999999999999998e-205 < t < 92

   1. Initial program 94.1%

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

      1. associate-+l+ 94.1%

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

      2. associate-*l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in x around inf 52.5%

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

   if -2.59999999999999995e-31 < t < -4.20000000000000003e-173 or -2.80000000000000009e-218 < t < 2.5999999999999998e-205

   1. Initial program 91.5%

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

      1. associate-+l+ 91.5%

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

      2. associate-*l* 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in y around inf 40.7%

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

      1. *-commutative 40.7%

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

   6. Simplified 40.7%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+33}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-173}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-218}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-205}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;t \leq 92:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 6: 39.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;a \leq -1.28 \cdot 10^{-54}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-302}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 930:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3e+18)
   (* b (* z a))
   (if (<= a -1.28e-54)
     (* a t)
     (if (<= a -7e-198)
       x
       (if (<= a -1.6e-302)
         (* z y)
         (if (<= a 3.5e-100) x (if (<= a 930.0) (* z y) (* a t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3e+18) {
		tmp = b * (z * a);
	} else if (a <= -1.28e-54) {
		tmp = a * t;
	} else if (a <= -7e-198) {
		tmp = x;
	} else if (a <= -1.6e-302) {
		tmp = z * y;
	} else if (a <= 3.5e-100) {
		tmp = x;
	} else if (a <= 930.0) {
		tmp = 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 <= (-3d+18)) then
        tmp = b * (z * a)
    else if (a <= (-1.28d-54)) then
        tmp = a * t
    else if (a <= (-7d-198)) then
        tmp = x
    else if (a <= (-1.6d-302)) then
        tmp = z * y
    else if (a <= 3.5d-100) then
        tmp = x
    else if (a <= 930.0d0) then
        tmp = 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 <= -3e+18) {
		tmp = b * (z * a);
	} else if (a <= -1.28e-54) {
		tmp = a * t;
	} else if (a <= -7e-198) {
		tmp = x;
	} else if (a <= -1.6e-302) {
		tmp = z * y;
	} else if (a <= 3.5e-100) {
		tmp = x;
	} else if (a <= 930.0) {
		tmp = z * y;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3e+18:
		tmp = b * (z * a)
	elif a <= -1.28e-54:
		tmp = a * t
	elif a <= -7e-198:
		tmp = x
	elif a <= -1.6e-302:
		tmp = z * y
	elif a <= 3.5e-100:
		tmp = x
	elif a <= 930.0:
		tmp = z * y
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3e+18)
		tmp = Float64(b * Float64(z * a));
	elseif (a <= -1.28e-54)
		tmp = Float64(a * t);
	elseif (a <= -7e-198)
		tmp = x;
	elseif (a <= -1.6e-302)
		tmp = Float64(z * y);
	elseif (a <= 3.5e-100)
		tmp = x;
	elseif (a <= 930.0)
		tmp = 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 <= -3e+18)
		tmp = b * (z * a);
	elseif (a <= -1.28e-54)
		tmp = a * t;
	elseif (a <= -7e-198)
		tmp = x;
	elseif (a <= -1.6e-302)
		tmp = z * y;
	elseif (a <= 3.5e-100)
		tmp = x;
	elseif (a <= 930.0)
		tmp = z * y;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3e+18], N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.28e-54], N[(a * t), $MachinePrecision], If[LessEqual[a, -7e-198], x, If[LessEqual[a, -1.6e-302], N[(z * y), $MachinePrecision], If[LessEqual[a, 3.5e-100], x, If[LessEqual[a, 930.0], N[(z * y), $MachinePrecision], N[(a * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3e18

   1. Initial program 87.8%

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

      1. +-commutative 87.8%

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

      2. +-commutative 87.8%

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

      3. associate-+l+ 87.8%

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

      4. associate-+r+ 87.8%

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

      5. *-commutative 87.8%

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

      6. associate-*l* 82.3%

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

      7. *-commutative 82.3%

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

      8. distribute-lft-out 86.4%

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

      9. fma-def 88.4%

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

      10. fma-def 88.4%

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

      11. +-commutative 88.4%

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

      12. fma-def 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in y around 0 92.1%

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

   5. Taylor expanded in t around 0 62.1%

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

   6. Taylor expanded in a around inf 58.2%

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

   7. Taylor expanded in b around 0 58.2%

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

      1. associate-*r* 52.6%

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

      2. *-commutative 52.6%

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

      3. associate-*r* 62.0%

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

   9. Simplified 62.0%

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

   if -3e18 < a < -1.2800000000000001e-54 or 930 < a

   1. Initial program 85.8%

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

      1. associate-+l+ 85.8%

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

      2. associate-*l* 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around inf 48.2%

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

   if -1.2800000000000001e-54 < a < -7.0000000000000005e-198 or -1.59999999999999989e-302 < a < 3.5000000000000001e-100

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-*l* 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in x around inf 48.0%

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

   if -7.0000000000000005e-198 < a < -1.59999999999999989e-302 or 3.5000000000000001e-100 < a < 930

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in y around inf 50.7%

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

      1. *-commutative 50.7%

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

   6. Simplified 50.7%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;a \leq -1.28 \cdot 10^{-54}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-302}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 930:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 7: 74.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot y\\ t_2 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -7 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.4:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{+33}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z y))) (t_2 (* a (+ t (* z b)))))
   (if (<= a -7e-21)
     t_2
     (if (<= a 3.4)
       t_1
       (if (<= a 9.8e+33) (+ x (* a t)) (if (<= a 1.6e+55) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * y);
	double t_2 = a * (t + (z * b));
	double tmp;
	if (a <= -7e-21) {
		tmp = t_2;
	} else if (a <= 3.4) {
		tmp = t_1;
	} else if (a <= 9.8e+33) {
		tmp = x + (a * t);
	} else if (a <= 1.6e+55) {
		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 * y)
    t_2 = a * (t + (z * b))
    if (a <= (-7d-21)) then
        tmp = t_2
    else if (a <= 3.4d0) then
        tmp = t_1
    else if (a <= 9.8d+33) then
        tmp = x + (a * t)
    else if (a <= 1.6d+55) 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 * y);
	double t_2 = a * (t + (z * b));
	double tmp;
	if (a <= -7e-21) {
		tmp = t_2;
	} else if (a <= 3.4) {
		tmp = t_1;
	} else if (a <= 9.8e+33) {
		tmp = x + (a * t);
	} else if (a <= 1.6e+55) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * y)
	t_2 = a * (t + (z * b))
	tmp = 0
	if a <= -7e-21:
		tmp = t_2
	elif a <= 3.4:
		tmp = t_1
	elif a <= 9.8e+33:
		tmp = x + (a * t)
	elif a <= 1.6e+55:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * y))
	t_2 = Float64(a * Float64(t + Float64(z * b)))
	tmp = 0.0
	if (a <= -7e-21)
		tmp = t_2;
	elseif (a <= 3.4)
		tmp = t_1;
	elseif (a <= 9.8e+33)
		tmp = Float64(x + Float64(a * t));
	elseif (a <= 1.6e+55)
		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 * y);
	t_2 = a * (t + (z * b));
	tmp = 0.0;
	if (a <= -7e-21)
		tmp = t_2;
	elseif (a <= 3.4)
		tmp = t_1;
	elseif (a <= 9.8e+33)
		tmp = x + (a * t);
	elseif (a <= 1.6e+55)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7e-21], t$95$2, If[LessEqual[a, 3.4], t$95$1, If[LessEqual[a, 9.8e+33], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+55], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.0000000000000007e-21 or 1.6000000000000001e55 < a

   1. Initial program 85.3%

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

      1. associate-+l+ 85.3%

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

      2. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in a around inf 83.6%

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

   if -7.0000000000000007e-21 < a < 3.39999999999999991 or 9.80000000000000027e33 < a < 1.6000000000000001e55

   1. Initial program 98.7%

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

      1. associate-+l+ 98.7%

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

      2. associate-*l* 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in a around 0 76.7%

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

   if 3.39999999999999991 < a < 9.80000000000000027e33

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 82.8%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 3.4:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{+33}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+55}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 8: 86.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{-23} \lor \neg \left(b \leq 6 \cdot 10^{+84}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a \cdot t\right) + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.4e-23) (not (<= b 6e+84)))
   (+ x (* a (+ t (* z b))))
   (+ (+ x (* a t)) (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.4e-23) || !(b <= 6e+84)) {
		tmp = x + (a * (t + (z * b)));
	} 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 ((b <= (-5.4d-23)) .or. (.not. (b <= 6d+84))) then
        tmp = x + (a * (t + (z * b)))
    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 ((b <= -5.4e-23) || !(b <= 6e+84)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (x + (a * t)) + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.4e-23) or not (b <= 6e+84):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = (x + (a * t)) + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.4e-23) || !(b <= 6e+84))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(Float64(x + 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 ((b <= -5.4e-23) || ~((b <= 6e+84)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = (x + (a * t)) + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.4e-23], N[Not[LessEqual[b, 6e+84]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.3999999999999997e-23 or 5.99999999999999992e84 < b

   1. Initial program 93.6%

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

      1. associate-+l+ 93.7%

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

      2. +-commutative 93.7%

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

      3. *-commutative 93.7%

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

      4. associate-*l* 90.8%

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

      5. distribute-lft-out 91.7%

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

      6. fma-def 91.7%

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

      7. +-commutative 91.7%

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

      8. fma-def 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in y around 0 86.6%

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

   if -5.3999999999999997e-23 < b < 5.99999999999999992e84

   1. Initial program 93.3%

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

      1. associate-+l+ 93.3%

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

      2. associate-*l* 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in b around 0 95.4%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{-23} \lor \neg \left(b \leq 6 \cdot 10^{+84}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a \cdot t\right) + z \cdot y\\ \end{array} \]

Alternative 9: 80.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+150}:\\ \;\;\;\;a \cdot t + z \cdot y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+131}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.7e+150)
   (+ (* a t) (* z y))
   (if (<= y 8e+131) (+ x (* a (+ t (* z b)))) (* z (+ y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.7e+150) {
		tmp = (a * t) + (z * y);
	} else if (y <= 8e+131) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = z * (y + (a * 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 <= (-1.7d+150)) then
        tmp = (a * t) + (z * y)
    else if (y <= 8d+131) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = z * (y + (a * 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 <= -1.7e+150) {
		tmp = (a * t) + (z * y);
	} else if (y <= 8e+131) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = z * (y + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.7e+150:
		tmp = (a * t) + (z * y)
	elif y <= 8e+131:
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = z * (y + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.7e+150)
		tmp = Float64(Float64(a * t) + Float64(z * y));
	elseif (y <= 8e+131)
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(z * Float64(y + Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.7e+150)
		tmp = (a * t) + (z * y);
	elseif (y <= 8e+131)
		tmp = x + (a * (t + (z * b)));
	else
		tmp = z * (y + (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.7e+150], N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+131], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.69999999999999991e150

   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. associate-+l+ 95.9%

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

      2. associate-*l* 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in b around 0 85.9%

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

   5. Taylor expanded in x around 0 78.8%

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

   if -1.69999999999999991e150 < y < 7.9999999999999993e131

   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. associate-+l+ 93.0%

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

      2. +-commutative 93.0%

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

      3. *-commutative 93.0%

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

      4. associate-*l* 96.3%

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

      5. distribute-lft-out 96.9%

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

      6. fma-def 96.9%

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

      7. +-commutative 96.9%

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

      8. fma-def 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in y around 0 86.6%

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

   if 7.9999999999999993e131 < y

   1. Initial program 94.6%

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

      1. associate-+l+ 94.6%

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

      2. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in z around inf 82.4%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+150}:\\ \;\;\;\;a \cdot t + z \cdot y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+131}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 10: 72.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-120} \lor \neg \left(z \leq 5.6 \cdot 10^{-11}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.8e-120) (not (<= z 5.6e-11)))
   (* z (+ y (* a b)))
   (+ x (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.8e-120) || !(z <= 5.6e-11)) {
		tmp = z * (y + (a * b));
	} 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 <= (-1.8d-120)) .or. (.not. (z <= 5.6d-11))) then
        tmp = z * (y + (a * b))
    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 <= -1.8e-120) || !(z <= 5.6e-11)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.8e-120) or not (z <= 5.6e-11):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (a * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.8e-120) || !(z <= 5.6e-11))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	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 <= -1.8e-120) || ~((z <= 5.6e-11)))
		tmp = z * (y + (a * b));
	else
		tmp = x + (a * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.8e-120], N[Not[LessEqual[z, 5.6e-11]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8000000000000001e-120 or 5.6e-11 < z

   1. Initial program 89.8%

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

      1. associate-+l+ 89.8%

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

      2. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in z around inf 67.4%

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

   if -1.8000000000000001e-120 < z < 5.6e-11

   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. associate-+l+ 97.7%

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

      2. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 77.7%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-120} \lor \neg \left(z \leq 5.6 \cdot 10^{-11}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \]

Alternative 11: 58.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+149}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+142}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.4e+149) (* z y) (if (<= y 7.2e+142) (+ x (* a t)) (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.4e+149) {
		tmp = z * y;
	} else if (y <= 7.2e+142) {
		tmp = x + (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 <= (-7.4d+149)) then
        tmp = z * y
    else if (y <= 7.2d+142) then
        tmp = x + (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 <= -7.4e+149) {
		tmp = z * y;
	} else if (y <= 7.2e+142) {
		tmp = x + (a * t);
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7.4e+149:
		tmp = z * y
	elif y <= 7.2e+142:
		tmp = x + (a * t)
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.4e+149)
		tmp = Float64(z * y);
	elseif (y <= 7.2e+142)
		tmp = Float64(x + 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 <= -7.4e+149)
		tmp = z * y;
	elseif (y <= 7.2e+142)
		tmp = x + (a * t);
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.4e+149], N[(z * y), $MachinePrecision], If[LessEqual[y, 7.2e+142], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.39999999999999957e149 or 7.2000000000000003e142 < y

   1. Initial program 94.8%

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

      1. associate-+l+ 94.8%

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

      2. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in y around inf 66.9%

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

      1. *-commutative 66.9%

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

   6. Simplified 66.9%

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

   if -7.39999999999999957e149 < y < 7.2000000000000003e142

   1. Initial program 93.1%

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

      1. associate-+l+ 93.1%

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

      2. associate-*l* 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 64.5%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+149}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+142}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 12: 61.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;a \leq 0.35:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.5e+18)
   (* b (* z a))
   (if (<= a 0.35) (+ x (* z y)) (+ x (* a t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.5e+18) {
		tmp = b * (z * a);
	} else if (a <= 0.35) {
		tmp = x + (z * 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 (a <= (-3.5d+18)) then
        tmp = b * (z * a)
    else if (a <= 0.35d0) then
        tmp = x + (z * 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 (a <= -3.5e+18) {
		tmp = b * (z * a);
	} else if (a <= 0.35) {
		tmp = x + (z * y);
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.5e+18:
		tmp = b * (z * a)
	elif a <= 0.35:
		tmp = x + (z * y)
	else:
		tmp = x + (a * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.5e+18)
		tmp = Float64(b * Float64(z * a));
	elseif (a <= 0.35)
		tmp = Float64(x + Float64(z * 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 (a <= -3.5e+18)
		tmp = b * (z * a);
	elseif (a <= 0.35)
		tmp = x + (z * y);
	else
		tmp = x + (a * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.5e+18], N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.35], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.5e18

   1. Initial program 87.8%

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

      1. +-commutative 87.8%

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

      2. +-commutative 87.8%

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

      3. associate-+l+ 87.8%

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

      4. associate-+r+ 87.8%

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

      5. *-commutative 87.8%

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

      6. associate-*l* 82.3%

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

      7. *-commutative 82.3%

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

      8. distribute-lft-out 86.4%

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

      9. fma-def 88.4%

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

      10. fma-def 88.4%

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

      11. +-commutative 88.4%

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

      12. fma-def 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in y around 0 92.1%

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

   5. Taylor expanded in t around 0 62.1%

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

   6. Taylor expanded in a around inf 58.2%

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

   7. Taylor expanded in b around 0 58.2%

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

      1. associate-*r* 52.6%

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

      2. *-commutative 52.6%

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

      3. associate-*r* 62.0%

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

   9. Simplified 62.0%

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

   if -3.5e18 < a < 0.34999999999999998

   1. Initial program 98.7%

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

      1. associate-+l+ 98.7%

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

      2. associate-*l* 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in a around 0 74.3%

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

   if 0.34999999999999998 < a

   1. Initial program 85.4%

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

      1. associate-+l+ 85.4%

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

      2. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in z around 0 65.5%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;a \leq 0.35:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \]

Alternative 13: 39.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+32}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq 0.059:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.8e+32) (* a t) (if (<= t 0.059) x (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.8e+32) {
		tmp = a * t;
	} else if (t <= 0.059) {
		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 (t <= (-5.8d+32)) then
        tmp = a * t
    else if (t <= 0.059d0) 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 (t <= -5.8e+32) {
		tmp = a * t;
	} else if (t <= 0.059) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5.8e+32:
		tmp = a * t
	elif t <= 0.059:
		tmp = x
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.8e+32)
		tmp = Float64(a * t);
	elseif (t <= 0.059)
		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 (t <= -5.8e+32)
		tmp = a * t;
	elseif (t <= 0.059)
		tmp = x;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.8e+32], N[(a * t), $MachinePrecision], If[LessEqual[t, 0.059], x, N[(a * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.80000000000000006e32 or 0.058999999999999997 < t

   1. Initial program 94.3%

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

      1. associate-+l+ 94.3%

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

      2. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in t around inf 54.8%

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

   if -5.80000000000000006e32 < t < 0.058999999999999997

   1. Initial program 92.7%

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

      1. associate-+l+ 92.7%

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

      2. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 36.9%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+32}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq 0.059:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 14: 27.0% 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 93.5%

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

   1. associate-+l+ 93.5%

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

   2. associate-*l* 95.3%

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

3. Simplified 95.3%

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

4. Taylor expanded in x around inf 26.2%

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

5. Final simplification 26.2%

   \[\leadsto x \]

Developer target: 97.4% 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 2023215 
(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)))