Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 91.8% → 95.9%

Time: 15.2s

Alternatives: 16

Speedup: 0.5×

• 32.4% 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: 91.8% 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: 95.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot a + \left(x + y \cdot z\right)\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+284}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), \mathsf{fma}\left(t, a, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (* t a) (+ x (* y z))) (* (* z a) b))))
   (if (<= t_1 5e+284) t_1 (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 t_1 = ((t * a) + (x + (y * z))) + ((z * a) * b);
	double tmp;
	if (t_1 <= 5e+284) {
		tmp = t_1;
	} else {
		tmp = fma(z, fma(a, b, y), fma(t, a, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t * a) + Float64(x + Float64(y * z))) + Float64(Float64(z * a) * b))
	tmp = 0.0
	if (t_1 <= 5e+284)
		tmp = t_1;
	else
		tmp = fma(z, fma(a, b, y), fma(t, a, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+284], t$95$1, N[(z * N[(a * b + y), $MachinePrecision] + N[(t * a + x), $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)) < 4.9999999999999999e284

   1. Initial program 99.0%

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

   if 4.9999999999999999e284 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 70.7%

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

      1. +-commutative 70.7%

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

      2. +-commutative 70.7%

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

      3. associate-+l+ 70.7%

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

      4. associate-+r+ 70.7%

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

      5. *-commutative 70.7%

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

      6. associate-*l* 84.1%

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

      7. *-commutative 84.1%

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

      8. distribute-lft-out 93.2%

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

      9. fma-def 97.7%

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

      10. fma-def 97.7%

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

      11. +-commutative 97.7%

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

      12. fma-def 97.7%

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

   3. Simplified 97.7%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t \cdot a + \left(x + y \cdot z\right)\right) + \left(z \cdot a\right) \cdot b \leq 5 \cdot 10^{+284}:\\ \;\;\;\;\left(t \cdot a + \left(x + y \cdot z\right)\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), \mathsf{fma}\left(t, a, x\right)\right)\\ \end{array} \]

Alternative 2: 95.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot a + \left(x + y \cdot z\right)\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;t_1 \leq 10^{+200}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t + z \cdot b, \mathsf{fma}\left(y, z, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (* t a) (+ x (* y z))) (* (* z a) b))))
   (if (<= t_1 1e+200) t_1 (fma a (+ t (* z b)) (fma y z x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t * a) + (x + (y * z))) + ((z * a) * b);
	double tmp;
	if (t_1 <= 1e+200) {
		tmp = t_1;
	} else {
		tmp = fma(a, (t + (z * b)), fma(y, z, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t * a) + Float64(x + Float64(y * z))) + Float64(Float64(z * a) * b))
	tmp = 0.0
	if (t_1 <= 1e+200)
		tmp = t_1;
	else
		tmp = fma(a, Float64(t + Float64(z * b)), fma(y, z, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+200], t$95$1, N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(y * z + x), $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)) < 9.9999999999999997e199

   1. Initial program 98.9%

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

   if 9.9999999999999997e199 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 82.3%

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

      1. associate-+l+ 82.3%

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

      2. +-commutative 82.3%

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

      3. *-commutative 82.3%

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

      4. associate-*l* 89.0%

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

      5. distribute-lft-out 91.8%

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

      6. fma-def 93.2%

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

      7. +-commutative 93.2%

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

      8. fma-def 93.2%

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

   3. Simplified 93.2%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t \cdot a + \left(x + y \cdot z\right)\right) + \left(z \cdot a\right) \cdot b \leq 10^{+200}:\\ \;\;\;\;\left(t \cdot a + \left(x + y \cdot z\right)\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t + z \cdot b, \mathsf{fma}\left(y, z, x\right)\right)\\ \end{array} \]

Alternative 3: 96.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(y + N[(a * 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 97.6%

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

   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. 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 z around inf 77.8%

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

4. Final simplification 96.9%

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

Alternative 4: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+76}:\\ \;\;\;\;y \cdot z + a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-14} \lor \neg \left(a \leq 1.05 \cdot 10^{+54}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -1.35e+128)
     t_1
     (if (<= a -1.8e+76)
       (+ (* y z) (* a (* z b)))
       (if (or (<= a -1.42e-14) (not (<= a 1.05e+54))) t_1 (+ x (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double tmp;
	if (a <= -1.35e+128) {
		tmp = t_1;
	} else if (a <= -1.8e+76) {
		tmp = (y * z) + (a * (z * b));
	} else if ((a <= -1.42e-14) || !(a <= 1.05e+54)) {
		tmp = t_1;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t + (z * b))
    if (a <= (-1.35d+128)) then
        tmp = t_1
    else if (a <= (-1.8d+76)) then
        tmp = (y * z) + (a * (z * b))
    else if ((a <= (-1.42d-14)) .or. (.not. (a <= 1.05d+54))) then
        tmp = t_1
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double tmp;
	if (a <= -1.35e+128) {
		tmp = t_1;
	} else if (a <= -1.8e+76) {
		tmp = (y * z) + (a * (z * b));
	} else if ((a <= -1.42e-14) || !(a <= 1.05e+54)) {
		tmp = t_1;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	tmp = 0
	if a <= -1.35e+128:
		tmp = t_1
	elif a <= -1.8e+76:
		tmp = (y * z) + (a * (z * b))
	elif (a <= -1.42e-14) or not (a <= 1.05e+54):
		tmp = t_1
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + Float64(z * b)))
	tmp = 0.0
	if (a <= -1.35e+128)
		tmp = t_1;
	elseif (a <= -1.8e+76)
		tmp = Float64(Float64(y * z) + Float64(a * Float64(z * b)));
	elseif ((a <= -1.42e-14) || !(a <= 1.05e+54))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + (z * b));
	tmp = 0.0;
	if (a <= -1.35e+128)
		tmp = t_1;
	elseif (a <= -1.8e+76)
		tmp = (y * z) + (a * (z * b));
	elseif ((a <= -1.42e-14) || ~((a <= 1.05e+54)))
		tmp = t_1;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.35e+128], t$95$1, If[LessEqual[a, -1.8e+76], N[(N[(y * z), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -1.42e-14], N[Not[LessEqual[a, 1.05e+54]], $MachinePrecision]], t$95$1, N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.35000000000000001e128 or -1.8000000000000001e76 < a < -1.42000000000000004e-14 or 1.04999999999999993e54 < a

   1. Initial program 90.1%

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

      1. associate-+l+ 90.1%

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

      2. associate-*l* 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 a around inf 80.6%

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

   if -1.35000000000000001e128 < a < -1.8000000000000001e76

   1. Initial program 77.5%

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

      1. associate-+l+ 77.5%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 99.9%

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

   5. Taylor expanded in x around 0 77.5%

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

   if -1.42000000000000004e-14 < a < 1.04999999999999993e54

   1. Initial program 98.5%

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

      1. associate-+l+ 98.5%

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

      2. associate-*l* 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in a around 0 73.3%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+76}:\\ \;\;\;\;y \cdot z + a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-14} \lor \neg \left(a \leq 1.05 \cdot 10^{+54}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 5: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-85} \lor \neg \left(t \leq 9 \cdot 10^{-22}\right):\\ \;\;\;\;y \cdot z + \left(x + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right) + \left(x + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1e-85) (not (<= t 9e-22)))
   (+ (* y z) (+ x (* t a)))
   (+ (* a (* z b)) (+ x (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1e-85) || !(t <= 9e-22)) {
		tmp = (y * z) + (x + (t * a));
	} else {
		tmp = (a * (z * b)) + (x + (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1d-85)) .or. (.not. (t <= 9d-22))) then
        tmp = (y * z) + (x + (t * a))
    else
        tmp = (a * (z * b)) + (x + (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1e-85) || !(t <= 9e-22)) {
		tmp = (y * z) + (x + (t * a));
	} else {
		tmp = (a * (z * b)) + (x + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1e-85) or not (t <= 9e-22):
		tmp = (y * z) + (x + (t * a))
	else:
		tmp = (a * (z * b)) + (x + (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1e-85) || !(t <= 9e-22))
		tmp = Float64(Float64(y * z) + Float64(x + Float64(t * a)));
	else
		tmp = Float64(Float64(a * Float64(z * b)) + Float64(x + Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1e-85) || ~((t <= 9e-22)))
		tmp = (y * z) + (x + (t * a));
	else
		tmp = (a * (z * b)) + (x + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1e-85], N[Not[LessEqual[t, 9e-22]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.9999999999999998e-86 or 8.99999999999999973e-22 < t

   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* 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in b around 0 83.8%

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

   if -9.9999999999999998e-86 < t < 8.99999999999999973e-22

   1. Initial program 94.5%

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

      1. associate-+l+ 94.5%

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

      2. associate-*l* 94.6%

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

   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 0 92.1%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-85} \lor \neg \left(t \leq 9 \cdot 10^{-22}\right):\\ \;\;\;\;y \cdot z + \left(x + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right) + \left(x + y \cdot z\right)\\ \end{array} \]

Alternative 6: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+64} \lor \neg \left(b \leq 2.25 \cdot 10^{+102}\right):\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(x + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -9e+64) (not (<= b 2.25e+102)))
   (+ (* (* z a) b) (+ x (* y z)))
   (+ (* y z) (+ x (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9e+64) || !(b <= 2.25e+102)) {
		tmp = ((z * a) * b) + (x + (y * z));
	} else {
		tmp = (y * z) + (x + (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-9d+64)) .or. (.not. (b <= 2.25d+102))) then
        tmp = ((z * a) * b) + (x + (y * z))
    else
        tmp = (y * z) + (x + (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9e+64) || !(b <= 2.25e+102)) {
		tmp = ((z * a) * b) + (x + (y * z));
	} else {
		tmp = (y * z) + (x + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -9e+64) or not (b <= 2.25e+102):
		tmp = ((z * a) * b) + (x + (y * z))
	else:
		tmp = (y * z) + (x + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -9e+64) || !(b <= 2.25e+102))
		tmp = Float64(Float64(Float64(z * a) * b) + Float64(x + Float64(y * z)));
	else
		tmp = Float64(Float64(y * z) + Float64(x + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -9e+64) || ~((b <= 2.25e+102)))
		tmp = ((z * a) * b) + (x + (y * z));
	else
		tmp = (y * z) + (x + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -9e+64], N[Not[LessEqual[b, 2.25e+102]], $MachinePrecision]], N[(N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.99999999999999946e64 or 2.2500000000000001e102 < b

   1. Initial program 95.5%

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

      1. associate-+l+ 95.5%

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

      2. associate-*l* 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in t around 0 75.6%

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

   5. Taylor expanded in b around 0 75.6%

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

      1. associate-*r* 82.2%

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

      2. *-commutative 82.2%

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

      3. associate-*r* 85.0%

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

   7. Simplified 85.0%

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

   if -8.99999999999999946e64 < b < 2.2500000000000001e102

   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. associate-+l+ 93.4%

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

      2. associate-*l* 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in b around 0 92.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+64} \lor \neg \left(b \leq 2.25 \cdot 10^{+102}\right):\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(x + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + t \cdot a\right)\\ \end{array} \]

Alternative 7: 91.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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* 93.5%

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

3. Simplified 93.5%

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

4. Final simplification 93.5%

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

Alternative 8: 39.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-64}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-214}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-259}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-156}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -8.6e-64)
   (* t a)
   (if (<= t -1e-214)
     (* a (* z b))
     (if (<= t 1.5e-259)
       x
       (if (<= t 6.8e-156) (* y z) (if (<= t 7.6e+27) x (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.6e-64) {
		tmp = t * a;
	} else if (t <= -1e-214) {
		tmp = a * (z * b);
	} else if (t <= 1.5e-259) {
		tmp = x;
	} else if (t <= 6.8e-156) {
		tmp = y * z;
	} else if (t <= 7.6e+27) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-8.6d-64)) then
        tmp = t * a
    else if (t <= (-1d-214)) then
        tmp = a * (z * b)
    else if (t <= 1.5d-259) then
        tmp = x
    else if (t <= 6.8d-156) then
        tmp = y * z
    else if (t <= 7.6d+27) then
        tmp = x
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.6e-64) {
		tmp = t * a;
	} else if (t <= -1e-214) {
		tmp = a * (z * b);
	} else if (t <= 1.5e-259) {
		tmp = x;
	} else if (t <= 6.8e-156) {
		tmp = y * z;
	} else if (t <= 7.6e+27) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -8.6e-64:
		tmp = t * a
	elif t <= -1e-214:
		tmp = a * (z * b)
	elif t <= 1.5e-259:
		tmp = x
	elif t <= 6.8e-156:
		tmp = y * z
	elif t <= 7.6e+27:
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -8.6e-64)
		tmp = Float64(t * a);
	elseif (t <= -1e-214)
		tmp = Float64(a * Float64(z * b));
	elseif (t <= 1.5e-259)
		tmp = x;
	elseif (t <= 6.8e-156)
		tmp = Float64(y * z);
	elseif (t <= 7.6e+27)
		tmp = x;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -8.6e-64)
		tmp = t * a;
	elseif (t <= -1e-214)
		tmp = a * (z * b);
	elseif (t <= 1.5e-259)
		tmp = x;
	elseif (t <= 6.8e-156)
		tmp = y * z;
	elseif (t <= 7.6e+27)
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -8.6e-64], N[(t * a), $MachinePrecision], If[LessEqual[t, -1e-214], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e-259], x, If[LessEqual[t, 6.8e-156], N[(y * z), $MachinePrecision], If[LessEqual[t, 7.6e+27], x, N[(t * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.59999999999999947e-64 or 7.60000000000000043e27 < t

   1. Initial program 94.4%

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

      1. associate-+l+ 94.4%

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

      2. associate-*l* 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in t around inf 49.8%

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

   if -8.59999999999999947e-64 < t < -9.99999999999999913e-215

   1. Initial program 95.1%

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

      1. associate-+l+ 95.1%

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

      2. associate-*l* 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in a around inf 46.6%

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

   5. Taylor expanded in t around 0 46.5%

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

   if -9.99999999999999913e-215 < t < 1.5000000000000001e-259 or 6.79999999999999981e-156 < t < 7.60000000000000043e27

   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. associate-+l+ 95.8%

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

      2. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in x around inf 48.6%

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

   if 1.5000000000000001e-259 < t < 6.79999999999999981e-156

   1. Initial program 84.2%

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

      1. associate-+l+ 84.2%

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

      2. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around inf 59.3%

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

      1. *-commutative 59.3%

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

   6. Simplified 59.3%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-64}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-214}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-259}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-156}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]

Alternative 9: 60.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-233}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-46}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ y (* a b)))))
   (if (<= z -9e-7)
     t_1
     (if (<= z 8.2e-233) (+ x (* y z)) (if (<= z 1.55e-46) (* t a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + (a * b));
	double tmp;
	if (z <= -9e-7) {
		tmp = t_1;
	} else if (z <= 8.2e-233) {
		tmp = x + (y * z);
	} else if (z <= 1.55e-46) {
		tmp = t * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y + (a * b))
    if (z <= (-9d-7)) then
        tmp = t_1
    else if (z <= 8.2d-233) then
        tmp = x + (y * z)
    else if (z <= 1.55d-46) then
        tmp = t * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + (a * b));
	double tmp;
	if (z <= -9e-7) {
		tmp = t_1;
	} else if (z <= 8.2e-233) {
		tmp = x + (y * z);
	} else if (z <= 1.55e-46) {
		tmp = t * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (y + (a * b))
	tmp = 0
	if z <= -9e-7:
		tmp = t_1
	elif z <= 8.2e-233:
		tmp = x + (y * z)
	elif z <= 1.55e-46:
		tmp = t * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (z <= -9e-7)
		tmp = t_1;
	elseif (z <= 8.2e-233)
		tmp = Float64(x + Float64(y * z));
	elseif (z <= 1.55e-46)
		tmp = Float64(t * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (y + (a * b));
	tmp = 0.0;
	if (z <= -9e-7)
		tmp = t_1;
	elseif (z <= 8.2e-233)
		tmp = x + (y * z);
	elseif (z <= 1.55e-46)
		tmp = t * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e-7], t$95$1, If[LessEqual[z, 8.2e-233], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-46], N[(t * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.99999999999999959e-7 or 1.55e-46 < z

   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. associate-*l* 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in z around inf 73.5%

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

   if -8.99999999999999959e-7 < z < 8.2000000000000009e-233

   1. Initial program 98.9%

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

      1. associate-+l+ 98.9%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 62.1%

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

   if 8.2000000000000009e-233 < z < 1.55e-46

   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* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 56.5%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-233}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-46}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 10: 80.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+197} \lor \neg \left(b \leq 1.65 \cdot 10^{+213}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.5e+197) (not (<= b 1.65e+213)))
   (* z (+ y (* a b)))
   (+ (* y z) (+ x (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.5e+197) || !(b <= 1.65e+213)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = (y * z) + (x + (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-4.5d+197)) .or. (.not. (b <= 1.65d+213))) then
        tmp = z * (y + (a * b))
    else
        tmp = (y * z) + (x + (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.5e+197) || !(b <= 1.65e+213)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = (y * z) + (x + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.5e+197) or not (b <= 1.65e+213):
		tmp = z * (y + (a * b))
	else:
		tmp = (y * z) + (x + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.5e+197) || !(b <= 1.65e+213))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(Float64(y * z) + Float64(x + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.5e+197) || ~((b <= 1.65e+213)))
		tmp = z * (y + (a * b));
	else
		tmp = (y * z) + (x + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.5e+197], N[Not[LessEqual[b, 1.65e+213]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.5000000000000003e197 or 1.6500000000000001e213 < b

   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* 84.4%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in z around inf 71.6%

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

   if -4.5000000000000003e197 < b < 1.6500000000000001e213

   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* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in b around 0 86.2%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+197} \lor \neg \left(b \leq 1.65 \cdot 10^{+213}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + t \cdot a\right)\\ \end{array} \]

Alternative 11: 80.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+198}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+213}:\\ \;\;\;\;y \cdot z + \left(x + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(z \cdot a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4e+198)
   (* z (+ y (* a b)))
   (if (<= b 2.9e+213) (+ (* y z) (+ x (* t a))) (+ (* y z) (* (* z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4e+198) {
		tmp = z * (y + (a * b));
	} else if (b <= 2.9e+213) {
		tmp = (y * z) + (x + (t * a));
	} else {
		tmp = (y * z) + ((z * 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 (b <= (-4d+198)) then
        tmp = z * (y + (a * b))
    else if (b <= 2.9d+213) then
        tmp = (y * z) + (x + (t * a))
    else
        tmp = (y * z) + ((z * 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 (b <= -4e+198) {
		tmp = z * (y + (a * b));
	} else if (b <= 2.9e+213) {
		tmp = (y * z) + (x + (t * a));
	} else {
		tmp = (y * z) + ((z * a) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4e+198:
		tmp = z * (y + (a * b))
	elif b <= 2.9e+213:
		tmp = (y * z) + (x + (t * a))
	else:
		tmp = (y * z) + ((z * a) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4e+198)
		tmp = Float64(z * Float64(y + Float64(a * b)));
	elseif (b <= 2.9e+213)
		tmp = Float64(Float64(y * z) + Float64(x + Float64(t * a)));
	else
		tmp = Float64(Float64(y * z) + Float64(Float64(z * a) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4e+198)
		tmp = z * (y + (a * b));
	elseif (b <= 2.9e+213)
		tmp = (y * z) + (x + (t * a));
	else
		tmp = (y * z) + ((z * a) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4e+198], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.9e+213], N[(N[(y * z), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.00000000000000007e198

   1. Initial program 89.5%

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

      1. associate-+l+ 89.5%

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

      2. associate-*l* 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in z around inf 74.5%

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

   if -4.00000000000000007e198 < b < 2.9000000000000003e213

   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* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in b around 0 86.2%

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

   if 2.9000000000000003e213 < b

   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* 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in z around inf 68.5%

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

      1. +-commutative 68.5%

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

      2. distribute-rgt-in 68.5%

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

      3. *-commutative 68.5%

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

      4. associate-*r* 78.3%

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

      5. *-commutative 78.3%

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

   6. Applied egg-rr 78.3%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+198}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+213}:\\ \;\;\;\;y \cdot z + \left(x + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(z \cdot a\right) \cdot b\\ \end{array} \]

Alternative 12: 40.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-46}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{-255}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-148}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.1e-46)
   (* t a)
   (if (<= t 3.45e-255)
     x
     (if (<= t 6.4e-148) (* y z) (if (<= t 3.8e+26) x (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.1e-46) {
		tmp = t * a;
	} else if (t <= 3.45e-255) {
		tmp = x;
	} else if (t <= 6.4e-148) {
		tmp = y * z;
	} else if (t <= 3.8e+26) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.1d-46)) then
        tmp = t * a
    else if (t <= 3.45d-255) then
        tmp = x
    else if (t <= 6.4d-148) then
        tmp = y * z
    else if (t <= 3.8d+26) then
        tmp = x
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.1e-46) {
		tmp = t * a;
	} else if (t <= 3.45e-255) {
		tmp = x;
	} else if (t <= 6.4e-148) {
		tmp = y * z;
	} else if (t <= 3.8e+26) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.1e-46:
		tmp = t * a
	elif t <= 3.45e-255:
		tmp = x
	elif t <= 6.4e-148:
		tmp = y * z
	elif t <= 3.8e+26:
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.1e-46)
		tmp = Float64(t * a);
	elseif (t <= 3.45e-255)
		tmp = x;
	elseif (t <= 6.4e-148)
		tmp = Float64(y * z);
	elseif (t <= 3.8e+26)
		tmp = x;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.1e-46)
		tmp = t * a;
	elseif (t <= 3.45e-255)
		tmp = x;
	elseif (t <= 6.4e-148)
		tmp = y * z;
	elseif (t <= 3.8e+26)
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.1e-46], N[(t * a), $MachinePrecision], If[LessEqual[t, 3.45e-255], x, If[LessEqual[t, 6.4e-148], N[(y * z), $MachinePrecision], If[LessEqual[t, 3.8e+26], x, N[(t * a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e-46 or 3.8000000000000002e26 < 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* 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in t around inf 50.2%

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

   if -1.1e-46 < t < 3.4499999999999998e-255 or 6.39999999999999987e-148 < t < 3.8000000000000002e26

   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. associate-+l+ 95.6%

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

      2. associate-*l* 94.0%

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

   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 x around inf 42.4%

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

   if 3.4499999999999998e-255 < t < 6.39999999999999987e-148

   1. Initial program 84.2%

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

      1. associate-+l+ 84.2%

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

      2. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around inf 59.3%

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

      1. *-commutative 59.3%

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

   6. Simplified 59.3%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-46}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{-255}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-148}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]

Alternative 13: 59.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+234}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+127}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+167}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.05e+234)
   (* a (* z b))
   (if (<= a -1.3e+127) (* t a) (if (<= a 1.45e+167) (+ x (* y z)) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.05e+234) {
		tmp = a * (z * b);
	} else if (a <= -1.3e+127) {
		tmp = t * a;
	} else if (a <= 1.45e+167) {
		tmp = x + (y * z);
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.05d+234)) then
        tmp = a * (z * b)
    else if (a <= (-1.3d+127)) then
        tmp = t * a
    else if (a <= 1.45d+167) then
        tmp = x + (y * z)
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.05e+234) {
		tmp = a * (z * b);
	} else if (a <= -1.3e+127) {
		tmp = t * a;
	} else if (a <= 1.45e+167) {
		tmp = x + (y * z);
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.05e+234:
		tmp = a * (z * b)
	elif a <= -1.3e+127:
		tmp = t * a
	elif a <= 1.45e+167:
		tmp = x + (y * z)
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.05e+234)
		tmp = Float64(a * Float64(z * b));
	elseif (a <= -1.3e+127)
		tmp = Float64(t * a);
	elseif (a <= 1.45e+167)
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.05e+234)
		tmp = a * (z * b);
	elseif (a <= -1.3e+127)
		tmp = t * a;
	elseif (a <= 1.45e+167)
		tmp = x + (y * z);
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.05e+234], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.3e+127], N[(t * a), $MachinePrecision], If[LessEqual[a, 1.45e+167], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.05e234

   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* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around inf 90.1%

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

   5. Taylor expanded in t around 0 70.6%

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

   if -1.05e234 < a < -1.3000000000000001e127 or 1.44999999999999987e167 < a

   1. Initial program 84.1%

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

      1. associate-+l+ 84.1%

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

      2. associate-*l* 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in t around inf 59.8%

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

   if -1.3000000000000001e127 < a < 1.44999999999999987e167

   1. Initial program 96.4%

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

      1. associate-+l+ 96.4%

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

      2. associate-*l* 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 a around 0 64.8%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+234}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+127}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+167}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]

Alternative 14: 74.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-15} \lor \neg \left(a \leq 7.8 \cdot 10^{+52}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -7e-15) (not (<= a 7.8e+52)))
   (* a (+ t (* z b)))
   (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7e-15) || !(a <= 7.8e+52)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-7d-15)) .or. (.not. (a <= 7.8d+52))) then
        tmp = a * (t + (z * b))
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7e-15) || !(a <= 7.8e+52)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -7e-15) or not (a <= 7.8e+52):
		tmp = a * (t + (z * b))
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -7e-15) || !(a <= 7.8e+52))
		tmp = Float64(a * Float64(t + Float64(z * b)));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -7e-15) || ~((a <= 7.8e+52)))
		tmp = a * (t + (z * b));
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -7e-15], N[Not[LessEqual[a, 7.8e+52]], $MachinePrecision]], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.0000000000000001e-15 or 7.7999999999999999e52 < a

   1. Initial program 88.7%

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

      1. associate-+l+ 88.7%

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

      2. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in a around inf 76.0%

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

   if -7.0000000000000001e-15 < a < 7.7999999999999999e52

   1. Initial program 98.5%

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

      1. associate-+l+ 98.5%

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

      2. associate-*l* 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in a around 0 73.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-15} \lor \neg \left(a \leq 7.8 \cdot 10^{+52}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 15: 40.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{-49}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.15e-49) (* t a) (if (<= t 5.5e+26) x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.15e-49) {
		tmp = t * a;
	} else if (t <= 5.5e+26) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.15d-49)) then
        tmp = t * a
    else if (t <= 5.5d+26) then
        tmp = x
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.15e-49) {
		tmp = t * a;
	} else if (t <= 5.5e+26) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.15e-49:
		tmp = t * a
	elif t <= 5.5e+26:
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.15e-49)
		tmp = Float64(t * a);
	elseif (t <= 5.5e+26)
		tmp = x;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.15e-49)
		tmp = t * a;
	elseif (t <= 5.5e+26)
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.15e-49], N[(t * a), $MachinePrecision], If[LessEqual[t, 5.5e+26], x, N[(t * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1499999999999998e-49 or 5.4999999999999997e26 < 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* 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in t around inf 50.2%

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

   if -3.1499999999999998e-49 < t < 5.4999999999999997e26

   1. Initial program 94.0%

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

      1. associate-+l+ 94.0%

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

      2. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in x around inf 40.4%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{-49}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]

Alternative 16: 27.5% 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 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* 93.5%

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

3. Simplified 93.5%

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

4. Taylor expanded in x around inf 28.4%

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

5. Final simplification 28.4%

   \[\leadsto x \]

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 2023278 
(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)))