Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.0% → 95.0%

Time: 9.3s

Alternatives: 14

Speedup: 0.8×

• 33.1% 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: 92.0% 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: 95.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], Infinity], N[(a * t$95$1 + N[(y * z + x), $MachinePrecision]), $MachinePrecision], N[(a * t$95$1), $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 96.3%

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

      1. associate-+l+ 96.3%

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

      2. +-commutative 96.3%

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

      3. *-commutative 96.3%

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

      4. *-commutative 96.3%

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

      5. associate-*l* 97.1%

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

      6. distribute-rgt-out 97.1%

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

      7. fma-def 97.1%

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

      8. *-commutative 97.1%

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

      9. +-commutative 97.1%

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

      10. fma-def 97.1%

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

   3. Simplified 97.1%

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

   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. *-commutative 0.0%

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

      2. associate-*l* 11.1%

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

   3. Simplified 11.1%

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

   4. Taylor expanded in a around inf 94.4%

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

4. Final simplification 97.0%

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

Alternative 2: 96.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* y z)) (* t a)) (* (* z a) b))))
   (if (<= t_1 INFINITY) 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 + (y * z)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = 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 + (y * z)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = a * (t + (z * b));
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(z * a) * b))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = 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 + (y * z)) + (t * a)) + ((z * a) * b);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = 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[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, 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 96.3%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l* 11.1%

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

   3. Simplified 11.1%

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

   4. Taylor expanded in a around inf 94.4%

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

4. Final simplification 96.2%

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

Alternative 3: 36.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+55}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-111}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-194}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-82}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq 950:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+36} \lor \neg \left(b \leq 2.25 \cdot 10^{+99}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= b -2.2e+165)
     t_1
     (if (<= b -1.05e+55)
       (* t a)
       (if (<= b -3.1e-111)
         (* y z)
         (if (<= b -8.5e-238)
           x
           (if (<= b 4.5e-194)
             (* y z)
             (if (<= b 2.8e-82)
               (* t a)
               (if (<= b 950.0)
                 (* y z)
                 (if (<= b 2e+25)
                   x
                   (if (or (<= b 3e+36) (not (<= b 2.25e+99))) t_1 x)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (b <= -2.2e+165) {
		tmp = t_1;
	} else if (b <= -1.05e+55) {
		tmp = t * a;
	} else if (b <= -3.1e-111) {
		tmp = y * z;
	} else if (b <= -8.5e-238) {
		tmp = x;
	} else if (b <= 4.5e-194) {
		tmp = y * z;
	} else if (b <= 2.8e-82) {
		tmp = t * a;
	} else if (b <= 950.0) {
		tmp = y * z;
	} else if (b <= 2e+25) {
		tmp = x;
	} else if ((b <= 3e+36) || !(b <= 2.25e+99)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (b <= (-2.2d+165)) then
        tmp = t_1
    else if (b <= (-1.05d+55)) then
        tmp = t * a
    else if (b <= (-3.1d-111)) then
        tmp = y * z
    else if (b <= (-8.5d-238)) then
        tmp = x
    else if (b <= 4.5d-194) then
        tmp = y * z
    else if (b <= 2.8d-82) then
        tmp = t * a
    else if (b <= 950.0d0) then
        tmp = y * z
    else if (b <= 2d+25) then
        tmp = x
    else if ((b <= 3d+36) .or. (.not. (b <= 2.25d+99))) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (b <= -2.2e+165) {
		tmp = t_1;
	} else if (b <= -1.05e+55) {
		tmp = t * a;
	} else if (b <= -3.1e-111) {
		tmp = y * z;
	} else if (b <= -8.5e-238) {
		tmp = x;
	} else if (b <= 4.5e-194) {
		tmp = y * z;
	} else if (b <= 2.8e-82) {
		tmp = t * a;
	} else if (b <= 950.0) {
		tmp = y * z;
	} else if (b <= 2e+25) {
		tmp = x;
	} else if ((b <= 3e+36) || !(b <= 2.25e+99)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if b <= -2.2e+165:
		tmp = t_1
	elif b <= -1.05e+55:
		tmp = t * a
	elif b <= -3.1e-111:
		tmp = y * z
	elif b <= -8.5e-238:
		tmp = x
	elif b <= 4.5e-194:
		tmp = y * z
	elif b <= 2.8e-82:
		tmp = t * a
	elif b <= 950.0:
		tmp = y * z
	elif b <= 2e+25:
		tmp = x
	elif (b <= 3e+36) or not (b <= 2.25e+99):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (b <= -2.2e+165)
		tmp = t_1;
	elseif (b <= -1.05e+55)
		tmp = Float64(t * a);
	elseif (b <= -3.1e-111)
		tmp = Float64(y * z);
	elseif (b <= -8.5e-238)
		tmp = x;
	elseif (b <= 4.5e-194)
		tmp = Float64(y * z);
	elseif (b <= 2.8e-82)
		tmp = Float64(t * a);
	elseif (b <= 950.0)
		tmp = Float64(y * z);
	elseif (b <= 2e+25)
		tmp = x;
	elseif ((b <= 3e+36) || !(b <= 2.25e+99))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (b <= -2.2e+165)
		tmp = t_1;
	elseif (b <= -1.05e+55)
		tmp = t * a;
	elseif (b <= -3.1e-111)
		tmp = y * z;
	elseif (b <= -8.5e-238)
		tmp = x;
	elseif (b <= 4.5e-194)
		tmp = y * z;
	elseif (b <= 2.8e-82)
		tmp = t * a;
	elseif (b <= 950.0)
		tmp = y * z;
	elseif (b <= 2e+25)
		tmp = x;
	elseif ((b <= 3e+36) || ~((b <= 2.25e+99)))
		tmp = t_1;
	else
		tmp = x;
	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[b, -2.2e+165], t$95$1, If[LessEqual[b, -1.05e+55], N[(t * a), $MachinePrecision], If[LessEqual[b, -3.1e-111], N[(y * z), $MachinePrecision], If[LessEqual[b, -8.5e-238], x, If[LessEqual[b, 4.5e-194], N[(y * z), $MachinePrecision], If[LessEqual[b, 2.8e-82], N[(t * a), $MachinePrecision], If[LessEqual[b, 950.0], N[(y * z), $MachinePrecision], If[LessEqual[b, 2e+25], x, If[Or[LessEqual[b, 3e+36], N[Not[LessEqual[b, 2.25e+99]], $MachinePrecision]], t$95$1, x]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.1999999999999999e165 or 2.00000000000000018e25 < b < 3e36 or 2.25e99 < b

   1. Initial program 83.0%

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

      1. *-commutative 83.0%

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

      2. associate-*l* 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in a around inf 76.1%

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

   5. Taylor expanded in t around 0 72.3%

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

   if -2.1999999999999999e165 < b < -1.05e55 or 4.4999999999999999e-194 < b < 2.80000000000000024e-82

   1. Initial program 87.7%

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

      1. *-commutative 87.7%

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

      2. associate-*l* 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in t around inf 53.4%

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

   if -1.05e55 < b < -3.10000000000000014e-111 or -8.5000000000000006e-238 < b < 4.4999999999999999e-194 or 2.80000000000000024e-82 < b < 950

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-*l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in y around inf 50.3%

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

      1. *-commutative 50.3%

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

   6. Simplified 50.3%

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

   if -3.10000000000000014e-111 < b < -8.5000000000000006e-238 or 950 < b < 2.00000000000000018e25 or 3e36 < b < 2.25e99

   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. *-commutative 93.6%

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

      2. associate-*l* 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in x around inf 51.5%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+165}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+55}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-111}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-194}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-82}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq 950:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+36} \lor \neg \left(b \leq 2.25 \cdot 10^{+99}\right):\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 37.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;b \leq -2 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{+55}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-111}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-243}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 8.7 \cdot 10^{-193}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-82}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq 1.8:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* z a) b)))
   (if (<= b -2e+165)
     t_1
     (if (<= b -1.22e+55)
       (* t a)
       (if (<= b -4e-111)
         (* y z)
         (if (<= b -1.1e-243)
           x
           (if (<= b 8.7e-193)
             (* y z)
             (if (<= b 1.7e-82)
               (* t a)
               (if (<= b 1.8)
                 (* y z)
                 (if (<= b 2.5e+25)
                   x
                   (if (<= b 6.6e+36)
                     (* a (* z b))
                     (if (<= b 1.4e+98) x t_1))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * a) * b;
	double tmp;
	if (b <= -2e+165) {
		tmp = t_1;
	} else if (b <= -1.22e+55) {
		tmp = t * a;
	} else if (b <= -4e-111) {
		tmp = y * z;
	} else if (b <= -1.1e-243) {
		tmp = x;
	} else if (b <= 8.7e-193) {
		tmp = y * z;
	} else if (b <= 1.7e-82) {
		tmp = t * a;
	} else if (b <= 1.8) {
		tmp = y * z;
	} else if (b <= 2.5e+25) {
		tmp = x;
	} else if (b <= 6.6e+36) {
		tmp = a * (z * b);
	} else if (b <= 1.4e+98) {
		tmp = 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 * a) * b
    if (b <= (-2d+165)) then
        tmp = t_1
    else if (b <= (-1.22d+55)) then
        tmp = t * a
    else if (b <= (-4d-111)) then
        tmp = y * z
    else if (b <= (-1.1d-243)) then
        tmp = x
    else if (b <= 8.7d-193) then
        tmp = y * z
    else if (b <= 1.7d-82) then
        tmp = t * a
    else if (b <= 1.8d0) then
        tmp = y * z
    else if (b <= 2.5d+25) then
        tmp = x
    else if (b <= 6.6d+36) then
        tmp = a * (z * b)
    else if (b <= 1.4d+98) then
        tmp = 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 * a) * b;
	double tmp;
	if (b <= -2e+165) {
		tmp = t_1;
	} else if (b <= -1.22e+55) {
		tmp = t * a;
	} else if (b <= -4e-111) {
		tmp = y * z;
	} else if (b <= -1.1e-243) {
		tmp = x;
	} else if (b <= 8.7e-193) {
		tmp = y * z;
	} else if (b <= 1.7e-82) {
		tmp = t * a;
	} else if (b <= 1.8) {
		tmp = y * z;
	} else if (b <= 2.5e+25) {
		tmp = x;
	} else if (b <= 6.6e+36) {
		tmp = a * (z * b);
	} else if (b <= 1.4e+98) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * a) * b
	tmp = 0
	if b <= -2e+165:
		tmp = t_1
	elif b <= -1.22e+55:
		tmp = t * a
	elif b <= -4e-111:
		tmp = y * z
	elif b <= -1.1e-243:
		tmp = x
	elif b <= 8.7e-193:
		tmp = y * z
	elif b <= 1.7e-82:
		tmp = t * a
	elif b <= 1.8:
		tmp = y * z
	elif b <= 2.5e+25:
		tmp = x
	elif b <= 6.6e+36:
		tmp = a * (z * b)
	elif b <= 1.4e+98:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * a) * b)
	tmp = 0.0
	if (b <= -2e+165)
		tmp = t_1;
	elseif (b <= -1.22e+55)
		tmp = Float64(t * a);
	elseif (b <= -4e-111)
		tmp = Float64(y * z);
	elseif (b <= -1.1e-243)
		tmp = x;
	elseif (b <= 8.7e-193)
		tmp = Float64(y * z);
	elseif (b <= 1.7e-82)
		tmp = Float64(t * a);
	elseif (b <= 1.8)
		tmp = Float64(y * z);
	elseif (b <= 2.5e+25)
		tmp = x;
	elseif (b <= 6.6e+36)
		tmp = Float64(a * Float64(z * b));
	elseif (b <= 1.4e+98)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * a) * b;
	tmp = 0.0;
	if (b <= -2e+165)
		tmp = t_1;
	elseif (b <= -1.22e+55)
		tmp = t * a;
	elseif (b <= -4e-111)
		tmp = y * z;
	elseif (b <= -1.1e-243)
		tmp = x;
	elseif (b <= 8.7e-193)
		tmp = y * z;
	elseif (b <= 1.7e-82)
		tmp = t * a;
	elseif (b <= 1.8)
		tmp = y * z;
	elseif (b <= 2.5e+25)
		tmp = x;
	elseif (b <= 6.6e+36)
		tmp = a * (z * b);
	elseif (b <= 1.4e+98)
		tmp = 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 * a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2e+165], t$95$1, If[LessEqual[b, -1.22e+55], N[(t * a), $MachinePrecision], If[LessEqual[b, -4e-111], N[(y * z), $MachinePrecision], If[LessEqual[b, -1.1e-243], x, If[LessEqual[b, 8.7e-193], N[(y * z), $MachinePrecision], If[LessEqual[b, 1.7e-82], N[(t * a), $MachinePrecision], If[LessEqual[b, 1.8], N[(y * z), $MachinePrecision], If[LessEqual[b, 2.5e+25], x, If[LessEqual[b, 6.6e+36], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e+98], x, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.9999999999999998e165 or 1.4e98 < b

   1. Initial program 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-*l* 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in z around inf 79.9%

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

   5. Taylor expanded in y around 0 72.0%

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

   6. Taylor expanded in z around 0 72.2%

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

      1. associate-*r* 72.0%

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

      2. *-commutative 72.0%

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

      3. associate-*r* 75.3%

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

   8. Simplified 75.3%

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

   if -1.9999999999999998e165 < b < -1.22e55 or 8.6999999999999997e-193 < b < 1.69999999999999988e-82

   1. Initial program 87.7%

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

      1. *-commutative 87.7%

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

      2. associate-*l* 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in t around inf 53.4%

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

   if -1.22e55 < b < -4.00000000000000035e-111 or -1.1e-243 < b < 8.6999999999999997e-193 or 1.69999999999999988e-82 < b < 1.80000000000000004

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-*l* 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in y around inf 50.3%

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

      1. *-commutative 50.3%

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

   6. Simplified 50.3%

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

   if -4.00000000000000035e-111 < b < -1.1e-243 or 1.80000000000000004 < b < 2.50000000000000012e25 or 6.5999999999999997e36 < b < 1.4e98

   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. *-commutative 93.6%

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

      2. associate-*l* 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in x around inf 51.5%

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

   if 2.50000000000000012e25 < b < 6.5999999999999997e36

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around inf 75.2%

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

   5. Taylor expanded in t around 0 75.3%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+165}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{+55}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-111}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-243}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 8.7 \cdot 10^{-193}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-82}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq 1.8:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \]

Alternative 5: 56.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot a\\ t_2 := x + y \cdot z\\ t_3 := \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+165}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -3.25 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.75 \cdot 10^{-194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t a))) (t_2 (+ x (* y z))) (t_3 (* (* z a) b)))
   (if (<= b -3.4e+165)
     t_3
     (if (<= b -3.25e+56)
       t_1
       (if (<= b -2.8e-46)
         t_2
         (if (<= b -7.5e-227)
           t_1
           (if (<= b 4.75e-194)
             t_2
             (if (<= b 2.2e-82) t_1 (if (<= b 1.5e+105) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double t_2 = x + (y * z);
	double t_3 = (z * a) * b;
	double tmp;
	if (b <= -3.4e+165) {
		tmp = t_3;
	} else if (b <= -3.25e+56) {
		tmp = t_1;
	} else if (b <= -2.8e-46) {
		tmp = t_2;
	} else if (b <= -7.5e-227) {
		tmp = t_1;
	} else if (b <= 4.75e-194) {
		tmp = t_2;
	} else if (b <= 2.2e-82) {
		tmp = t_1;
	} else if (b <= 1.5e+105) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (t * a)
    t_2 = x + (y * z)
    t_3 = (z * a) * b
    if (b <= (-3.4d+165)) then
        tmp = t_3
    else if (b <= (-3.25d+56)) then
        tmp = t_1
    else if (b <= (-2.8d-46)) then
        tmp = t_2
    else if (b <= (-7.5d-227)) then
        tmp = t_1
    else if (b <= 4.75d-194) then
        tmp = t_2
    else if (b <= 2.2d-82) then
        tmp = t_1
    else if (b <= 1.5d+105) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double t_2 = x + (y * z);
	double t_3 = (z * a) * b;
	double tmp;
	if (b <= -3.4e+165) {
		tmp = t_3;
	} else if (b <= -3.25e+56) {
		tmp = t_1;
	} else if (b <= -2.8e-46) {
		tmp = t_2;
	} else if (b <= -7.5e-227) {
		tmp = t_1;
	} else if (b <= 4.75e-194) {
		tmp = t_2;
	} else if (b <= 2.2e-82) {
		tmp = t_1;
	} else if (b <= 1.5e+105) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * a)
	t_2 = x + (y * z)
	t_3 = (z * a) * b
	tmp = 0
	if b <= -3.4e+165:
		tmp = t_3
	elif b <= -3.25e+56:
		tmp = t_1
	elif b <= -2.8e-46:
		tmp = t_2
	elif b <= -7.5e-227:
		tmp = t_1
	elif b <= 4.75e-194:
		tmp = t_2
	elif b <= 2.2e-82:
		tmp = t_1
	elif b <= 1.5e+105:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * a))
	t_2 = Float64(x + Float64(y * z))
	t_3 = Float64(Float64(z * a) * b)
	tmp = 0.0
	if (b <= -3.4e+165)
		tmp = t_3;
	elseif (b <= -3.25e+56)
		tmp = t_1;
	elseif (b <= -2.8e-46)
		tmp = t_2;
	elseif (b <= -7.5e-227)
		tmp = t_1;
	elseif (b <= 4.75e-194)
		tmp = t_2;
	elseif (b <= 2.2e-82)
		tmp = t_1;
	elseif (b <= 1.5e+105)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * a);
	t_2 = x + (y * z);
	t_3 = (z * a) * b;
	tmp = 0.0;
	if (b <= -3.4e+165)
		tmp = t_3;
	elseif (b <= -3.25e+56)
		tmp = t_1;
	elseif (b <= -2.8e-46)
		tmp = t_2;
	elseif (b <= -7.5e-227)
		tmp = t_1;
	elseif (b <= 4.75e-194)
		tmp = t_2;
	elseif (b <= 2.2e-82)
		tmp = t_1;
	elseif (b <= 1.5e+105)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -3.4e+165], t$95$3, If[LessEqual[b, -3.25e+56], t$95$1, If[LessEqual[b, -2.8e-46], t$95$2, If[LessEqual[b, -7.5e-227], t$95$1, If[LessEqual[b, 4.75e-194], t$95$2, If[LessEqual[b, 2.2e-82], t$95$1, If[LessEqual[b, 1.5e+105], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.40000000000000011e165 or 1.5e105 < b

   1. Initial program 81.9%

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

      1. *-commutative 81.9%

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

      2. associate-*l* 74.0%

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

   3. Simplified 74.0%

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

   4. Taylor expanded in z around inf 79.7%

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

   5. Taylor expanded in y around 0 72.9%

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

   6. Taylor expanded in z around 0 73.0%

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

      1. associate-*r* 72.9%

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

      2. *-commutative 72.9%

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

      3. associate-*r* 76.2%

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

   8. Simplified 76.2%

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

   if -3.40000000000000011e165 < b < -3.25e56 or -2.7999999999999998e-46 < b < -7.49999999999999988e-227 or 4.75000000000000005e-194 < b < 2.19999999999999986e-82

   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. *-commutative 89.1%

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

      2. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in z around 0 74.4%

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

   if -3.25e56 < b < -2.7999999999999998e-46 or -7.49999999999999988e-227 < b < 4.75000000000000005e-194 or 2.19999999999999986e-82 < b < 1.5e105

   1. Initial program 95.8%

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

      1. *-commutative 95.8%

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

      2. associate-*l* 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in a around 0 71.5%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+165}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;b \leq -3.25 \cdot 10^{+56}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-46}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-227}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;b \leq 4.75 \cdot 10^{-194}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-82}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+105}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \]

Alternative 6: 94.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+103}:\\ \;\;\;\;x + t_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+182}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -3.2e+103)
     (+ x t_1)
     (if (<= a 1.7e+182) (+ (+ (+ x (* y z)) (* t a)) (* z (* a b))) t_1))))

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 <= -3.2e+103) {
		tmp = x + t_1;
	} else if (a <= 1.7e+182) {
		tmp = ((x + (y * z)) + (t * a)) + (z * (a * b));
	} 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 = a * (t + (z * b))
    if (a <= (-3.2d+103)) then
        tmp = x + t_1
    else if (a <= 1.7d+182) then
        tmp = ((x + (y * z)) + (t * a)) + (z * (a * b))
    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 = a * (t + (z * b));
	double tmp;
	if (a <= -3.2e+103) {
		tmp = x + t_1;
	} else if (a <= 1.7e+182) {
		tmp = ((x + (y * z)) + (t * a)) + (z * (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	tmp = 0
	if a <= -3.2e+103:
		tmp = x + t_1
	elif a <= 1.7e+182:
		tmp = ((x + (y * z)) + (t * a)) + (z * (a * b))
	else:
		tmp = t_1
	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 <= -3.2e+103)
		tmp = Float64(x + t_1);
	elseif (a <= 1.7e+182)
		tmp = Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(z * Float64(a * b)));
	else
		tmp = t_1;
	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 <= -3.2e+103)
		tmp = x + t_1;
	elseif (a <= 1.7e+182)
		tmp = ((x + (y * z)) + (t * a)) + (z * (a * b));
	else
		tmp = t_1;
	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, -3.2e+103], N[(x + t$95$1), $MachinePrecision], If[LessEqual[a, 1.7e+182], N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.19999999999999993e103

   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. +-commutative 77.5%

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

      3. *-commutative 77.5%

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

      4. *-commutative 77.5%

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

      5. associate-*l* 85.6%

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

      6. distribute-rgt-out 97.0%

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

      7. fma-def 97.0%

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

      8. *-commutative 97.0%

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

      9. +-commutative 97.0%

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

      10. fma-def 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in y around 0 92.0%

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

   if -3.19999999999999993e103 < a < 1.69999999999999993e182

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

      2. associate-*l* 96.8%

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

   3. Simplified 96.8%

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

   if 1.69999999999999993e182 < a

   1. Initial program 68.5%

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

      1. *-commutative 68.5%

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

      2. associate-*l* 66.2%

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

   3. Simplified 66.2%

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

   4. Taylor expanded in a around inf 97.1%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+103}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+182}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + z \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 7: 81.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+43} \lor \neg \left(z \leq 5.6 \cdot 10^{-11}\right) \land \left(z \leq 2.6 \cdot 10^{+37} \lor \neg \left(z \leq 4 \cdot 10^{+88}\right)\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9e+43)
         (and (not (<= z 5.6e-11)) (or (<= z 2.6e+37) (not (<= z 4e+88)))))
   (* z (+ y (* a b)))
   (+ x (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9e+43) || (!(z <= 5.6e-11) && ((z <= 2.6e+37) || !(z <= 4e+88)))) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * (t + (z * 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 ((z <= (-9d+43)) .or. (.not. (z <= 5.6d-11)) .and. (z <= 2.6d+37) .or. (.not. (z <= 4d+88))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + (a * (t + (z * 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 ((z <= -9e+43) || (!(z <= 5.6e-11) && ((z <= 2.6e+37) || !(z <= 4e+88)))) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9e+43) or (not (z <= 5.6e-11) and ((z <= 2.6e+37) or not (z <= 4e+88))):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9e+43) || (!(z <= 5.6e-11) && ((z <= 2.6e+37) || !(z <= 4e+88))))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9e+43) || (~((z <= 5.6e-11)) && ((z <= 2.6e+37) || ~((z <= 4e+88)))))
		tmp = z * (y + (a * b));
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9e+43], And[N[Not[LessEqual[z, 5.6e-11]], $MachinePrecision], Or[LessEqual[z, 2.6e+37], N[Not[LessEqual[z, 4e+88]], $MachinePrecision]]]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9e43 or 5.6e-11 < z < 2.5999999999999999e37 or 3.99999999999999984e88 < z

   1. Initial program 78.8%

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

      1. *-commutative 78.8%

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

      2. associate-*l* 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in z around inf 86.9%

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

   if -9e43 < z < 5.6e-11 or 2.5999999999999999e37 < z < 3.99999999999999984e88

   1. Initial program 96.2%

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

      1. associate-+l+ 96.2%

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

      2. +-commutative 96.2%

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

      3. *-commutative 96.2%

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

      4. *-commutative 96.2%

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

      5. associate-*l* 97.4%

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

      6. distribute-rgt-out 99.3%

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

      7. fma-def 99.3%

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

      8. *-commutative 99.3%

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

      9. +-commutative 99.3%

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

      10. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 90.8%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+43} \lor \neg \left(z \leq 5.6 \cdot 10^{-11}\right) \land \left(z \leq 2.6 \cdot 10^{+37} \lor \neg \left(z \leq 4 \cdot 10^{+88}\right)\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 8: 72.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-59} \lor \neg \left(a \leq 1.9 \cdot 10^{-71}\right) \land \left(a \leq 4.6 \cdot 10^{+16} \lor \neg \left(a \leq 1.4 \cdot 10^{+86}\right)\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.9e-59)
         (and (not (<= a 1.9e-71)) (or (<= a 4.6e+16) (not (<= a 1.4e+86)))))
   (* 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 <= -1.9e-59) || (!(a <= 1.9e-71) && ((a <= 4.6e+16) || !(a <= 1.4e+86)))) {
		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 <= (-1.9d-59)) .or. (.not. (a <= 1.9d-71)) .and. (a <= 4.6d+16) .or. (.not. (a <= 1.4d+86))) 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 <= -1.9e-59) || (!(a <= 1.9e-71) && ((a <= 4.6e+16) || !(a <= 1.4e+86)))) {
		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 <= -1.9e-59) or (not (a <= 1.9e-71) and ((a <= 4.6e+16) or not (a <= 1.4e+86))):
		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 <= -1.9e-59) || (!(a <= 1.9e-71) && ((a <= 4.6e+16) || !(a <= 1.4e+86))))
		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 <= -1.9e-59) || (~((a <= 1.9e-71)) && ((a <= 4.6e+16) || ~((a <= 1.4e+86)))))
		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, -1.9e-59], And[N[Not[LessEqual[a, 1.9e-71]], $MachinePrecision], Or[LessEqual[a, 4.6e+16], N[Not[LessEqual[a, 1.4e+86]], $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 < -1.89999999999999992e-59 or 1.89999999999999996e-71 < a < 4.6e16 or 1.40000000000000002e86 < 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. *-commutative 85.4%

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

      2. associate-*l* 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in a around inf 75.6%

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

   if -1.89999999999999992e-59 < a < 1.89999999999999996e-71 or 4.6e16 < a < 1.40000000000000002e86

   1. Initial program 95.3%

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

      1. *-commutative 95.3%

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

      2. associate-*l* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in a around 0 79.9%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-59} \lor \neg \left(a \leq 1.9 \cdot 10^{-71}\right) \land \left(a \leq 4.6 \cdot 10^{+16} \lor \neg \left(a \leq 1.4 \cdot 10^{+86}\right)\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 9: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-92} \lor \neg \left(z \leq 1.75 \cdot 10^{-12} \lor \neg \left(z \leq 8.5 \cdot 10^{+49}\right) \land z \leq 1.12 \cdot 10^{+69}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.32e-92)
         (not (or (<= z 1.75e-12) (and (not (<= z 8.5e+49)) (<= z 1.12e+69)))))
   (* z (+ y (* a b)))
   (+ x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.32e-92) || !((z <= 1.75e-12) || (!(z <= 8.5e+49) && (z <= 1.12e+69)))) {
		tmp = z * (y + (a * b));
	} else {
		tmp = 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 ((z <= (-1.32d-92)) .or. (.not. (z <= 1.75d-12) .or. (.not. (z <= 8.5d+49)) .and. (z <= 1.12d+69))) then
        tmp = z * (y + (a * b))
    else
        tmp = 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 ((z <= -1.32e-92) || !((z <= 1.75e-12) || (!(z <= 8.5e+49) && (z <= 1.12e+69)))) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.32e-92) or not ((z <= 1.75e-12) or (not (z <= 8.5e+49) and (z <= 1.12e+69))):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.32e-92) || !((z <= 1.75e-12) || (!(z <= 8.5e+49) && (z <= 1.12e+69))))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.32e-92) || ~(((z <= 1.75e-12) || (~((z <= 8.5e+49)) && (z <= 1.12e+69)))))
		tmp = z * (y + (a * b));
	else
		tmp = x + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.32e-92], N[Not[Or[LessEqual[z, 1.75e-12], And[N[Not[LessEqual[z, 8.5e+49]], $MachinePrecision], LessEqual[z, 1.12e+69]]]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3200000000000001e-92 or 1.75e-12 < z < 8.4999999999999996e49 or 1.12e69 < z

   1. Initial program 83.5%

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

      1. *-commutative 83.5%

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

      2. associate-*l* 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in z around inf 82.2%

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

   if -1.3200000000000001e-92 < z < 1.75e-12 or 8.4999999999999996e49 < z < 1.12e69

   1. Initial program 95.9%

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

      1. *-commutative 95.9%

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

      2. associate-*l* 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in z around 0 76.3%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-92} \lor \neg \left(z \leq 1.75 \cdot 10^{-12} \lor \neg \left(z \leq 8.5 \cdot 10^{+49}\right) \land z \leq 1.12 \cdot 10^{+69}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]

Alternative 10: 56.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot a\\ t_2 := \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;b \leq -1.5 \cdot 10^{+166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -55000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-45}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t a))) (t_2 (* (* z a) b)))
   (if (<= b -1.5e+166)
     t_2
     (if (<= b -55000.0)
       t_1
       (if (<= b -5e-45) (* y z) (if (<= b 1.75e+118) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double t_2 = (z * a) * b;
	double tmp;
	if (b <= -1.5e+166) {
		tmp = t_2;
	} else if (b <= -55000.0) {
		tmp = t_1;
	} else if (b <= -5e-45) {
		tmp = y * z;
	} else if (b <= 1.75e+118) {
		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 + (t * a)
    t_2 = (z * a) * b
    if (b <= (-1.5d+166)) then
        tmp = t_2
    else if (b <= (-55000.0d0)) then
        tmp = t_1
    else if (b <= (-5d-45)) then
        tmp = y * z
    else if (b <= 1.75d+118) 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 + (t * a);
	double t_2 = (z * a) * b;
	double tmp;
	if (b <= -1.5e+166) {
		tmp = t_2;
	} else if (b <= -55000.0) {
		tmp = t_1;
	} else if (b <= -5e-45) {
		tmp = y * z;
	} else if (b <= 1.75e+118) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * a)
	t_2 = (z * a) * b
	tmp = 0
	if b <= -1.5e+166:
		tmp = t_2
	elif b <= -55000.0:
		tmp = t_1
	elif b <= -5e-45:
		tmp = y * z
	elif b <= 1.75e+118:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * a))
	t_2 = Float64(Float64(z * a) * b)
	tmp = 0.0
	if (b <= -1.5e+166)
		tmp = t_2;
	elseif (b <= -55000.0)
		tmp = t_1;
	elseif (b <= -5e-45)
		tmp = Float64(y * z);
	elseif (b <= 1.75e+118)
		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 + (t * a);
	t_2 = (z * a) * b;
	tmp = 0.0;
	if (b <= -1.5e+166)
		tmp = t_2;
	elseif (b <= -55000.0)
		tmp = t_1;
	elseif (b <= -5e-45)
		tmp = y * z;
	elseif (b <= 1.75e+118)
		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[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.5e+166], t$95$2, If[LessEqual[b, -55000.0], t$95$1, If[LessEqual[b, -5e-45], N[(y * z), $MachinePrecision], If[LessEqual[b, 1.75e+118], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.49999999999999999e166 or 1.75000000000000008e118 < b

   1. Initial program 81.4%

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

      1. *-commutative 81.4%

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

      2. associate-*l* 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in z around inf 80.8%

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

   5. Taylor expanded in y around 0 73.7%

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

   6. Taylor expanded in z around 0 73.9%

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

      1. associate-*r* 73.7%

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

      2. *-commutative 73.7%

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

      3. associate-*r* 77.1%

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

   8. Simplified 77.1%

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

   if -1.49999999999999999e166 < b < -55000 or -4.99999999999999976e-45 < b < 1.75000000000000008e118

   1. Initial program 92.3%

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

      1. *-commutative 92.3%

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

      2. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around 0 63.4%

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

   if -55000 < b < -4.99999999999999976e-45

   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. *-commutative 100.0%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 86.1%

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

      1. *-commutative 86.1%

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

   6. Simplified 86.1%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+166}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;b \leq -55000:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-45}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+118}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \]

Alternative 11: 86.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+83} \lor \neg \left(b \leq 2.1 \cdot 10^{+65}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.5e+83) (not (<= b 2.1e+65)))
   (+ x (* a (+ t (* z b))))
   (+ x (+ (* t a) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.5e+83) || !(b <= 2.1e+65)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + ((t * a) + (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 ((b <= (-3.5d+83)) .or. (.not. (b <= 2.1d+65))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = x + ((t * a) + (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 ((b <= -3.5e+83) || !(b <= 2.1e+65)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + ((t * a) + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.5e+83) or not (b <= 2.1e+65):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = x + ((t * a) + (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.5e+83) || !(b <= 2.1e+65))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(x + Float64(Float64(t * a) + Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.5e+83) || ~((b <= 2.1e+65)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = x + ((t * a) + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.5e+83], N[Not[LessEqual[b, 2.1e+65]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.49999999999999977e83 or 2.09999999999999991e65 < b

   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. +-commutative 85.3%

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

      3. *-commutative 85.3%

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

      4. *-commutative 85.3%

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

      5. associate-*l* 80.4%

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

      6. distribute-rgt-out 87.8%

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

      7. fma-def 87.8%

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

      8. *-commutative 87.8%

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

      9. +-commutative 87.8%

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

      10. fma-def 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in y around 0 88.8%

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

   if -3.49999999999999977e83 < b < 2.09999999999999991e65

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

      2. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in b around 0 93.1%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+83} \lor \neg \left(b \leq 2.1 \cdot 10^{+65}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \]

Alternative 12: 40.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-64}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-216}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-258}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.45e-64)
   (* y z)
   (if (<= z -2.2e-216)
     x
     (if (<= z 5e-258) (* t a) (if (<= z 3.4e-11) x (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.45e-64) {
		tmp = y * z;
	} else if (z <= -2.2e-216) {
		tmp = x;
	} else if (z <= 5e-258) {
		tmp = t * a;
	} else if (z <= 3.4e-11) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-2.45d-64)) then
        tmp = y * z
    else if (z <= (-2.2d-216)) then
        tmp = x
    else if (z <= 5d-258) then
        tmp = t * a
    else if (z <= 3.4d-11) then
        tmp = x
    else
        tmp = 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 (z <= -2.45e-64) {
		tmp = y * z;
	} else if (z <= -2.2e-216) {
		tmp = x;
	} else if (z <= 5e-258) {
		tmp = t * a;
	} else if (z <= 3.4e-11) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.45e-64:
		tmp = y * z
	elif z <= -2.2e-216:
		tmp = x
	elif z <= 5e-258:
		tmp = t * a
	elif z <= 3.4e-11:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.45e-64)
		tmp = Float64(y * z);
	elseif (z <= -2.2e-216)
		tmp = x;
	elseif (z <= 5e-258)
		tmp = Float64(t * a);
	elseif (z <= 3.4e-11)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.45e-64)
		tmp = y * z;
	elseif (z <= -2.2e-216)
		tmp = x;
	elseif (z <= 5e-258)
		tmp = t * a;
	elseif (z <= 3.4e-11)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.45e-64], N[(y * z), $MachinePrecision], If[LessEqual[z, -2.2e-216], x, If[LessEqual[z, 5e-258], N[(t * a), $MachinePrecision], If[LessEqual[z, 3.4e-11], x, N[(y * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4500000000000001e-64 or 3.3999999999999999e-11 < z

   1. Initial program 82.6%

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

      1. *-commutative 82.6%

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

      2. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in y around inf 44.7%

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

      1. *-commutative 44.7%

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

   6. Simplified 44.7%

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

   if -2.4500000000000001e-64 < z < -2.1999999999999999e-216 or 4.9999999999999999e-258 < z < 3.3999999999999999e-11

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

      2. associate-*l* 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in x around inf 40.2%

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

   if -2.1999999999999999e-216 < z < 4.9999999999999999e-258

   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. *-commutative 100.0%

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

      2. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in t around inf 60.7%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-64}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-216}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-258}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 13: 39.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{+81}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -7.5e+67) x (if (<= x 1.76e+81) (* t a) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.5e+67) {
		tmp = x;
	} else if (x <= 1.76e+81) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-7.5d+67)) then
        tmp = x
    else if (x <= 1.76d+81) then
        tmp = t * a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -7.5e+67) {
		tmp = x;
	} else if (x <= 1.76e+81) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -7.5e+67:
		tmp = x
	elif x <= 1.76e+81:
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -7.5e+67)
		tmp = x;
	elseif (x <= 1.76e+81)
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -7.5e+67)
		tmp = x;
	elseif (x <= 1.76e+81)
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -7.5e+67], x, If[LessEqual[x, 1.76e+81], N[(t * a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5000000000000005e67 or 1.76000000000000002e81 < x

   1. Initial program 91.6%

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

      1. *-commutative 91.6%

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

      2. associate-*l* 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in x around inf 53.4%

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

   if -7.5000000000000005e67 < x < 1.76000000000000002e81

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

      2. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in t around inf 34.3%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{+81}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 25.6% 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 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. *-commutative 89.5%

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

   2. associate-*l* 88.8%

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

3. Simplified 88.8%

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

4. Taylor expanded in x around inf 24.4%

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

5. Final simplification 24.4%

   \[\leadsto x \]

Developer target: 97.3% 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 2023271 
(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)))