Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.2% → 97.8%

Time: 11.0s

Alternatives: 14

Speedup: 0.8×

• 32.6% 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: 92.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+103}:\\ \;\;\;\;a \cdot \left(t + \left(b \cdot z + \left(\frac{x}{a} + \frac{z \cdot y}{a}\right)\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+95}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot \left(y + a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + b \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1e+103)
   (* a (+ t (+ (* b z) (+ (/ x a) (/ (* z y) a)))))
   (if (<= a 3.5e+95)
     (+ x (+ (* a t) (* z (+ y (* a b)))))
     (+ (fma y z x) (* a (+ t (* b z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1e+103) {
		tmp = a * (t + ((b * z) + ((x / a) + ((z * y) / a))));
	} else if (a <= 3.5e+95) {
		tmp = x + ((a * t) + (z * (y + (a * b))));
	} else {
		tmp = fma(y, z, x) + (a * (t + (b * z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1e+103)
		tmp = Float64(a * Float64(t + Float64(Float64(b * z) + Float64(Float64(x / a) + Float64(Float64(z * y) / a)))));
	elseif (a <= 3.5e+95)
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * Float64(y + Float64(a * b)))));
	else
		tmp = Float64(fma(y, z, x) + Float64(a * Float64(t + Float64(b * z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1e+103], N[(a * N[(t + N[(N[(b * z), $MachinePrecision] + N[(N[(x / a), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e+95], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z + x), $MachinePrecision] + N[(a * N[(t + N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1e103

   1. Initial program 76.4%

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

      1. associate-+l+ 76.4%

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

      2. associate-*l* 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in a around inf 97.6%

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

   if -1e103 < a < 3.5e95

   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* 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in z around 0 98.8%

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

   if 3.5e95 < a

   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. associate-+l+ 91.6%

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

      2. +-commutative 91.6%

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

      3. fma-define 91.6%

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

      4. associate-*l* 95.6%

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

      5. *-commutative 95.6%

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

      6. *-commutative 95.6%

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

      7. distribute-rgt-out 100.0%

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

      8. *-commutative 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+103}:\\ \;\;\;\;a \cdot \left(t + \left(b \cdot z + \left(\frac{x}{a} + \frac{z \cdot y}{a}\right)\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+95}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot \left(y + a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + b \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + \left(x + z \cdot y\right)\right) + b \cdot \left(a \cdot z\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (* a t) (+ x (* z y))) (* b (* a z)))))
   (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 = ((a * t) + (x + (z * y))) + (b * (a * z));
	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 = ((a * t) + (x + (z * y))) + (b * (a * z));
	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 = ((a * t) + (x + (z * y))) + (b * (a * z))
	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(a * t) + Float64(x + Float64(z * y))) + Float64(b * Float64(a * z)))
	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 = ((a * t) + (x + (z * y))) + (b * (a * z));
	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[(a * t), $MachinePrecision] + N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * z), $MachinePrecision]), $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 97.5%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   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* 5.6%

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

   3. Simplified 5.6%

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

   5. Taylor expanded in z around inf 83.3%

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

4. Final simplification 96.6%

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

Alternative 3: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+102} \lor \neg \left(a \leq 1.76 \cdot 10^{+96}\right):\\ \;\;\;\;a \cdot \left(t + \left(b \cdot z + \left(\frac{x}{a} + \frac{z \cdot y}{a}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot \left(y + a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.5e+102) (not (<= a 1.76e+96)))
   (* a (+ t (+ (* b z) (+ (/ x a) (/ (* z y) a)))))
   (+ x (+ (* a t) (* z (+ y (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.5e+102) || !(a <= 1.76e+96)) {
		tmp = a * (t + ((b * z) + ((x / a) + ((z * y) / a))));
	} else {
		tmp = x + ((a * t) + (z * (y + (a * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-3.5d+102)) .or. (.not. (a <= 1.76d+96))) then
        tmp = a * (t + ((b * z) + ((x / a) + ((z * y) / a))))
    else
        tmp = x + ((a * t) + (z * (y + (a * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.5e+102) || !(a <= 1.76e+96)) {
		tmp = a * (t + ((b * z) + ((x / a) + ((z * y) / a))));
	} else {
		tmp = x + ((a * t) + (z * (y + (a * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -3.5e+102) or not (a <= 1.76e+96):
		tmp = a * (t + ((b * z) + ((x / a) + ((z * y) / a))))
	else:
		tmp = x + ((a * t) + (z * (y + (a * b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3.5e+102) || !(a <= 1.76e+96))
		tmp = Float64(a * Float64(t + Float64(Float64(b * z) + Float64(Float64(x / a) + Float64(Float64(z * y) / a)))));
	else
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * Float64(y + Float64(a * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -3.5e+102) || ~((a <= 1.76e+96)))
		tmp = a * (t + ((b * z) + ((x / a) + ((z * y) / a))));
	else
		tmp = x + ((a * t) + (z * (y + (a * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3.5e+102], N[Not[LessEqual[a, 1.76e+96]], $MachinePrecision]], N[(a * N[(t + N[(N[(b * z), $MachinePrecision] + N[(N[(x / a), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.50000000000000011e102 or 1.7599999999999999e96 < a

   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* 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in a around inf 98.8%

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

   if -3.50000000000000011e102 < a < 1.7599999999999999e96

   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* 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in z around 0 98.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+102} \lor \neg \left(a \leq 1.76 \cdot 10^{+96}\right):\\ \;\;\;\;a \cdot \left(t + \left(b \cdot z + \left(\frac{x}{a} + \frac{z \cdot y}{a}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot \left(y + a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+262}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-28} \lor \neg \left(a \leq 7.5 \cdot 10^{+112}\right):\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.3e+262)
   (* z (* a b))
   (if (or (<= a -4.6e-28) (not (<= a 7.5e+112)))
     (+ x (* a t))
     (+ x (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.3e+262) {
		tmp = z * (a * b);
	} else if ((a <= -4.6e-28) || !(a <= 7.5e+112)) {
		tmp = x + (a * t);
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.3d+262)) then
        tmp = z * (a * b)
    else if ((a <= (-4.6d-28)) .or. (.not. (a <= 7.5d+112))) then
        tmp = x + (a * t)
    else
        tmp = x + (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.3e+262) {
		tmp = z * (a * b);
	} else if ((a <= -4.6e-28) || !(a <= 7.5e+112)) {
		tmp = x + (a * t);
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.3e+262:
		tmp = z * (a * b)
	elif (a <= -4.6e-28) or not (a <= 7.5e+112):
		tmp = x + (a * t)
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.3e+262)
		tmp = Float64(z * Float64(a * b));
	elseif ((a <= -4.6e-28) || !(a <= 7.5e+112))
		tmp = Float64(x + Float64(a * t));
	else
		tmp = Float64(x + Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.3e+262)
		tmp = z * (a * b);
	elseif ((a <= -4.6e-28) || ~((a <= 7.5e+112)))
		tmp = x + (a * t);
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.3e+262], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -4.6e-28], N[Not[LessEqual[a, 7.5e+112]], $MachinePrecision]], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.3e262

   1. Initial program 71.4%

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

      1. associate-+l+ 71.4%

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

      2. associate-*l* 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in z around inf 72.6%

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

   6. Taylor expanded in y around 0 72.6%

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

   if -2.3e262 < a < -4.59999999999999971e-28 or 7.5e112 < a

   1. Initial program 86.0%

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

      1. associate-+l+ 86.0%

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

      2. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in z around 0 58.0%

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

   if -4.59999999999999971e-28 < a < 7.5e112

   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. associate-+l+ 95.3%

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

      2. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

      1. *-commutative 92.1%

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

      2. distribute-lft-in 92.8%

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

      3. add-cube-cbrt 92.5%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 92.4%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 92.4%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 92.4%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-define 92.4%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 92.4%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in a around 0 69.4%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+262}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-28} \lor \neg \left(a \leq 7.5 \cdot 10^{+112}\right):\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+144}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+245}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* a b))))
   (if (<= z -7.2e+33)
     t_1
     (if (<= z 4.8e+144) (+ x (* a t)) (if (<= z 4.4e+245) t_1 (* z y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double tmp;
	if (z <= -7.2e+33) {
		tmp = t_1;
	} else if (z <= 4.8e+144) {
		tmp = x + (a * t);
	} else if (z <= 4.4e+245) {
		tmp = t_1;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (a * b)
    if (z <= (-7.2d+33)) then
        tmp = t_1
    else if (z <= 4.8d+144) then
        tmp = x + (a * t)
    else if (z <= 4.4d+245) then
        tmp = t_1
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double tmp;
	if (z <= -7.2e+33) {
		tmp = t_1;
	} else if (z <= 4.8e+144) {
		tmp = x + (a * t);
	} else if (z <= 4.4e+245) {
		tmp = t_1;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (a * b)
	tmp = 0
	if z <= -7.2e+33:
		tmp = t_1
	elif z <= 4.8e+144:
		tmp = x + (a * t)
	elif z <= 4.4e+245:
		tmp = t_1
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(a * b))
	tmp = 0.0
	if (z <= -7.2e+33)
		tmp = t_1;
	elseif (z <= 4.8e+144)
		tmp = Float64(x + Float64(a * t));
	elseif (z <= 4.4e+245)
		tmp = t_1;
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (a * b);
	tmp = 0.0;
	if (z <= -7.2e+33)
		tmp = t_1;
	elseif (z <= 4.8e+144)
		tmp = x + (a * t);
	elseif (z <= 4.4e+245)
		tmp = t_1;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+33], t$95$1, If[LessEqual[z, 4.8e+144], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+245], t$95$1, N[(z * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2000000000000005e33 or 4.8000000000000001e144 < z < 4.4000000000000001e245

   1. Initial program 80.3%

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

      1. associate-+l+ 80.3%

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

      2. associate-*l* 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in z around inf 87.1%

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

   6. Taylor expanded in y around 0 55.1%

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

   if -7.2000000000000005e33 < z < 4.8000000000000001e144

   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* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in z around 0 63.9%

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

   if 4.4000000000000001e245 < z

   1. Initial program 86.7%

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

      1. associate-+l+ 86.7%

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

      2. associate-*l* 86.6%

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

   3. Simplified 86.6%

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

      1. *-commutative 86.6%

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

      2. distribute-lft-in 93.2%

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

      3. add-cube-cbrt 92.9%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 92.9%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 92.9%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 92.9%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-define 92.9%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 92.9%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in y around inf 61.9%

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

      1. *-commutative 61.9%

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

   9. Simplified 61.9%

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

Alternative 6: 38.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -8.8 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 550000000:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* a b))))
   (if (<= b -8.8e-54)
     t_1
     (if (<= b 550000000.0) (* z y) (if (<= b 2.9e+125) 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 <= -8.8e-54) {
		tmp = t_1;
	} else if (b <= 550000000.0) {
		tmp = z * y;
	} else if (b <= 2.9e+125) {
		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 <= (-8.8d-54)) then
        tmp = t_1
    else if (b <= 550000000.0d0) then
        tmp = z * y
    else if (b <= 2.9d+125) 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 <= -8.8e-54) {
		tmp = t_1;
	} else if (b <= 550000000.0) {
		tmp = z * y;
	} else if (b <= 2.9e+125) {
		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 <= -8.8e-54:
		tmp = t_1
	elif b <= 550000000.0:
		tmp = z * y
	elif b <= 2.9e+125:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(a * b))
	tmp = 0.0
	if (b <= -8.8e-54)
		tmp = t_1;
	elseif (b <= 550000000.0)
		tmp = Float64(z * y);
	elseif (b <= 2.9e+125)
		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 <= -8.8e-54)
		tmp = t_1;
	elseif (b <= 550000000.0)
		tmp = z * y;
	elseif (b <= 2.9e+125)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.8e-54], t$95$1, If[LessEqual[b, 550000000.0], N[(z * y), $MachinePrecision], If[LessEqual[b, 2.9e+125], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.7999999999999998e-54 or 2.89999999999999993e125 < b

   1. Initial program 87.4%

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

      1. associate-+l+ 87.4%

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

      2. associate-*l* 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in z around inf 64.8%

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

   6. Taylor expanded in y around 0 52.1%

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

   if -8.7999999999999998e-54 < b < 5.5e8

   1. Initial program 94.2%

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

      1. associate-+l+ 94.2%

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

      2. associate-*l* 98.3%

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

   3. Simplified 98.3%

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

      1. *-commutative 98.3%

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

      2. distribute-lft-in 99.1%

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

      3. add-cube-cbrt 98.7%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 98.6%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 98.6%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 98.6%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-define 98.6%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 98.6%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in y around inf 40.3%

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

      1. *-commutative 40.3%

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

   9. Simplified 40.3%

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

   if 5.5e8 < b < 2.89999999999999993e125

   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* 89.4%

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

   3. Simplified 89.4%

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

      1. *-commutative 89.4%

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

      2. distribute-lft-in 89.4%

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

      3. add-cube-cbrt 89.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 89.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 89.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 89.3%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-define 89.3%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 89.3%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in x around inf 52.8%

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

Alternative 7: 38.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot z\right)\\ \mathbf{if}\;b \leq -8.8 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1000000000:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+124}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* b z))))
   (if (<= b -8.8e-54)
     t_1
     (if (<= b 1000000000.0) (* z y) (if (<= b 2.6e+124) x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (b * z);
	double tmp;
	if (b <= -8.8e-54) {
		tmp = t_1;
	} else if (b <= 1000000000.0) {
		tmp = z * y;
	} else if (b <= 2.6e+124) {
		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 = a * (b * z)
    if (b <= (-8.8d-54)) then
        tmp = t_1
    else if (b <= 1000000000.0d0) then
        tmp = z * y
    else if (b <= 2.6d+124) 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 = a * (b * z);
	double tmp;
	if (b <= -8.8e-54) {
		tmp = t_1;
	} else if (b <= 1000000000.0) {
		tmp = z * y;
	} else if (b <= 2.6e+124) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (b * z)
	tmp = 0
	if b <= -8.8e-54:
		tmp = t_1
	elif b <= 1000000000.0:
		tmp = z * y
	elif b <= 2.6e+124:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(b * z))
	tmp = 0.0
	if (b <= -8.8e-54)
		tmp = t_1;
	elseif (b <= 1000000000.0)
		tmp = Float64(z * y);
	elseif (b <= 2.6e+124)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (b * z);
	tmp = 0.0;
	if (b <= -8.8e-54)
		tmp = t_1;
	elseif (b <= 1000000000.0)
		tmp = z * y;
	elseif (b <= 2.6e+124)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(b * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.8e-54], t$95$1, If[LessEqual[b, 1000000000.0], N[(z * y), $MachinePrecision], If[LessEqual[b, 2.6e+124], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.7999999999999998e-54 or 2.6e124 < b

   1. Initial program 87.4%

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

      1. associate-+l+ 87.4%

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

      2. associate-*l* 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in a around inf 81.1%

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

   6. Taylor expanded in b around inf 67.5%

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

   7. Taylor expanded in t around 0 51.2%

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

   if -8.7999999999999998e-54 < b < 1e9

   1. Initial program 94.2%

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

      1. associate-+l+ 94.2%

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

      2. associate-*l* 98.3%

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

   3. Simplified 98.3%

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

      1. *-commutative 98.3%

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

      2. distribute-lft-in 99.1%

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

      3. add-cube-cbrt 98.7%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 98.6%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 98.6%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 98.6%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-define 98.6%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 98.6%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in y around inf 40.3%

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

      1. *-commutative 40.3%

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

   9. Simplified 40.3%

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

   if 1e9 < b < 2.6e124

   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* 89.4%

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

   3. Simplified 89.4%

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

      1. *-commutative 89.4%

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

      2. distribute-lft-in 89.4%

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

      3. add-cube-cbrt 89.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 89.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 89.3%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 89.3%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-define 89.3%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 89.3%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in x around inf 52.8%

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

Alternative 8: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{-54} \lor \neg \left(b \leq 1.45 \cdot 10^{+105}\right):\\ \;\;\;\;x + a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.5e-54) (not (<= b 1.45e+105)))
   (+ x (* a (+ t (* b z))))
   (+ x (+ (* a t) (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.5e-54) || !(b <= 1.45e+105)) {
		tmp = x + (a * (t + (b * z)));
	} else {
		tmp = x + ((a * t) + (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6.5d-54)) .or. (.not. (b <= 1.45d+105))) then
        tmp = x + (a * (t + (b * z)))
    else
        tmp = x + ((a * t) + (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.5e-54) || !(b <= 1.45e+105)) {
		tmp = x + (a * (t + (b * z)));
	} else {
		tmp = x + ((a * t) + (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.5e-54) or not (b <= 1.45e+105):
		tmp = x + (a * (t + (b * z)))
	else:
		tmp = x + ((a * t) + (z * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.5e-54) || !(b <= 1.45e+105))
		tmp = Float64(x + Float64(a * Float64(t + Float64(b * z))));
	else
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.5e-54) || ~((b <= 1.45e+105)))
		tmp = x + (a * (t + (b * z)));
	else
		tmp = x + ((a * t) + (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.5e-54], N[Not[LessEqual[b, 1.45e+105]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.49999999999999991e-54 or 1.45000000000000005e105 < b

   1. Initial program 87.5%

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

      1. associate-+l+ 87.5%

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

      2. +-commutative 87.5%

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

      3. fma-define 87.5%

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

      4. associate-*l* 84.2%

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

      5. *-commutative 84.2%

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

      6. *-commutative 84.2%

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

      7. distribute-rgt-out 90.9%

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

      8. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around 0 83.3%

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

   if -6.49999999999999991e-54 < b < 1.45000000000000005e105

   1. Initial program 93.5%

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

      1. associate-+l+ 93.5%

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

      2. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in b around 0 93.0%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{-54} \lor \neg \left(b \leq 1.45 \cdot 10^{+105}\right):\\ \;\;\;\;x + a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{+138}:\\ \;\;\;\;a \cdot t + z \cdot y\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+153}:\\ \;\;\;\;x + a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + \frac{z \cdot y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.26e+138)
   (+ (* a t) (* z y))
   (if (<= y 1.6e+153) (+ x (* a (+ t (* b z)))) (* a (+ t (/ (* z y) a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.26e+138) {
		tmp = (a * t) + (z * y);
	} else if (y <= 1.6e+153) {
		tmp = x + (a * (t + (b * z)));
	} else {
		tmp = a * (t + ((z * y) / 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 (y <= (-1.26d+138)) then
        tmp = (a * t) + (z * y)
    else if (y <= 1.6d+153) then
        tmp = x + (a * (t + (b * z)))
    else
        tmp = a * (t + ((z * y) / 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 (y <= -1.26e+138) {
		tmp = (a * t) + (z * y);
	} else if (y <= 1.6e+153) {
		tmp = x + (a * (t + (b * z)));
	} else {
		tmp = a * (t + ((z * y) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.26e+138:
		tmp = (a * t) + (z * y)
	elif y <= 1.6e+153:
		tmp = x + (a * (t + (b * z)))
	else:
		tmp = a * (t + ((z * y) / a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.26e+138)
		tmp = Float64(Float64(a * t) + Float64(z * y));
	elseif (y <= 1.6e+153)
		tmp = Float64(x + Float64(a * Float64(t + Float64(b * z))));
	else
		tmp = Float64(a * Float64(t + Float64(Float64(z * y) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.26e+138)
		tmp = (a * t) + (z * y);
	elseif (y <= 1.6e+153)
		tmp = x + (a * (t + (b * z)));
	else
		tmp = a * (t + ((z * y) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.26e+138], N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+153], N[(x + N[(a * N[(t + N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25999999999999994e138

   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* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in a around inf 78.8%

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

   6. Taylor expanded in y around inf 73.5%

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

   7. Taylor expanded in a around 0 86.3%

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

   if -1.25999999999999994e138 < y < 1.6000000000000001e153

   1. Initial program 91.7%

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

      1. associate-+l+ 91.7%

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

      2. +-commutative 91.7%

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

      3. fma-define 91.7%

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

      4. associate-*l* 91.7%

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

      5. *-commutative 91.7%

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

      6. *-commutative 91.7%

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

      7. distribute-rgt-out 95.6%

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

      8. *-commutative 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in y around 0 85.2%

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

   if 1.6000000000000001e153 < y

   1. Initial program 87.5%

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

      1. associate-+l+ 87.5%

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

      2. associate-*l* 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in a around inf 92.7%

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

   6. Taylor expanded in y around inf 83.3%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{+138}:\\ \;\;\;\;a \cdot t + z \cdot y\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+153}:\\ \;\;\;\;x + a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + \frac{z \cdot y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 95.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+78}:\\ \;\;\;\;x + a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot \left(y + a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.1e+78)
   (+ x (* a (+ t (* b z))))
   (+ x (+ (* a t) (* z (+ y (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.1e+78) {
		tmp = x + (a * (t + (b * z)));
	} else {
		tmp = x + ((a * t) + (z * (y + (a * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.1d+78)) then
        tmp = x + (a * (t + (b * z)))
    else
        tmp = x + ((a * t) + (z * (y + (a * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.1e+78) {
		tmp = x + (a * (t + (b * z)));
	} else {
		tmp = x + ((a * t) + (z * (y + (a * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.1e+78:
		tmp = x + (a * (t + (b * z)))
	else:
		tmp = x + ((a * t) + (z * (y + (a * b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.1e+78)
		tmp = Float64(x + Float64(a * Float64(t + Float64(b * z))));
	else
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * Float64(y + Float64(a * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.1e+78)
		tmp = x + (a * (t + (b * z)));
	else
		tmp = x + ((a * t) + (z * (y + (a * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.1e+78], N[(x + N[(a * N[(t + N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.10000000000000007e78

   1. Initial program 75.2%

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

      1. associate-+l+ 75.2%

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

      2. +-commutative 75.2%

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

      3. fma-define 75.2%

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

      4. associate-*l* 82.7%

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

      5. *-commutative 82.7%

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

      6. *-commutative 82.7%

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

      7. distribute-rgt-out 94.2%

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

      8. *-commutative 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in y around 0 94.1%

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

   if -1.10000000000000007e78 < a

   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* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around 0 97.0%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+78}:\\ \;\;\;\;x + a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot \left(y + a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+44} \lor \neg \left(a \leq 3.6 \cdot 10^{+14}\right):\\ \;\;\;\;a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -8.2e+44) (not (<= a 3.6e+14)))
   (* a (+ t (* b z)))
   (+ x (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -8.2e+44) || !(a <= 3.6e+14)) {
		tmp = a * (t + (b * z));
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-8.2d+44)) .or. (.not. (a <= 3.6d+14))) then
        tmp = a * (t + (b * z))
    else
        tmp = x + (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -8.2e+44) || !(a <= 3.6e+14)) {
		tmp = a * (t + (b * z));
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -8.2e+44) or not (a <= 3.6e+14):
		tmp = a * (t + (b * z))
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -8.2e+44) || !(a <= 3.6e+14))
		tmp = Float64(a * Float64(t + Float64(b * z)));
	else
		tmp = Float64(x + Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -8.2e+44) || ~((a <= 3.6e+14)))
		tmp = a * (t + (b * z));
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -8.2e+44], N[Not[LessEqual[a, 3.6e+14]], $MachinePrecision]], N[(a * N[(t + N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.1999999999999993e44 or 3.6e14 < a

   1. Initial program 83.9%

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

      1. associate-+l+ 83.9%

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

      2. associate-*l* 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in a around inf 96.7%

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

   6. Taylor expanded in b around inf 80.6%

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

   if -8.1999999999999993e44 < a < 3.6e14

   1. Initial program 97.0%

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

      1. associate-+l+ 97.0%

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

      2. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

      1. *-commutative 93.3%

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

      2. distribute-lft-in 93.3%

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

      3. add-cube-cbrt 93.0%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 92.9%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 92.9%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 92.9%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-define 92.9%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 92.9%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in a around 0 72.5%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+44} \lor \neg \left(a \leq 3.6 \cdot 10^{+14}\right):\\ \;\;\;\;a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-29} \lor \neg \left(a \leq 4.2 \cdot 10^{+115}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.55e-29) (not (<= a 4.2e+115))) (* a t) (* z y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.55e-29) || !(a <= 4.2e+115)) {
		tmp = a * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-1.55d-29)) .or. (.not. (a <= 4.2d+115))) then
        tmp = a * t
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.55e-29) || !(a <= 4.2e+115)) {
		tmp = a * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.55e-29) or not (a <= 4.2e+115):
		tmp = a * t
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.55e-29) || !(a <= 4.2e+115))
		tmp = Float64(a * t);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.55e-29) || ~((a <= 4.2e+115)))
		tmp = a * t;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.55e-29], N[Not[LessEqual[a, 4.2e+115]], $MachinePrecision]], N[(a * t), $MachinePrecision], N[(z * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.55000000000000013e-29 or 4.20000000000000007e115 < a

   1. Initial program 84.0%

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

      1. associate-+l+ 84.0%

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

      2. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in a around inf 98.0%

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

   6. Taylor expanded in b around inf 83.8%

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

   7. Taylor expanded in t around inf 45.6%

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

   if -1.55000000000000013e-29 < a < 4.20000000000000007e115

   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. associate-+l+ 95.3%

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

      2. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

      1. *-commutative 92.1%

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

      2. distribute-lft-in 92.8%

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

      3. add-cube-cbrt 92.5%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 92.4%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 92.4%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 92.4%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-define 92.4%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 92.4%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in y around inf 39.6%

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

      1. *-commutative 39.6%

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

   9. Simplified 39.6%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-29} \lor \neg \left(a \leq 4.2 \cdot 10^{+115}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+88} \lor \neg \left(a \leq 3100000\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.7e+88) (not (<= a 3100000.0))) (* a t) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.7e+88) || !(a <= 3100000.0)) {
		tmp = a * t;
	} 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 ((a <= (-2.7d+88)) .or. (.not. (a <= 3100000.0d0))) then
        tmp = a * t
    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 ((a <= -2.7e+88) || !(a <= 3100000.0)) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.7e+88) or not (a <= 3100000.0):
		tmp = a * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.7e+88) || !(a <= 3100000.0))
		tmp = Float64(a * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.7e+88) || ~((a <= 3100000.0)))
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.7e+88], N[Not[LessEqual[a, 3100000.0]], $MachinePrecision]], N[(a * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -2.70000000000000016e88 or 3.1e6 < a

   1. Initial program 83.9%

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

      1. associate-+l+ 83.9%

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

      2. associate-*l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in a around inf 96.5%

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

   6. Taylor expanded in b around inf 80.8%

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

   7. Taylor expanded in t around inf 43.7%

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

   if -2.70000000000000016e88 < a < 3.1e6

   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* 92.9%

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

   3. Simplified 92.9%

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

      1. *-commutative 92.9%

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

      2. distribute-lft-in 92.9%

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

      3. add-cube-cbrt 92.5%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

      4. associate-*l* 92.5%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

      5. pow2 92.5%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

      6. +-commutative 92.5%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

      7. fma-define 92.5%

         \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

   6. Applied egg-rr 92.5%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

   7. Taylor expanded in x around inf 35.4%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+88} \lor \neg \left(a \leq 3100000\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 25.2% 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 90.7%

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

   1. associate-+l+ 90.7%

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

   2. associate-*l* 91.0%

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

3. Simplified 91.0%

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

   1. *-commutative 91.0%

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

   2. distribute-lft-in 94.6%

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

   3. add-cube-cbrt 94.1%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(t + z \cdot b\right) \]

   4. associate-*l* 94.1%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right)} \]

   5. pow2 94.1%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \left(\sqrt[3]{a} \cdot \left(t + z \cdot b\right)\right) \]

   6. +-commutative 94.1%

      \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\left(z \cdot b + t\right)}\right) \]

   7. fma-define 94.1%

      \[\leadsto \left(x + y \cdot z\right) + {\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \color{blue}{\mathsf{fma}\left(z, b, t\right)}\right) \]

6. Applied egg-rr 94.1%

   \[\leadsto \left(x + y \cdot z\right) + \color{blue}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \left(\sqrt[3]{a} \cdot \mathsf{fma}\left(z, b, t\right)\right)} \]

7. Taylor expanded in x around inf 23.9%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 97.5% accurate, 0.7× 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 2024137 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -11820553527347888000) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 47589743188364287/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a))))))

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