Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 91.9% → 96.6%

Time: 12.8s

Alternatives: 17

Speedup: 0.8×

• 32.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+185} \lor \neg \left(z \leq 8.5 \cdot 10^{+185}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.5e+185) (not (<= z 8.5e+185)))
   (+ (* z (+ y (* a b))) x)
   (+ (fma y z x) (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.5e+185) || !(z <= 8.5e+185)) {
		tmp = (z * (y + (a * b))) + x;
	} else {
		tmp = fma(y, z, x) + (a * (t + (z * b)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.5e+185) || !(z <= 8.5e+185))
		tmp = Float64(Float64(z * Float64(y + Float64(a * b))) + x);
	else
		tmp = Float64(fma(y, z, x) + Float64(a * Float64(t + Float64(z * b))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.5e+185], N[Not[LessEqual[z, 8.5e+185]], $MachinePrecision]], N[(N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(y * z + x), $MachinePrecision] + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5000000000000002e185 or 8.50000000000000013e185 < z

   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. *-commutative 71.4%

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

      3. associate-*l* 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in t around 0 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-*r* 85.7%

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

      3. distribute-rgt-in 98.2%

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

      4. +-commutative 98.2%

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

   6. Simplified 98.2%

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

   if -4.5000000000000002e185 < z < 8.50000000000000013e185

   1. Initial program 96.1%

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

      1. associate-+l+ 96.1%

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

      2. +-commutative 96.1%

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

      3. fma-def 96.1%

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

      4. associate-*l* 97.5%

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

      5. *-commutative 97.5%

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

      6. *-commutative 97.5%

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

      7. distribute-rgt-out 98.5%

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

      8. *-commutative 98.5%

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

   3. Simplified 98.5%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+185} \lor \neg \left(z \leq 8.5 \cdot 10^{+185}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 2: 95.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+185}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t + z \cdot b, \mathsf{fma}\left(y, z, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2e+185)
   (+ (* z (+ y (* a b))) x)
   (fma a (+ t (* z b)) (fma y z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2e+185) {
		tmp = (z * (y + (a * b))) + x;
	} else {
		tmp = fma(a, (t + (z * b)), fma(y, z, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2e+185)
		tmp = Float64(Float64(z * Float64(y + Float64(a * b))) + x);
	else
		tmp = fma(a, Float64(t + Float64(z * b)), fma(y, z, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2e+185], N[(N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(y * z + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2e185

   1. Initial program 69.6%

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

      1. associate-+l+ 69.6%

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

      2. *-commutative 69.6%

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

      3. associate-*l* 69.6%

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

   3. Simplified 69.6%

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

   4. Taylor expanded in t around 0 69.9%

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

      1. +-commutative 69.9%

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

      2. associate-*r* 82.6%

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

      3. distribute-rgt-in 100.0%

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

      4. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   if -2e185 < z

   1. Initial program 92.8%

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

      1. associate-+l+ 92.8%

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

      2. +-commutative 92.8%

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

      3. *-commutative 92.8%

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

      4. associate-*l* 94.1%

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

      5. *-commutative 94.1%

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

      6. distribute-lft-out 96.2%

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

      7. fma-def 96.6%

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

      8. *-commutative 96.6%

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

      9. +-commutative 96.6%

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

      10. fma-def 96.6%

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

   3. Simplified 96.6%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+185}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t + z \cdot b, \mathsf{fma}\left(y, z, x\right)\right)\\ \end{array} \]

Alternative 3: 96.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* z y)) (* a t)) (* b (* z a)))))
   (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 = ((x + (z * y)) + (a * t)) + (b * (z * a));
	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 = ((x + (z * y)) + (a * t)) + (b * (z * a));
	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 = ((x + (z * y)) + (a * t)) + (b * (z * a))
	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(x + Float64(z * y)) + Float64(a * t)) + Float64(b * Float64(z * a)))
	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 = ((x + (z * y)) + (a * t)) + (b * (z * a));
	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[(x + N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b * N[(z * a), $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 97.2%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*l* 5.9%

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

   3. Simplified 5.9%

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

   4. Taylor expanded in z around inf 82.4%

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

4. Final simplification 96.2%

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

Alternative 4: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + a \cdot b\right) + x\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-9}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+185}:\\ \;\;\;\;\left(a \cdot t + z \cdot y\right) + b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (+ y (* a b))) x)))
   (if (<= z -3.7e-8)
     t_1
     (if (<= z 2.8e-9)
       (+ x (* a (+ t (* z b))))
       (if (<= z 5.8e+185) (+ (+ (* a t) (* z y)) (* b (* z a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (y + (a * b))) + x;
	double tmp;
	if (z <= -3.7e-8) {
		tmp = t_1;
	} else if (z <= 2.8e-9) {
		tmp = x + (a * (t + (z * b)));
	} else if (z <= 5.8e+185) {
		tmp = ((a * t) + (z * y)) + (b * (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * (y + (a * b))) + x
    if (z <= (-3.7d-8)) then
        tmp = t_1
    else if (z <= 2.8d-9) then
        tmp = x + (a * (t + (z * b)))
    else if (z <= 5.8d+185) then
        tmp = ((a * t) + (z * y)) + (b * (z * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (y + (a * b))) + x;
	double tmp;
	if (z <= -3.7e-8) {
		tmp = t_1;
	} else if (z <= 2.8e-9) {
		tmp = x + (a * (t + (z * b)));
	} else if (z <= 5.8e+185) {
		tmp = ((a * t) + (z * y)) + (b * (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (y + (a * b))) + x
	tmp = 0
	if z <= -3.7e-8:
		tmp = t_1
	elif z <= 2.8e-9:
		tmp = x + (a * (t + (z * b)))
	elif z <= 5.8e+185:
		tmp = ((a * t) + (z * y)) + (b * (z * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(y + Float64(a * b))) + x)
	tmp = 0.0
	if (z <= -3.7e-8)
		tmp = t_1;
	elseif (z <= 2.8e-9)
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	elseif (z <= 5.8e+185)
		tmp = Float64(Float64(Float64(a * t) + Float64(z * y)) + Float64(b * Float64(z * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (y + (a * b))) + x;
	tmp = 0.0;
	if (z <= -3.7e-8)
		tmp = t_1;
	elseif (z <= 2.8e-9)
		tmp = x + (a * (t + (z * b)));
	elseif (z <= 5.8e+185)
		tmp = ((a * t) + (z * y)) + (b * (z * a));
	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[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -3.7e-8], t$95$1, If[LessEqual[z, 2.8e-9], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+185], N[(N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7e-8 or 5.79999999999999976e185 < z

   1. Initial program 80.7%

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

      1. associate-+l+ 80.7%

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

      2. *-commutative 80.7%

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

      3. associate-*l* 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in t around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. associate-*r* 88.6%

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

      3. distribute-rgt-in 96.1%

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

      4. +-commutative 96.1%

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

   6. Simplified 96.1%

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

   if -3.7e-8 < z < 2.79999999999999984e-9

   1. Initial program 99.1%

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

      1. associate-+l+ 99.1%

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

      2. +-commutative 99.1%

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

      3. fma-def 99.1%

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

      4. associate-*l* 99.1%

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

      5. *-commutative 99.1%

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

      6. *-commutative 99.1%

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

      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. Taylor expanded in y around 0 89.9%

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

   if 2.79999999999999984e-9 < z < 5.79999999999999976e185

   1. Initial program 90.6%

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

   2. Taylor expanded in x around 0 88.8%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right) + x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-9}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+185}:\\ \;\;\;\;\left(a \cdot t + z \cdot y\right) + b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right) + x\\ \end{array} \]

Alternative 5: 95.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+199} \lor \neg \left(a \leq 1.9 \cdot 10^{+73}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z \cdot y\right) + \left(a \cdot t + z \cdot \left(a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.6e+199) (not (<= a 1.9e+73)))
   (+ x (* a (+ t (* z b))))
   (+ (+ x (* z y)) (+ (* a t) (* z (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.6e+199) || !(a <= 1.9e+73)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (x + (z * y)) + ((a * t) + (z * (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2.6d+199)) .or. (.not. (a <= 1.9d+73))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = (x + (z * y)) + ((a * t) + (z * (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.6e+199) || !(a <= 1.9e+73)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (x + (z * y)) + ((a * t) + (z * (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.6e+199) or not (a <= 1.9e+73):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = (x + (z * y)) + ((a * t) + (z * (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.6e+199) || !(a <= 1.9e+73))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(Float64(x + Float64(z * y)) + Float64(Float64(a * t) + Float64(z * Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.6e+199) || ~((a <= 1.9e+73)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = (x + (z * y)) + ((a * t) + (z * (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.6e+199], N[Not[LessEqual[a, 1.9e+73]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] + N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.6000000000000001e199 or 1.90000000000000011e73 < a

   1. Initial program 80.1%

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

      1. associate-+l+ 80.1%

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

      2. +-commutative 80.1%

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

      3. fma-def 80.1%

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

      4. associate-*l* 86.4%

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

      5. *-commutative 86.4%

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

      6. *-commutative 86.4%

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

      7. distribute-rgt-out 96.6%

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

      8. *-commutative 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in y around 0 91.3%

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

   if -2.6000000000000001e199 < a < 1.90000000000000011e73

   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. *-commutative 96.4%

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

      3. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+199} \lor \neg \left(a \leq 1.9 \cdot 10^{+73}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z \cdot y\right) + \left(a \cdot t + z \cdot \left(a \cdot b\right)\right)\\ \end{array} \]

Alternative 6: 39.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;a \leq -3.85 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-148}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 0.0215:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+156} \lor \neg \left(a \leq 1.55 \cdot 10^{+235}\right) \land a \leq 1.22 \cdot 10^{+275}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= a -3.85e-19)
     t_1
     (if (<= a 4.6e-148)
       (* z y)
       (if (<= a 0.0215)
         x
         (if (or (<= a 2.3e+156) (and (not (<= a 1.55e+235)) (<= a 1.22e+275)))
           t_1
           (* a t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -3.85e-19) {
		tmp = t_1;
	} else if (a <= 4.6e-148) {
		tmp = z * y;
	} else if (a <= 0.0215) {
		tmp = x;
	} else if ((a <= 2.3e+156) || (!(a <= 1.55e+235) && (a <= 1.22e+275))) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (a <= (-3.85d-19)) then
        tmp = t_1
    else if (a <= 4.6d-148) then
        tmp = z * y
    else if (a <= 0.0215d0) then
        tmp = x
    else if ((a <= 2.3d+156) .or. (.not. (a <= 1.55d+235)) .and. (a <= 1.22d+275)) then
        tmp = t_1
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -3.85e-19) {
		tmp = t_1;
	} else if (a <= 4.6e-148) {
		tmp = z * y;
	} else if (a <= 0.0215) {
		tmp = x;
	} else if ((a <= 2.3e+156) || (!(a <= 1.55e+235) && (a <= 1.22e+275))) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if a <= -3.85e-19:
		tmp = t_1
	elif a <= 4.6e-148:
		tmp = z * y
	elif a <= 0.0215:
		tmp = x
	elif (a <= 2.3e+156) or (not (a <= 1.55e+235) and (a <= 1.22e+275)):
		tmp = t_1
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (a <= -3.85e-19)
		tmp = t_1;
	elseif (a <= 4.6e-148)
		tmp = Float64(z * y);
	elseif (a <= 0.0215)
		tmp = x;
	elseif ((a <= 2.3e+156) || (!(a <= 1.55e+235) && (a <= 1.22e+275)))
		tmp = t_1;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (a <= -3.85e-19)
		tmp = t_1;
	elseif (a <= 4.6e-148)
		tmp = z * y;
	elseif (a <= 0.0215)
		tmp = x;
	elseif ((a <= 2.3e+156) || (~((a <= 1.55e+235)) && (a <= 1.22e+275)))
		tmp = t_1;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.85e-19], t$95$1, If[LessEqual[a, 4.6e-148], N[(z * y), $MachinePrecision], If[LessEqual[a, 0.0215], x, If[Or[LessEqual[a, 2.3e+156], And[N[Not[LessEqual[a, 1.55e+235]], $MachinePrecision], LessEqual[a, 1.22e+275]]], t$95$1, N[(a * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.85000000000000022e-19 or 0.021499999999999998 < a < 2.2999999999999999e156 or 1.55000000000000005e235 < a < 1.22e275

   1. Initial program 85.9%

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

      1. associate-+l+ 85.9%

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

      2. *-commutative 85.9%

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

      3. associate-*l* 80.6%

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

   3. Simplified 80.6%

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

      1. *-commutative 80.6%

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

      2. associate-*r* 91.8%

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

      3. distribute-rgt-in 97.2%

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

      4. add-cube-cbrt 96.5%

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

      5. associate-*r* 96.6%

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

      6. cbrt-unprod 93.2%

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

      7. pow2 93.2%

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

      8. +-commutative 93.2%

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

      9. fma-def 93.2%

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

      10. +-commutative 93.2%

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

      11. fma-def 93.2%

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

   5. Applied egg-rr 93.2%

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

   6. Taylor expanded in b around inf 50.9%

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

   if -3.85000000000000022e-19 < a < 4.59999999999999995e-148

   1. Initial program 97.6%

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

      1. associate-+l+ 97.6%

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

      2. *-commutative 97.6%

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

      3. associate-*l* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in y around inf 51.2%

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

      1. *-commutative 51.2%

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

   6. Simplified 51.2%

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

   if 4.59999999999999995e-148 < a < 0.021499999999999998

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 45.2%

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

   if 2.2999999999999999e156 < a < 1.55000000000000005e235 or 1.22e275 < a

   1. Initial program 79.3%

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

      1. associate-+l+ 79.3%

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

      2. *-commutative 79.3%

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

      3. associate-*l* 72.7%

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

   3. Simplified 72.7%

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

      1. *-commutative 72.7%

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

      2. associate-*r* 82.7%

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

      3. distribute-rgt-in 93.1%

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

      4. add-cube-cbrt 92.5%

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

      5. associate-*r* 92.4%

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

      6. cbrt-unprod 89.5%

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

      7. pow2 89.5%

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

      8. +-commutative 89.5%

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

      9. fma-def 89.5%

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

      10. +-commutative 89.5%

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

      11. fma-def 89.5%

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

   5. Applied egg-rr 89.5%

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

   6. Taylor expanded in t around inf 66.4%

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

      1. *-commutative 66.4%

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

   8. Simplified 66.4%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.85 \cdot 10^{-19}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-148}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 0.0215:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+156} \lor \neg \left(a \leq 1.55 \cdot 10^{+235}\right) \land a \leq 1.22 \cdot 10^{+275}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 7: 39.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00095:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-155}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-261}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-204}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+35}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.00095)
   (* z y)
   (if (<= z -5e-155)
     (* a t)
     (if (<= z 2.5e-261)
       x
       (if (<= z 1.02e-204)
         (* a t)
         (if (<= z 1.8e-153) x (if (<= z 5.7e+35) (* a t) (* z y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.00095) {
		tmp = z * y;
	} else if (z <= -5e-155) {
		tmp = a * t;
	} else if (z <= 2.5e-261) {
		tmp = x;
	} else if (z <= 1.02e-204) {
		tmp = a * t;
	} else if (z <= 1.8e-153) {
		tmp = x;
	} else if (z <= 5.7e+35) {
		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 (z <= (-0.00095d0)) then
        tmp = z * y
    else if (z <= (-5d-155)) then
        tmp = a * t
    else if (z <= 2.5d-261) then
        tmp = x
    else if (z <= 1.02d-204) then
        tmp = a * t
    else if (z <= 1.8d-153) then
        tmp = x
    else if (z <= 5.7d+35) 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 (z <= -0.00095) {
		tmp = z * y;
	} else if (z <= -5e-155) {
		tmp = a * t;
	} else if (z <= 2.5e-261) {
		tmp = x;
	} else if (z <= 1.02e-204) {
		tmp = a * t;
	} else if (z <= 1.8e-153) {
		tmp = x;
	} else if (z <= 5.7e+35) {
		tmp = a * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.00095:
		tmp = z * y
	elif z <= -5e-155:
		tmp = a * t
	elif z <= 2.5e-261:
		tmp = x
	elif z <= 1.02e-204:
		tmp = a * t
	elif z <= 1.8e-153:
		tmp = x
	elif z <= 5.7e+35:
		tmp = a * t
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.00095)
		tmp = Float64(z * y);
	elseif (z <= -5e-155)
		tmp = Float64(a * t);
	elseif (z <= 2.5e-261)
		tmp = x;
	elseif (z <= 1.02e-204)
		tmp = Float64(a * t);
	elseif (z <= 1.8e-153)
		tmp = x;
	elseif (z <= 5.7e+35)
		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 (z <= -0.00095)
		tmp = z * y;
	elseif (z <= -5e-155)
		tmp = a * t;
	elseif (z <= 2.5e-261)
		tmp = x;
	elseif (z <= 1.02e-204)
		tmp = a * t;
	elseif (z <= 1.8e-153)
		tmp = x;
	elseif (z <= 5.7e+35)
		tmp = a * t;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.00095], N[(z * y), $MachinePrecision], If[LessEqual[z, -5e-155], N[(a * t), $MachinePrecision], If[LessEqual[z, 2.5e-261], x, If[LessEqual[z, 1.02e-204], N[(a * t), $MachinePrecision], If[LessEqual[z, 1.8e-153], x, If[LessEqual[z, 5.7e+35], N[(a * t), $MachinePrecision], N[(z * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.49999999999999998e-4 or 5.69999999999999993e35 < z

   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. associate-+l+ 83.0%

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

      2. *-commutative 83.0%

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

      3. associate-*l* 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in y around inf 46.1%

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

      1. *-commutative 46.1%

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

   6. Simplified 46.1%

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

   if -9.49999999999999998e-4 < z < -4.9999999999999999e-155 or 2.4999999999999999e-261 < z < 1.0200000000000001e-204 or 1.7999999999999999e-153 < z < 5.69999999999999993e35

   1. Initial program 97.4%

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

      1. associate-+l+ 97.4%

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

      2. *-commutative 97.4%

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

      3. associate-*l* 85.3%

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

   3. Simplified 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-*r* 97.3%

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

      3. distribute-rgt-in 99.9%

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

      4. add-cube-cbrt 99.0%

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

      5. associate-*r* 99.0%

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

      6. cbrt-unprod 83.5%

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

      7. pow2 83.5%

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

      8. +-commutative 83.5%

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

      9. fma-def 83.5%

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

      10. +-commutative 83.5%

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

      11. fma-def 83.5%

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

   5. Applied egg-rr 83.5%

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

   6. Taylor expanded in t around inf 47.2%

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

      1. *-commutative 47.2%

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

   8. Simplified 47.2%

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

   if -4.9999999999999999e-155 < z < 2.4999999999999999e-261 or 1.0200000000000001e-204 < z < 1.7999999999999999e-153

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*l* 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in x around inf 60.3%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00095:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-155}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-261}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-204}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+35}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 8: 40.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-148}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 0.005:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+160} \lor \neg \left(a \leq 7.6 \cdot 10^{+234}\right):\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4.4e-15)
   (* a (* z b))
   (if (<= a 2.05e-148)
     (* z y)
     (if (<= a 0.005)
       x
       (if (or (<= a 2.05e+160) (not (<= a 7.6e+234)))
         (* b (* z a))
         (* a t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.4e-15) {
		tmp = a * (z * b);
	} else if (a <= 2.05e-148) {
		tmp = z * y;
	} else if (a <= 0.005) {
		tmp = x;
	} else if ((a <= 2.05e+160) || !(a <= 7.6e+234)) {
		tmp = b * (z * a);
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-4.4d-15)) then
        tmp = a * (z * b)
    else if (a <= 2.05d-148) then
        tmp = z * y
    else if (a <= 0.005d0) then
        tmp = x
    else if ((a <= 2.05d+160) .or. (.not. (a <= 7.6d+234))) then
        tmp = b * (z * a)
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.4e-15) {
		tmp = a * (z * b);
	} else if (a <= 2.05e-148) {
		tmp = z * y;
	} else if (a <= 0.005) {
		tmp = x;
	} else if ((a <= 2.05e+160) || !(a <= 7.6e+234)) {
		tmp = b * (z * a);
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.4e-15:
		tmp = a * (z * b)
	elif a <= 2.05e-148:
		tmp = z * y
	elif a <= 0.005:
		tmp = x
	elif (a <= 2.05e+160) or not (a <= 7.6e+234):
		tmp = b * (z * a)
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.4e-15)
		tmp = Float64(a * Float64(z * b));
	elseif (a <= 2.05e-148)
		tmp = Float64(z * y);
	elseif (a <= 0.005)
		tmp = x;
	elseif ((a <= 2.05e+160) || !(a <= 7.6e+234))
		tmp = Float64(b * Float64(z * a));
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4.4e-15)
		tmp = a * (z * b);
	elseif (a <= 2.05e-148)
		tmp = z * y;
	elseif (a <= 0.005)
		tmp = x;
	elseif ((a <= 2.05e+160) || ~((a <= 7.6e+234)))
		tmp = b * (z * a);
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.4e-15], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.05e-148], N[(z * y), $MachinePrecision], If[LessEqual[a, 0.005], x, If[Or[LessEqual[a, 2.05e+160], N[Not[LessEqual[a, 7.6e+234]], $MachinePrecision]], N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision], N[(a * t), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.39999999999999971e-15

   1. Initial program 81.1%

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

      1. associate-+l+ 81.1%

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

      2. *-commutative 81.1%

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

      3. associate-*l* 80.9%

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

   3. Simplified 80.9%

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

      1. *-commutative 80.9%

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

      2. associate-*r* 91.0%

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

      3. distribute-rgt-in 96.9%

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

      4. add-cube-cbrt 96.4%

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

      5. associate-*r* 96.4%

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

      6. cbrt-unprod 94.7%

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

      7. pow2 94.7%

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

      8. +-commutative 94.7%

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

      9. fma-def 94.7%

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

      10. +-commutative 94.7%

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

      11. fma-def 94.7%

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

   5. Applied egg-rr 94.7%

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

   6. Taylor expanded in b around inf 48.9%

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

   if -4.39999999999999971e-15 < a < 2.0500000000000001e-148

   1. Initial program 97.6%

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

      1. associate-+l+ 97.6%

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

      2. *-commutative 97.6%

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

      3. associate-*l* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in y around inf 51.2%

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

      1. *-commutative 51.2%

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

   6. Simplified 51.2%

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

   if 2.0500000000000001e-148 < a < 0.0050000000000000001

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 45.2%

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

   if 0.0050000000000000001 < a < 2.04999999999999999e160 or 7.6000000000000001e234 < a

   1. Initial program 88.4%

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

      1. associate-+l+ 88.4%

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

      2. *-commutative 88.4%

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

      3. associate-*l* 75.4%

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

   3. Simplified 75.4%

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

      1. *-commutative 75.4%

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

      2. associate-*r* 88.4%

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

      3. distribute-rgt-in 96.1%

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

      4. add-cube-cbrt 95.3%

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

      5. associate-*r* 95.3%

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

      6. cbrt-unprod 90.2%

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

      7. pow2 90.2%

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

      8. +-commutative 90.2%

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

      9. fma-def 90.2%

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

      10. +-commutative 90.2%

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

      11. fma-def 90.2%

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

   5. Applied egg-rr 90.2%

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

   6. Taylor expanded in b around inf 49.8%

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

      1. associate-*r* 46.1%

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

      2. *-commutative 46.1%

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

      3. associate-*l* 51.5%

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

   8. Simplified 51.5%

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

   if 2.04999999999999999e160 < a < 7.6000000000000001e234

   1. Initial program 85.7%

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

      1. associate-+l+ 85.7%

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

      2. *-commutative 85.7%

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

      3. associate-*l* 81.3%

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

   3. Simplified 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-*r* 90.4%

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

      3. distribute-rgt-in 95.2%

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

      4. add-cube-cbrt 94.6%

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

      5. associate-*r* 94.5%

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

      6. cbrt-unprod 90.3%

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

      7. pow2 90.3%

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

      8. +-commutative 90.3%

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

      9. fma-def 90.3%

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

      10. +-commutative 90.3%

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

      11. fma-def 90.3%

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

   5. Applied egg-rr 90.3%

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

   6. Taylor expanded in t around inf 63.0%

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

      1. *-commutative 63.0%

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

   8. Simplified 63.0%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-148}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 0.005:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+160} \lor \neg \left(a \leq 7.6 \cdot 10^{+234}\right):\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]

Alternative 9: 74.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-14} \lor \neg \left(a \leq -5 \cdot 10^{-102} \lor \neg \left(a \leq -6.1 \cdot 10^{-118}\right) \land a \leq 0.00021\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.7e-14)
         (not (or (<= a -5e-102) (and (not (<= a -6.1e-118)) (<= a 0.00021)))))
   (* a (+ t (* z b)))
   (+ x (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.7e-14) || !((a <= -5e-102) || (!(a <= -6.1e-118) && (a <= 0.00021)))) {
		tmp = a * (t + (z * b));
	} 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 <= (-2.7d-14)) .or. (.not. (a <= (-5d-102)) .or. (.not. (a <= (-6.1d-118))) .and. (a <= 0.00021d0))) then
        tmp = a * (t + (z * b))
    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 <= -2.7e-14) || !((a <= -5e-102) || (!(a <= -6.1e-118) && (a <= 0.00021)))) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.7e-14) or not ((a <= -5e-102) or (not (a <= -6.1e-118) and (a <= 0.00021))):
		tmp = a * (t + (z * b))
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.7e-14) || !((a <= -5e-102) || (!(a <= -6.1e-118) && (a <= 0.00021))))
		tmp = Float64(a * Float64(t + Float64(z * b)));
	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 <= -2.7e-14) || ~(((a <= -5e-102) || (~((a <= -6.1e-118)) && (a <= 0.00021)))))
		tmp = a * (t + (z * b));
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.7e-14], N[Not[Or[LessEqual[a, -5e-102], And[N[Not[LessEqual[a, -6.1e-118]], $MachinePrecision], LessEqual[a, 0.00021]]]], $MachinePrecision]], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.6999999999999999e-14 or -5.00000000000000026e-102 < a < -6.09999999999999985e-118 or 2.1000000000000001e-4 < a

   1. Initial program 85.3%

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

      1. associate-+l+ 85.3%

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

      2. *-commutative 85.3%

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

      3. associate-*l* 80.1%

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

   3. Simplified 80.1%

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

      1. *-commutative 80.1%

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

      2. associate-*r* 90.5%

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

      3. distribute-rgt-in 96.5%

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

      4. add-cube-cbrt 95.8%

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

      5. associate-*r* 95.8%

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

      6. cbrt-unprod 90.2%

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

      7. pow2 90.2%

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

      8. +-commutative 90.2%

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

      9. fma-def 90.2%

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

      10. +-commutative 90.2%

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

      11. fma-def 90.2%

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

   5. Applied egg-rr 90.2%

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

   6. Taylor expanded in a around inf 77.3%

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

   if -2.6999999999999999e-14 < a < -5.00000000000000026e-102 or -6.09999999999999985e-118 < a < 2.1000000000000001e-4

   1. Initial program 98.1%

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

      1. associate-+l+ 98.1%

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

      2. *-commutative 98.1%

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

      3. associate-*l* 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in a around 0 83.2%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-14} \lor \neg \left(a \leq -5 \cdot 10^{-102} \lor \neg \left(a \leq -6.1 \cdot 10^{-118}\right) \land a \leq 0.00021\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]

Alternative 10: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + a \cdot b\right) + x\\ \mathbf{if}\;z \leq -0.0009:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+22}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+130}:\\ \;\;\;\;\left(x + z \cdot y\right) + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (+ y (* a b))) x)))
   (if (<= z -0.0009)
     t_1
     (if (<= z 2.1e+22)
       (+ x (* a (+ t (* z b))))
       (if (<= z 1.1e+130) (+ (+ x (* z y)) (* a t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (y + (a * b))) + x;
	double tmp;
	if (z <= -0.0009) {
		tmp = t_1;
	} else if (z <= 2.1e+22) {
		tmp = x + (a * (t + (z * b)));
	} else if (z <= 1.1e+130) {
		tmp = (x + (z * y)) + (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * (y + (a * b))) + x
    if (z <= (-0.0009d0)) then
        tmp = t_1
    else if (z <= 2.1d+22) then
        tmp = x + (a * (t + (z * b)))
    else if (z <= 1.1d+130) then
        tmp = (x + (z * y)) + (a * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (y + (a * b))) + x;
	double tmp;
	if (z <= -0.0009) {
		tmp = t_1;
	} else if (z <= 2.1e+22) {
		tmp = x + (a * (t + (z * b)));
	} else if (z <= 1.1e+130) {
		tmp = (x + (z * y)) + (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (y + (a * b))) + x
	tmp = 0
	if z <= -0.0009:
		tmp = t_1
	elif z <= 2.1e+22:
		tmp = x + (a * (t + (z * b)))
	elif z <= 1.1e+130:
		tmp = (x + (z * y)) + (a * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(y + Float64(a * b))) + x)
	tmp = 0.0
	if (z <= -0.0009)
		tmp = t_1;
	elseif (z <= 2.1e+22)
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	elseif (z <= 1.1e+130)
		tmp = Float64(Float64(x + Float64(z * y)) + Float64(a * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (y + (a * b))) + x;
	tmp = 0.0;
	if (z <= -0.0009)
		tmp = t_1;
	elseif (z <= 2.1e+22)
		tmp = x + (a * (t + (z * b)));
	elseif (z <= 1.1e+130)
		tmp = (x + (z * y)) + (a * t);
	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[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -0.0009], t$95$1, If[LessEqual[z, 2.1e+22], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+130], N[(N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999998e-4 or 1.09999999999999997e130 < z

   1. Initial program 83.3%

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

      1. associate-+l+ 83.3%

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

      2. *-commutative 83.3%

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

      3. associate-*l* 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in t around 0 83.1%

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

      1. +-commutative 83.1%

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

      2. associate-*r* 89.3%

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

      3. distribute-rgt-in 95.8%

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

      4. +-commutative 95.8%

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

   6. Simplified 95.8%

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

   if -8.9999999999999998e-4 < z < 2.0999999999999998e22

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. +-commutative 99.2%

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

      3. fma-def 99.2%

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

      4. associate-*l* 99.1%

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

      5. *-commutative 99.1%

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

      6. *-commutative 99.1%

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

      7. distribute-rgt-out 99.9%

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

      8. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 89.2%

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

   if 2.0999999999999998e22 < z < 1.09999999999999997e130

   1. Initial program 80.2%

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

      1. associate-+l+ 80.2%

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

      2. *-commutative 80.2%

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

      3. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in t around inf 88.0%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0009:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right) + x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+22}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+130}:\\ \;\;\;\;\left(x + z \cdot y\right) + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right) + x\\ \end{array} \]

Alternative 11: 55.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot y\\ t_2 := b \cdot \left(z \cdot a\right)\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 0.0066:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+18}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;b \leq 1.18 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z y))) (t_2 (* b (* z a))))
   (if (<= b -5.8e+26)
     t_2
     (if (<= b 0.0066)
       t_1
       (if (<= b 4.5e+18) (* a t) (if (<= b 1.18e+39) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * y);
	double t_2 = b * (z * a);
	double tmp;
	if (b <= -5.8e+26) {
		tmp = t_2;
	} else if (b <= 0.0066) {
		tmp = t_1;
	} else if (b <= 4.5e+18) {
		tmp = a * t;
	} else if (b <= 1.18e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * y)
    t_2 = b * (z * a)
    if (b <= (-5.8d+26)) then
        tmp = t_2
    else if (b <= 0.0066d0) then
        tmp = t_1
    else if (b <= 4.5d+18) then
        tmp = a * t
    else if (b <= 1.18d+39) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * y);
	double t_2 = b * (z * a);
	double tmp;
	if (b <= -5.8e+26) {
		tmp = t_2;
	} else if (b <= 0.0066) {
		tmp = t_1;
	} else if (b <= 4.5e+18) {
		tmp = a * t;
	} else if (b <= 1.18e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * y)
	t_2 = b * (z * a)
	tmp = 0
	if b <= -5.8e+26:
		tmp = t_2
	elif b <= 0.0066:
		tmp = t_1
	elif b <= 4.5e+18:
		tmp = a * t
	elif b <= 1.18e+39:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * y))
	t_2 = Float64(b * Float64(z * a))
	tmp = 0.0
	if (b <= -5.8e+26)
		tmp = t_2;
	elseif (b <= 0.0066)
		tmp = t_1;
	elseif (b <= 4.5e+18)
		tmp = Float64(a * t);
	elseif (b <= 1.18e+39)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * y);
	t_2 = b * (z * a);
	tmp = 0.0;
	if (b <= -5.8e+26)
		tmp = t_2;
	elseif (b <= 0.0066)
		tmp = t_1;
	elseif (b <= 4.5e+18)
		tmp = a * t;
	elseif (b <= 1.18e+39)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.8e+26], t$95$2, If[LessEqual[b, 0.0066], t$95$1, If[LessEqual[b, 4.5e+18], N[(a * t), $MachinePrecision], If[LessEqual[b, 1.18e+39], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.8e26 or 1.17999999999999996e39 < b

   1. Initial program 91.2%

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

      1. associate-+l+ 91.2%

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

      2. *-commutative 91.2%

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

      3. associate-*l* 76.2%

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

   3. Simplified 76.2%

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

      1. *-commutative 76.2%

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

      2. associate-*r* 83.7%

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

      3. distribute-rgt-in 88.6%

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

      4. add-cube-cbrt 88.1%

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

      5. associate-*r* 88.1%

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

      6. cbrt-unprod 74.7%

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

      7. pow2 74.7%

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

      8. +-commutative 74.7%

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

      9. fma-def 74.7%

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

      10. +-commutative 74.7%

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

      11. fma-def 74.7%

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

   5. Applied egg-rr 74.7%

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

   6. Taylor expanded in b around inf 54.1%

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

      1. associate-*r* 52.2%

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

      2. *-commutative 52.2%

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

      3. associate-*l* 56.0%

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

   8. Simplified 56.0%

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

   if -5.8e26 < b < 0.0066 or 4.5e18 < b < 1.17999999999999996e39

   1. Initial program 90.8%

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

      1. associate-+l+ 90.8%

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

      2. *-commutative 90.8%

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

      3. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in a around 0 67.7%

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

   if 0.0066 < b < 4.5e18

   1. Initial program 80.0%

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

      1. associate-+l+ 80.0%

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

      2. *-commutative 80.0%

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

      3. associate-*l* 80.0%

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

   3. Simplified 80.0%

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

      1. *-commutative 80.0%

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

      2. associate-*r* 80.0%

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

      3. distribute-rgt-in 100.0%

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

      4. add-cube-cbrt 99.4%

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

      5. associate-*r* 99.4%

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

      6. cbrt-unprod 99.7%

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

      7. pow2 99.7%

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

      8. +-commutative 99.7%

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

      9. fma-def 99.7%

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

      10. +-commutative 99.7%

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

      11. fma-def 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in t around inf 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+26}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;b \leq 0.0066:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+18}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;b \leq 1.18 \cdot 10^{+39}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \end{array} \]

Alternative 12: 82.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+115} \lor \neg \left(z \leq 1.2 \cdot 10^{+130}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.7e+115) (not (<= z 1.2e+130)))
   (* 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 <= -1.7e+115) || !(z <= 1.2e+130)) {
		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 <= (-1.7d+115)) .or. (.not. (z <= 1.2d+130))) 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 <= -1.7e+115) || !(z <= 1.2e+130)) {
		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 <= -1.7e+115) or not (z <= 1.2e+130):
		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 <= -1.7e+115) || !(z <= 1.2e+130))
		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 <= -1.7e+115) || ~((z <= 1.2e+130)))
		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, -1.7e+115], N[Not[LessEqual[z, 1.2e+130]], $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 < -1.7e115 or 1.20000000000000012e130 < z

   1. Initial program 80.7%

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

      1. associate-+l+ 80.7%

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

      2. *-commutative 80.7%

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

      3. associate-*l* 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in z around inf 92.4%

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

   if -1.7e115 < z < 1.20000000000000012e130

   1. Initial program 96.0%

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

      1. associate-+l+ 96.0%

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

      2. +-commutative 96.0%

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

      3. fma-def 96.0%

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

      4. associate-*l* 97.6%

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

      5. *-commutative 97.6%

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

      6. *-commutative 97.6%

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

      7. distribute-rgt-out 98.8%

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

      8. *-commutative 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in y around 0 83.4%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+115} \lor \neg \left(z \leq 1.2 \cdot 10^{+130}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 13: 87.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-5} \lor \neg \left(z \leq 1.25 \cdot 10^{+31}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.8e-5) (not (<= z 1.25e+31)))
   (+ (* z (+ y (* a b))) x)
   (+ x (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.8e-5) || !(z <= 1.25e+31)) {
		tmp = (z * (y + (a * b))) + x;
	} 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 <= (-4.8d-5)) .or. (.not. (z <= 1.25d+31))) then
        tmp = (z * (y + (a * b))) + x
    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 <= -4.8e-5) || !(z <= 1.25e+31)) {
		tmp = (z * (y + (a * b))) + x;
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.8e-5) or not (z <= 1.25e+31):
		tmp = (z * (y + (a * b))) + x
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.8e-5) || !(z <= 1.25e+31))
		tmp = Float64(Float64(z * Float64(y + Float64(a * b))) + x);
	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 <= -4.8e-5) || ~((z <= 1.25e+31)))
		tmp = (z * (y + (a * b))) + x;
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.8e-5], N[Not[LessEqual[z, 1.25e+31]], $MachinePrecision]], N[(N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8000000000000001e-5 or 1.25000000000000007e31 < z

   1. Initial program 83.3%

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

      1. associate-+l+ 83.3%

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

      2. *-commutative 83.3%

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

      3. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in t around 0 79.7%

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

      1. +-commutative 79.7%

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

      2. associate-*r* 85.6%

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

      3. distribute-rgt-in 91.0%

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

      4. +-commutative 91.0%

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

   6. Simplified 91.0%

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

   if -4.8000000000000001e-5 < z < 1.25000000000000007e31

   1. Initial program 98.4%

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

      1. associate-+l+ 98.4%

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

      2. +-commutative 98.4%

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

      3. fma-def 98.4%

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

      4. associate-*l* 98.3%

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

      5. *-commutative 98.3%

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

      6. *-commutative 98.3%

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

      7. distribute-rgt-out 99.9%

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

      8. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 89.4%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-5} \lor \neg \left(z \leq 1.25 \cdot 10^{+31}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 14: 74.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-15} \lor \neg \left(z \leq 6.5 \cdot 10^{-10}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2e-15) (not (<= z 6.5e-10)))
   (* z (+ y (* a b)))
   (+ x (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2e-15) || !(z <= 6.5e-10)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2d-15)) .or. (.not. (z <= 6.5d-10))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + (a * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2e-15) || !(z <= 6.5e-10)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2e-15) or not (z <= 6.5e-10):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (a * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2e-15) || !(z <= 6.5e-10))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(a * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2e-15) || ~((z <= 6.5e-10)))
		tmp = z * (y + (a * b));
	else
		tmp = x + (a * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2e-15], N[Not[LessEqual[z, 6.5e-10]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000002e-15 or 6.5000000000000003e-10 < z

   1. Initial program 84.4%

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

      1. associate-+l+ 84.4%

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

      2. *-commutative 84.4%

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

      3. associate-*l* 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in z around inf 80.6%

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

   if -2.0000000000000002e-15 < z < 6.5000000000000003e-10

   1. Initial program 99.1%

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

      1. associate-+l+ 99.1%

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

      2. *-commutative 99.1%

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

      3. associate-*l* 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in z around 0 78.9%

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

      1. +-commutative 78.9%

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

   6. Simplified 78.9%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-15} \lor \neg \left(z \leq 6.5 \cdot 10^{-10}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \]

Alternative 15: 63.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-12} \lor \neg \left(z \leq 6.6 \cdot 10^{+35}\right):\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.2e-12) (not (<= z 6.6e+35))) (+ x (* z y)) (+ x (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.2e-12) || !(z <= 6.6e+35)) {
		tmp = x + (z * y);
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-7.2d-12)) .or. (.not. (z <= 6.6d+35))) then
        tmp = x + (z * y)
    else
        tmp = x + (a * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.2e-12) || !(z <= 6.6e+35)) {
		tmp = x + (z * y);
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.2e-12) or not (z <= 6.6e+35):
		tmp = x + (z * y)
	else:
		tmp = x + (a * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.2e-12) || !(z <= 6.6e+35))
		tmp = Float64(x + Float64(z * y));
	else
		tmp = Float64(x + Float64(a * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.2e-12) || ~((z <= 6.6e+35)))
		tmp = x + (z * y);
	else
		tmp = x + (a * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.2e-12], N[Not[LessEqual[z, 6.6e+35]], $MachinePrecision]], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2e-12 or 6.6000000000000003e35 < z

   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. associate-+l+ 83.0%

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

      2. *-commutative 83.0%

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

      3. associate-*l* 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in a around 0 54.6%

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

   if -7.2e-12 < z < 6.6000000000000003e35

   1. Initial program 98.4%

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

      1. associate-+l+ 98.4%

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

      2. *-commutative 98.4%

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

      3. associate-*l* 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in z around 0 73.5%

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

      1. +-commutative 73.5%

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

   6. Simplified 73.5%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-12} \lor \neg \left(z \leq 6.6 \cdot 10^{+35}\right):\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \]

Alternative 16: 37.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+116} \lor \neg \left(a \leq 0.00185\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.4e+116) (not (<= a 0.00185))) (* a t) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.4e+116) || !(a <= 0.00185)) {
		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 <= (-3.4d+116)) .or. (.not. (a <= 0.00185d0))) 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 <= -3.4e+116) || !(a <= 0.00185)) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -3.4e+116) or not (a <= 0.00185):
		tmp = a * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3.4e+116) || !(a <= 0.00185))
		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 <= -3.4e+116) || ~((a <= 0.00185)))
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3.4e+116], N[Not[LessEqual[a, 0.00185]], $MachinePrecision]], N[(a * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -3.40000000000000023e116 or 0.0018500000000000001 < a

   1. Initial program 83.6%

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

      1. associate-+l+ 83.6%

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

      2. *-commutative 83.6%

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

      3. associate-*l* 77.1%

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

   3. Simplified 77.1%

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

      1. *-commutative 77.1%

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

      2. associate-*r* 89.1%

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

      3. distribute-rgt-in 96.6%

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

      4. add-cube-cbrt 95.9%

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

      5. associate-*r* 95.9%

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

      6. cbrt-unprod 92.0%

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

      7. pow2 92.0%

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

      8. +-commutative 92.0%

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

      9. fma-def 92.0%

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

      10. +-commutative 92.0%

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

      11. fma-def 92.0%

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

   5. Applied egg-rr 92.0%

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

   6. Taylor expanded in t around inf 43.3%

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

      1. *-commutative 43.3%

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

   8. Simplified 43.3%

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

   if -3.40000000000000023e116 < a < 0.0018500000000000001

   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. *-commutative 97.0%

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

      3. associate-*l* 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in x around inf 33.9%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+116} \lor \neg \left(a \leq 0.00185\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 26.1% 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. *-commutative 90.7%

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

   3. associate-*l* 87.7%

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

3. Simplified 87.7%

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

4. Taylor expanded in x around inf 23.4%

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

5. Final simplification 23.4%

   \[\leadsto x \]

Developer target: 97.2% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * ((b * a) + y)) + (x + (t * a))
    if (z < (-11820553527347888000.0d0)) then
        tmp = t_1
    else if (z < 4.7589743188364287d-122) then
        tmp = (((b * z) + t) * a) + ((z * y) + x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023306 
(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)))