Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.7% → 96.7%

Time: 12.4s

Alternatives: 14

Speedup: 0.4×

• 31.8% 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: 92.7% 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: 96.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.4%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. +-commutative 0.0%

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

      3. fma-define 0.0%

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

      4. associate-*l* 26.3%

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

      5. *-commutative 26.3%

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

      6. *-commutative 26.3%

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

      7. distribute-rgt-out 68.4%

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

      8. remove-double-neg 68.4%

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

      9. *-commutative 68.4%

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

      10. distribute-lft-neg-out 68.4%

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

      11. sub-neg 68.4%

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

      12. sub-neg 68.4%

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

      13. distribute-lft-neg-in 68.4%

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

      14. remove-double-neg 68.4%

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

   3. Simplified 68.4%

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

   5. Taylor expanded in y around 0 79.4%

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

   6. Taylor expanded in b around inf 10.5%

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

      1. associate-/l* 42.1%

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

      2. distribute-lft-out 84.2%

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

   8. Simplified 84.2%

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

4. Final simplification 97.3%

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

Alternative 2: 38.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-73}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-295}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+65}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* z a) b)))
   (if (<= z -2.8e+142)
     t_1
     (if (<= z -2.9e-73)
       (* y z)
       (if (<= z -8.6e-295)
         (* t a)
         (if (<= z 4.8e-40) x (if (<= z 2.4e+65) (* y z) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * a) * b;
	double tmp;
	if (z <= -2.8e+142) {
		tmp = t_1;
	} else if (z <= -2.9e-73) {
		tmp = y * z;
	} else if (z <= -8.6e-295) {
		tmp = t * a;
	} else if (z <= 4.8e-40) {
		tmp = x;
	} else if (z <= 2.4e+65) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * a) * b
    if (z <= (-2.8d+142)) then
        tmp = t_1
    else if (z <= (-2.9d-73)) then
        tmp = y * z
    else if (z <= (-8.6d-295)) then
        tmp = t * a
    else if (z <= 4.8d-40) then
        tmp = x
    else if (z <= 2.4d+65) then
        tmp = y * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * a) * b;
	double tmp;
	if (z <= -2.8e+142) {
		tmp = t_1;
	} else if (z <= -2.9e-73) {
		tmp = y * z;
	} else if (z <= -8.6e-295) {
		tmp = t * a;
	} else if (z <= 4.8e-40) {
		tmp = x;
	} else if (z <= 2.4e+65) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * a) * b
	tmp = 0
	if z <= -2.8e+142:
		tmp = t_1
	elif z <= -2.9e-73:
		tmp = y * z
	elif z <= -8.6e-295:
		tmp = t * a
	elif z <= 4.8e-40:
		tmp = x
	elif z <= 2.4e+65:
		tmp = y * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * a) * b)
	tmp = 0.0
	if (z <= -2.8e+142)
		tmp = t_1;
	elseif (z <= -2.9e-73)
		tmp = Float64(y * z);
	elseif (z <= -8.6e-295)
		tmp = Float64(t * a);
	elseif (z <= 4.8e-40)
		tmp = x;
	elseif (z <= 2.4e+65)
		tmp = Float64(y * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * a) * b;
	tmp = 0.0;
	if (z <= -2.8e+142)
		tmp = t_1;
	elseif (z <= -2.9e-73)
		tmp = y * z;
	elseif (z <= -8.6e-295)
		tmp = t * a;
	elseif (z <= 4.8e-40)
		tmp = x;
	elseif (z <= 2.4e+65)
		tmp = y * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[z, -2.8e+142], t$95$1, If[LessEqual[z, -2.9e-73], N[(y * z), $MachinePrecision], If[LessEqual[z, -8.6e-295], N[(t * a), $MachinePrecision], If[LessEqual[z, 4.8e-40], x, If[LessEqual[z, 2.4e+65], N[(y * z), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.8e142 or 2.4000000000000002e65 < z

   1. Initial program 79.8%

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

      1. add-cube-cbrt 79.7%

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

      2. pow3 79.7%

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

      3. *-commutative 79.7%

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

   4. Applied egg-rr 79.7%

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

   5. Taylor expanded in z around inf 83.2%

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

      1. +-commutative 83.2%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in a around inf 55.7%

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

      1. associate-*r* 57.7%

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

      2. *-commutative 57.7%

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

      3. associate-*r* 56.8%

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

   10. Simplified 56.8%

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

   if -2.8e142 < z < -2.9e-73 or 4.79999999999999982e-40 < z < 2.4000000000000002e65

   1. Initial program 94.1%

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

      1. add-cube-cbrt 93.9%

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

      2. pow3 93.9%

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

      3. *-commutative 93.9%

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

   4. Applied egg-rr 93.9%

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

   5. Taylor expanded in y around inf 44.4%

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

      1. *-commutative 44.4%

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

   7. Simplified 44.4%

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

   if -2.9e-73 < z < -8.59999999999999934e-295

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 86.2%

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

   6. Taylor expanded in x around 0 54.8%

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

   if -8.59999999999999934e-295 < z < 4.79999999999999982e-40

   1. Initial program 97.8%

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

      1. associate-+l+ 97.8%

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

      2. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around 0 79.2%

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

   6. Taylor expanded in x around inf 46.2%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+142}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-73}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-295}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+65}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 37.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-73}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-296}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+64}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= z -8.8e+151)
     t_1
     (if (<= z -7.5e-73)
       (* y z)
       (if (<= z -2.5e-296)
         (* t a)
         (if (<= z 2.2e-40) x (if (<= z 8e+64) (* y z) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (z <= -8.8e+151) {
		tmp = t_1;
	} else if (z <= -7.5e-73) {
		tmp = y * z;
	} else if (z <= -2.5e-296) {
		tmp = t * a;
	} else if (z <= 2.2e-40) {
		tmp = x;
	} else if (z <= 8e+64) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (z <= (-8.8d+151)) then
        tmp = t_1
    else if (z <= (-7.5d-73)) then
        tmp = y * z
    else if (z <= (-2.5d-296)) then
        tmp = t * a
    else if (z <= 2.2d-40) then
        tmp = x
    else if (z <= 8d+64) then
        tmp = y * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (z <= -8.8e+151) {
		tmp = t_1;
	} else if (z <= -7.5e-73) {
		tmp = y * z;
	} else if (z <= -2.5e-296) {
		tmp = t * a;
	} else if (z <= 2.2e-40) {
		tmp = x;
	} else if (z <= 8e+64) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if z <= -8.8e+151:
		tmp = t_1
	elif z <= -7.5e-73:
		tmp = y * z
	elif z <= -2.5e-296:
		tmp = t * a
	elif z <= 2.2e-40:
		tmp = x
	elif z <= 8e+64:
		tmp = y * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (z <= -8.8e+151)
		tmp = t_1;
	elseif (z <= -7.5e-73)
		tmp = Float64(y * z);
	elseif (z <= -2.5e-296)
		tmp = Float64(t * a);
	elseif (z <= 2.2e-40)
		tmp = x;
	elseif (z <= 8e+64)
		tmp = Float64(y * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (z <= -8.8e+151)
		tmp = t_1;
	elseif (z <= -7.5e-73)
		tmp = y * z;
	elseif (z <= -2.5e-296)
		tmp = t * a;
	elseif (z <= 2.2e-40)
		tmp = x;
	elseif (z <= 8e+64)
		tmp = y * z;
	else
		tmp = t_1;
	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[z, -8.8e+151], t$95$1, If[LessEqual[z, -7.5e-73], N[(y * z), $MachinePrecision], If[LessEqual[z, -2.5e-296], N[(t * a), $MachinePrecision], If[LessEqual[z, 2.2e-40], x, If[LessEqual[z, 8e+64], N[(y * z), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.80000000000000027e151 or 8.00000000000000017e64 < z

   1. Initial program 79.8%

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

      1. add-cube-cbrt 79.7%

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

      2. pow3 79.7%

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

      3. *-commutative 79.7%

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

   4. Applied egg-rr 79.7%

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

   5. Taylor expanded in z around inf 83.2%

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

      1. +-commutative 83.2%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in a around inf 55.7%

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

      1. *-commutative 55.7%

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

   10. Simplified 55.7%

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

   if -8.80000000000000027e151 < z < -7.5e-73 or 2.20000000000000009e-40 < z < 8.00000000000000017e64

   1. Initial program 94.1%

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

      1. add-cube-cbrt 93.9%

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

      2. pow3 93.9%

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

      3. *-commutative 93.9%

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

   4. Applied egg-rr 93.9%

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

   5. Taylor expanded in y around inf 44.4%

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

      1. *-commutative 44.4%

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

   7. Simplified 44.4%

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

   if -7.5e-73 < z < -2.50000000000000015e-296

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 86.2%

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

   6. Taylor expanded in x around 0 54.8%

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

   if -2.50000000000000015e-296 < z < 2.20000000000000009e-40

   1. Initial program 97.8%

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

      1. associate-+l+ 97.8%

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

      2. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around 0 79.2%

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

   6. Taylor expanded in x around inf 46.2%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+151}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-73}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-296}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+64}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+151}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-6}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))))
   (if (<= z -9.6e+151)
     (* (* z a) b)
     (if (<= z -3.7e-52)
       t_1
       (if (<= z 8.5e-6)
         (+ x (* t a))
         (if (<= z 5.2e+146) t_1 (* z (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if (z <= -9.6e+151) {
		tmp = (z * a) * b;
	} else if (z <= -3.7e-52) {
		tmp = t_1;
	} else if (z <= 8.5e-6) {
		tmp = x + (t * a);
	} else if (z <= 5.2e+146) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * z)
    if (z <= (-9.6d+151)) then
        tmp = (z * a) * b
    else if (z <= (-3.7d-52)) then
        tmp = t_1
    else if (z <= 8.5d-6) then
        tmp = x + (t * a)
    else if (z <= 5.2d+146) then
        tmp = t_1
    else
        tmp = 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 t_1 = x + (y * z);
	double tmp;
	if (z <= -9.6e+151) {
		tmp = (z * a) * b;
	} else if (z <= -3.7e-52) {
		tmp = t_1;
	} else if (z <= 8.5e-6) {
		tmp = x + (t * a);
	} else if (z <= 5.2e+146) {
		tmp = t_1;
	} else {
		tmp = z * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	tmp = 0
	if z <= -9.6e+151:
		tmp = (z * a) * b
	elif z <= -3.7e-52:
		tmp = t_1
	elif z <= 8.5e-6:
		tmp = x + (t * a)
	elif z <= 5.2e+146:
		tmp = t_1
	else:
		tmp = z * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	tmp = 0.0
	if (z <= -9.6e+151)
		tmp = Float64(Float64(z * a) * b);
	elseif (z <= -3.7e-52)
		tmp = t_1;
	elseif (z <= 8.5e-6)
		tmp = Float64(x + Float64(t * a));
	elseif (z <= 5.2e+146)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * z);
	tmp = 0.0;
	if (z <= -9.6e+151)
		tmp = (z * a) * b;
	elseif (z <= -3.7e-52)
		tmp = t_1;
	elseif (z <= 8.5e-6)
		tmp = x + (t * a);
	elseif (z <= 5.2e+146)
		tmp = t_1;
	else
		tmp = z * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e+151], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[z, -3.7e-52], t$95$1, If[LessEqual[z, 8.5e-6], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+146], t$95$1, N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.6000000000000004e151

   1. Initial program 78.5%

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

      1. add-cube-cbrt 78.4%

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

      2. pow3 78.4%

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

      3. *-commutative 78.4%

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

   4. Applied egg-rr 78.4%

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

   5. Taylor expanded in z around inf 89.5%

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

      1. +-commutative 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in a around inf 65.7%

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

      1. associate-*r* 65.8%

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

      2. *-commutative 65.8%

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

      3. associate-*r* 65.8%

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

   10. Simplified 65.8%

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

   if -9.6000000000000004e151 < z < -3.6999999999999997e-52 or 8.4999999999999999e-6 < z < 5.20000000000000028e146

   1. Initial program 93.2%

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

      1. add-cube-cbrt 93.1%

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

      2. pow3 93.1%

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

      3. *-commutative 93.1%

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in a around 0 63.2%

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

   if -3.6999999999999997e-52 < z < 8.4999999999999999e-6

   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. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around 0 80.8%

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

   if 5.20000000000000028e146 < z

   1. Initial program 75.5%

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

      1. add-cube-cbrt 75.3%

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

      2. pow3 75.3%

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

      3. *-commutative 75.3%

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

   4. Applied egg-rr 75.3%

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

   5. Taylor expanded in z around inf 83.2%

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

      1. +-commutative 83.2%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in a around inf 53.7%

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

      1. associate-*r* 56.2%

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

      2. *-commutative 56.2%

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

   10. Simplified 56.2%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+151}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-52}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-6}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+146}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.48 \cdot 10^{-64}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-301}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-49}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* a b))))
   (if (<= b -3.2e+83)
     t_1
     (if (<= b -1.48e-64)
       (* y z)
       (if (<= b -6.5e-301) (* t a) (if (<= b 2.2e-49) (* y z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double tmp;
	if (b <= -3.2e+83) {
		tmp = t_1;
	} else if (b <= -1.48e-64) {
		tmp = y * z;
	} else if (b <= -6.5e-301) {
		tmp = t * a;
	} else if (b <= 2.2e-49) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (a * b)
    if (b <= (-3.2d+83)) then
        tmp = t_1
    else if (b <= (-1.48d-64)) then
        tmp = y * z
    else if (b <= (-6.5d-301)) then
        tmp = t * a
    else if (b <= 2.2d-49) then
        tmp = y * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double tmp;
	if (b <= -3.2e+83) {
		tmp = t_1;
	} else if (b <= -1.48e-64) {
		tmp = y * z;
	} else if (b <= -6.5e-301) {
		tmp = t * a;
	} else if (b <= 2.2e-49) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (a * b)
	tmp = 0
	if b <= -3.2e+83:
		tmp = t_1
	elif b <= -1.48e-64:
		tmp = y * z
	elif b <= -6.5e-301:
		tmp = t * a
	elif b <= 2.2e-49:
		tmp = y * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(a * b))
	tmp = 0.0
	if (b <= -3.2e+83)
		tmp = t_1;
	elseif (b <= -1.48e-64)
		tmp = Float64(y * z);
	elseif (b <= -6.5e-301)
		tmp = Float64(t * a);
	elseif (b <= 2.2e-49)
		tmp = Float64(y * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (a * b);
	tmp = 0.0;
	if (b <= -3.2e+83)
		tmp = t_1;
	elseif (b <= -1.48e-64)
		tmp = y * z;
	elseif (b <= -6.5e-301)
		tmp = t * a;
	elseif (b <= 2.2e-49)
		tmp = y * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e+83], t$95$1, If[LessEqual[b, -1.48e-64], N[(y * z), $MachinePrecision], If[LessEqual[b, -6.5e-301], N[(t * a), $MachinePrecision], If[LessEqual[b, 2.2e-49], N[(y * z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.1999999999999999e83 or 2.1999999999999999e-49 < b

   1. Initial program 88.4%

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

      1. add-cube-cbrt 88.2%

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

      2. pow3 88.2%

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

      3. *-commutative 88.2%

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

   4. Applied egg-rr 88.2%

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

   5. Taylor expanded in z around inf 67.6%

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

      1. +-commutative 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in a around inf 49.2%

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

      1. associate-*r* 54.2%

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

      2. *-commutative 54.2%

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

   10. Simplified 54.2%

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

   if -3.1999999999999999e83 < b < -1.48e-64 or -6.49999999999999991e-301 < b < 2.1999999999999999e-49

   1. Initial program 93.5%

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

      1. add-cube-cbrt 93.5%

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

      2. pow3 93.5%

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

      3. *-commutative 93.5%

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

   4. Applied egg-rr 93.5%

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

   5. Taylor expanded in y around inf 45.2%

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

      1. *-commutative 45.2%

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

   7. Simplified 45.2%

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

   if -1.48e-64 < b < -6.49999999999999991e-301

   1. Initial program 94.6%

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

      1. associate-+l+ 94.6%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 81.6%

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

   6. Taylor expanded in x around 0 50.3%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+83}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -1.48 \cdot 10^{-64}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-301}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-49}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+115} \lor \neg \left(b \leq 5.8 \cdot 10^{-48}\right):\\ \;\;\;\;x + b \cdot \left(a \cdot \left(z + \frac{t}{b}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.02e+115) (not (<= b 5.8e-48)))
   (+ x (* b (* a (+ z (/ t b)))))
   (+ x (+ (* t a) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.02e+115) || !(b <= 5.8e-48)) {
		tmp = x + (b * (a * (z + (t / b))));
	} else {
		tmp = x + ((t * a) + (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.02d+115)) .or. (.not. (b <= 5.8d-48))) then
        tmp = x + (b * (a * (z + (t / b))))
    else
        tmp = x + ((t * a) + (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.02e+115) || !(b <= 5.8e-48)) {
		tmp = x + (b * (a * (z + (t / b))));
	} else {
		tmp = x + ((t * a) + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.02e+115) or not (b <= 5.8e-48):
		tmp = x + (b * (a * (z + (t / b))))
	else:
		tmp = x + ((t * a) + (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.02e+115) || !(b <= 5.8e-48))
		tmp = Float64(x + Float64(b * Float64(a * Float64(z + Float64(t / b)))));
	else
		tmp = Float64(x + Float64(Float64(t * a) + Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.02e+115) || ~((b <= 5.8e-48)))
		tmp = x + (b * (a * (z + (t / b))));
	else
		tmp = x + ((t * a) + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.02e+115], N[Not[LessEqual[b, 5.8e-48]], $MachinePrecision]], N[(x + N[(b * N[(a * N[(z + N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.02e115 or 5.8000000000000006e-48 < b

   1. Initial program 87.6%

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

      1. associate-+l+ 87.6%

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

      2. +-commutative 87.6%

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

      3. fma-define 87.6%

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

      4. associate-*l* 80.5%

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

      5. *-commutative 80.5%

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

      6. *-commutative 80.5%

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

      7. distribute-rgt-out 87.1%

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

      8. remove-double-neg 87.1%

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

      9. *-commutative 87.1%

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

      10. distribute-lft-neg-out 87.1%

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

      11. sub-neg 87.1%

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

      12. sub-neg 87.1%

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

      13. distribute-lft-neg-in 87.1%

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

      14. remove-double-neg 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in y around 0 81.6%

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

   6. Taylor expanded in b around inf 77.3%

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

      1. associate-/l* 82.2%

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

      2. distribute-lft-out 85.5%

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

   8. Simplified 85.5%

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

   if -1.02e115 < b < 5.8000000000000006e-48

   1. Initial program 94.2%

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

      1. associate-+l+ 94.2%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in b around 0 95.7%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+115} \lor \neg \left(b \leq 5.8 \cdot 10^{-48}\right):\\ \;\;\;\;x + b \cdot \left(a \cdot \left(z + \frac{t}{b}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.7% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 1.7d+131) then
        tmp = (x + (y * z)) + ((a * (z * b)) + (t * a))
    else
        tmp = x + (t * (a + (a * (b * (z / t)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.7e+131) {
		tmp = (x + (y * z)) + ((a * (z * b)) + (t * a));
	} else {
		tmp = x + (t * (a + (a * (b * (z / t)))));
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if t < 1.69999999999999993e131

   1. Initial program 91.9%

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

      1. associate-+l+ 91.9%

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

      2. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   if 1.69999999999999993e131 < t

   1. Initial program 86.4%

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

      1. associate-+l+ 86.4%

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

      2. +-commutative 86.4%

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

      3. fma-define 86.4%

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

      4. associate-*l* 76.3%

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

      5. *-commutative 76.3%

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

      6. *-commutative 76.3%

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

      7. distribute-rgt-out 84.4%

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

      8. remove-double-neg 84.4%

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

      9. *-commutative 84.4%

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

      10. distribute-lft-neg-out 84.4%

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

      11. sub-neg 84.4%

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

      12. sub-neg 84.4%

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

      13. distribute-lft-neg-in 84.4%

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

      14. remove-double-neg 84.4%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in y around 0 84.8%

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

   6. Taylor expanded in t around inf 84.8%

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

      1. associate-/l* 84.8%

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

      2. associate-/l* 94.9%

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

   8. Simplified 94.9%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.7 \cdot 10^{+131}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(a \cdot \left(z \cdot b\right) + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(a + a \cdot \left(b \cdot \frac{z}{t}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{-10} \lor \neg \left(y \leq 35000\right):\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.3e-10) (not (<= y 35000.0)))
   (+ x (+ (* t a) (* 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 ((y <= -5.3e-10) || !(y <= 35000.0)) {
		tmp = x + ((t * a) + (y * z));
	} 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 ((y <= (-5.3d-10)) .or. (.not. (y <= 35000.0d0))) then
        tmp = x + ((t * a) + (y * z))
    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 ((y <= -5.3e-10) || !(y <= 35000.0)) {
		tmp = x + ((t * a) + (y * z));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.3e-10) or not (y <= 35000.0):
		tmp = x + ((t * a) + (y * z))
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.3e-10) || !(y <= 35000.0))
		tmp = Float64(x + Float64(Float64(t * a) + Float64(y * z)));
	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 ((y <= -5.3e-10) || ~((y <= 35000.0)))
		tmp = x + ((t * a) + (y * z));
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.3e-10], N[Not[LessEqual[y, 35000.0]], $MachinePrecision]], N[(x + N[(N[(t * a), $MachinePrecision] + N[(y * z), $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 y < -5.3000000000000003e-10 or 35000 < y

   1. Initial program 92.2%

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

      1. associate-+l+ 92.2%

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

      2. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in b around 0 88.6%

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

   if -5.3000000000000003e-10 < y < 35000

   1. Initial program 89.9%

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

      1. associate-+l+ 89.9%

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

      2. +-commutative 89.9%

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

      3. fma-define 89.9%

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

      4. associate-*l* 89.2%

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

      5. *-commutative 89.2%

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

      6. *-commutative 89.2%

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

      7. distribute-rgt-out 94.8%

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

      8. remove-double-neg 94.8%

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

      9. *-commutative 94.8%

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

      10. distribute-lft-neg-out 94.8%

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

      11. sub-neg 94.8%

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

      12. sub-neg 94.8%

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

      13. distribute-lft-neg-in 94.8%

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

      14. remove-double-neg 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in y around 0 91.8%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{-10} \lor \neg \left(y \leq 35000\right):\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-47} \lor \neg \left(a \leq 1.2 \cdot 10^{-149}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -8.5e-47) (not (<= a 1.2e-149)))
   (+ x (* a (+ t (* z b))))
   (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -8.5e-47) || !(a <= 1.2e-149)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-8.5d-47)) .or. (.not. (a <= 1.2d-149))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -8.5e-47) || !(a <= 1.2e-149)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -8.5e-47) or not (a <= 1.2e-149):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -8.5e-47) || !(a <= 1.2e-149))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -8.5e-47) || ~((a <= 1.2e-149)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -8.5e-47], N[Not[LessEqual[a, 1.2e-149]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.4999999999999999e-47 or 1.2000000000000001e-149 < a

   1. Initial program 87.7%

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

      1. associate-+l+ 87.7%

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

      2. +-commutative 87.7%

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

      3. fma-define 87.7%

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

      4. associate-*l* 91.4%

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

      5. *-commutative 91.4%

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

      6. *-commutative 91.4%

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

      7. distribute-rgt-out 96.4%

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

      8. remove-double-neg 96.4%

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

      9. *-commutative 96.4%

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

      10. distribute-lft-neg-out 96.4%

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

      11. sub-neg 96.4%

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

      12. sub-neg 96.4%

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

      13. distribute-lft-neg-in 96.4%

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

      14. remove-double-neg 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in y around 0 86.0%

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

   if -8.4999999999999999e-47 < a < 1.2000000000000001e-149

   1. Initial program 96.8%

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

      1. add-cube-cbrt 96.7%

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

      2. pow3 96.8%

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

      3. *-commutative 96.8%

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

   4. Applied egg-rr 96.8%

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

   5. Taylor expanded in a around 0 80.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-47} \lor \neg \left(a \leq 1.2 \cdot 10^{-149}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.55 \cdot 10^{-303}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+104}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.5e+20)
   x
   (if (<= x -2.55e-303) (* y z) (if (<= x 2.8e+104) (* t a) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.5e+20) {
		tmp = x;
	} else if (x <= -2.55e-303) {
		tmp = y * z;
	} else if (x <= 2.8e+104) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-4.5d+20)) then
        tmp = x
    else if (x <= (-2.55d-303)) then
        tmp = y * z
    else if (x <= 2.8d+104) then
        tmp = t * a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.5e+20) {
		tmp = x;
	} else if (x <= -2.55e-303) {
		tmp = y * z;
	} else if (x <= 2.8e+104) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.5e+20:
		tmp = x
	elif x <= -2.55e-303:
		tmp = y * z
	elif x <= 2.8e+104:
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.5e+20)
		tmp = x;
	elseif (x <= -2.55e-303)
		tmp = Float64(y * z);
	elseif (x <= 2.8e+104)
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.5e+20)
		tmp = x;
	elseif (x <= -2.55e-303)
		tmp = y * z;
	elseif (x <= 2.8e+104)
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.5e+20], x, If[LessEqual[x, -2.55e-303], N[(y * z), $MachinePrecision], If[LessEqual[x, 2.8e+104], N[(t * a), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5e20 or 2.8e104 < x

   1. Initial program 90.4%

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

      1. associate-+l+ 90.4%

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

      2. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in z around 0 62.2%

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

   6. Taylor expanded in x around inf 49.1%

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

   if -4.5e20 < x < -2.55e-303

   1. Initial program 94.0%

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

      1. add-cube-cbrt 93.9%

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

      2. pow3 93.9%

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

      3. *-commutative 93.9%

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

   4. Applied egg-rr 93.9%

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

   5. Taylor expanded in y around inf 42.8%

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

      1. *-commutative 42.8%

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

   7. Simplified 42.8%

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

   if -2.55e-303 < x < 2.8e104

   1. Initial program 89.6%

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

      1. associate-+l+ 89.6%

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

      2. associate-*l* 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in z around 0 44.1%

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

   6. Taylor expanded in x around 0 41.4%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.55 \cdot 10^{-303}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+104}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-36} \lor \neg \left(z \leq 0.88\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.6e-36) (not (<= z 0.88))) (* z (+ y (* a b))) (+ x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.6e-36) || !(z <= 0.88)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.6d-36)) .or. (.not. (z <= 0.88d0))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.6e-36) || !(z <= 0.88)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.6e-36) or not (z <= 0.88):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.6e-36) || !(z <= 0.88))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.6e-36) || ~((z <= 0.88)))
		tmp = z * (y + (a * b));
	else
		tmp = x + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.6e-36], N[Not[LessEqual[z, 0.88]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000011e-36 or 0.880000000000000004 < z

   1. Initial program 84.5%

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

      1. associate-+l+ 84.5%

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

      2. associate-*l* 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in z around inf 78.6%

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

   if -1.60000000000000011e-36 < z < 0.880000000000000004

   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. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around 0 80.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-36} \lor \neg \left(z \leq 0.88\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+30}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+67}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8.2e+30)
   (* (* z a) b)
   (if (<= z 6e+67) (+ x (* t a)) (* z (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.2e+30) {
		tmp = (z * a) * b;
	} else if (z <= 6e+67) {
		tmp = x + (t * a);
	} else {
		tmp = 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 (z <= (-8.2d+30)) then
        tmp = (z * a) * b
    else if (z <= 6d+67) then
        tmp = x + (t * a)
    else
        tmp = 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 (z <= -8.2e+30) {
		tmp = (z * a) * b;
	} else if (z <= 6e+67) {
		tmp = x + (t * a);
	} else {
		tmp = z * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8.2e+30:
		tmp = (z * a) * b
	elif z <= 6e+67:
		tmp = x + (t * a)
	else:
		tmp = z * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.2e+30)
		tmp = Float64(Float64(z * a) * b);
	elseif (z <= 6e+67)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = Float64(z * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8.2e+30)
		tmp = (z * a) * b;
	elseif (z <= 6e+67)
		tmp = x + (t * a);
	else
		tmp = z * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8.2e+30], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[z, 6e+67], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.20000000000000011e30

   1. Initial program 83.7%

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

      1. add-cube-cbrt 83.6%

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

      2. pow3 83.6%

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

      3. *-commutative 83.6%

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

   4. Applied egg-rr 83.6%

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

   5. Taylor expanded in z around inf 86.3%

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

      1. +-commutative 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in a around inf 52.8%

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

      1. associate-*r* 54.4%

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

      2. *-commutative 54.4%

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

      3. associate-*r* 54.4%

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

   10. Simplified 54.4%

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

   if -8.20000000000000011e30 < z < 6.0000000000000002e67

   1. Initial program 97.9%

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

      1. associate-+l+ 97.9%

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

      2. associate-*l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in z around 0 72.3%

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

   if 6.0000000000000002e67 < z

   1. Initial program 80.3%

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

      1. add-cube-cbrt 80.2%

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

      2. pow3 80.2%

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

      3. *-commutative 80.2%

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

   4. Applied egg-rr 80.2%

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

   5. Taylor expanded in z around inf 80.2%

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

      1. +-commutative 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in a around inf 49.3%

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

      1. associate-*r* 52.9%

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

      2. *-commutative 52.9%

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

   10. Simplified 52.9%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+30}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+67}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+104}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.35e-5) x (if (<= x 1.25e+104) (* t a) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.35e-5) {
		tmp = x;
	} else if (x <= 1.25e+104) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.35d-5)) then
        tmp = x
    else if (x <= 1.25d+104) then
        tmp = t * a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.35e-5) {
		tmp = x;
	} else if (x <= 1.25e+104) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.35e-5:
		tmp = x
	elif x <= 1.25e+104:
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.35e-5)
		tmp = x;
	elseif (x <= 1.25e+104)
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.35e-5)
		tmp = x;
	elseif (x <= 1.25e+104)
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.35e-5], x, If[LessEqual[x, 1.25e+104], N[(t * a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.34999999999999986e-5 or 1.2499999999999999e104 < x

   1. Initial program 90.7%

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

      1. associate-+l+ 90.7%

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

      2. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in z around 0 60.9%

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

   6. Taylor expanded in x around inf 48.3%

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

   if -2.34999999999999986e-5 < x < 1.2499999999999999e104

   1. Initial program 91.4%

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

      1. associate-+l+ 91.4%

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

      2. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in z around 0 40.2%

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

   6. Taylor expanded in x around 0 37.4%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+104}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 27.9% 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 91.1%

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

   1. associate-+l+ 91.1%

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

   2. associate-*l* 90.8%

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

3. Simplified 90.8%

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

5. Taylor expanded in z around 0 49.7%

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

6. Taylor expanded in x around inf 25.0%

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

Developer Target 1: 97.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{if}\;z < -11820553527347888000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024144 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

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

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