Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.4% → 99.2%

Time: 13.5s

Alternatives: 15

Speedup: 0.7×

• 32.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.4% 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: 99.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{+87}:\\ \;\;\;\;x + \left(y \cdot z + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (+ y (* a (+ b (/ t z))))))))
   (if (<= z -1.12e-86)
     t_1
     (if (<= z 1e+87) (+ x (+ (* y z) (* a (+ t (* z b))))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y + (a * (b + (t / z)))));
	double tmp;
	if (z <= -1.12e-86) {
		tmp = t_1;
	} else if (z <= 1e+87) {
		tmp = x + ((y * z) + (a * (t + (z * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y + (a * (b + (t / z)))))
    if (z <= (-1.12d-86)) then
        tmp = t_1
    else if (z <= 1d+87) then
        tmp = x + ((y * z) + (a * (t + (z * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y + (a * (b + (t / z)))));
	double tmp;
	if (z <= -1.12e-86) {
		tmp = t_1;
	} else if (z <= 1e+87) {
		tmp = x + ((y * z) + (a * (t + (z * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (y + (a * (b + (t / z)))))
	tmp = 0
	if z <= -1.12e-86:
		tmp = t_1
	elif z <= 1e+87:
		tmp = x + ((y * z) + (a * (t + (z * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(y + Float64(a * Float64(b + Float64(t / z))))))
	tmp = 0.0
	if (z <= -1.12e-86)
		tmp = t_1;
	elseif (z <= 1e+87)
		tmp = Float64(x + Float64(Float64(y * z) + Float64(a * Float64(t + Float64(z * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (y + (a * (b + (t / z)))));
	tmp = 0.0;
	if (z <= -1.12e-86)
		tmp = t_1;
	elseif (z <= 1e+87)
		tmp = x + ((y * z) + (a * (t + (z * b))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(y + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.12e-86], t$95$1, If[LessEqual[z, 1e+87], N[(x + N[(N[(y * z), $MachinePrecision] + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12e-86 or 9.9999999999999996e86 < z

   1. Initial program 85.6%

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

   3. Taylor expanded in z around inf

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. distribute-lft-in N/A

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

      5. *-commutative N/A

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

      6. associate-*l/ N/A

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

      7. associate-/l* N/A

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

      8. *-inverses N/A

         \[\leadsto z \cdot \left(\left(y + a \cdot b\right) + \frac{a \cdot t}{z}\right) + x \cdot 1 \]

      9. *-rgt-identity N/A

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

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(y + a \cdot b\right) + \frac{a \cdot t}{z}\right)\right), \color{blue}{x}\right) \]

   5. Simplified 99.9%

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

   if -1.12e-86 < z < 9.9999999999999996e86

   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
   3. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot a + \left(a \cdot z\right) \cdot b\right) + y \cdot z\right), \color{blue}{x}\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(t \cdot a + \left(a \cdot z\right) \cdot b\right), \left(y \cdot z\right)\right), x\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t + \left(a \cdot z\right) \cdot b\right), \left(y \cdot z\right)\right), x\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t + a \cdot \left(z \cdot b\right)\right), \left(y \cdot z\right)\right), x\right) \]

      9. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(t + z \cdot b\right)\right), \left(y \cdot z\right)\right), x\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(t + z \cdot b\right)\right), \left(y \cdot z\right)\right), x\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \left(z \cdot b\right)\right)\right), \left(y \cdot z\right)\right), x\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(z, b\right)\right)\right), \left(y \cdot z\right)\right), x\right) \]

      13. *-lowering-*.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(z, b\right)\right)\right), \mathsf{*.f64}\left(y, z\right)\right), x\right) \]

   4. Applied egg-rr 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-86}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \mathbf{elif}\;z \leq 10^{+87}:\\ \;\;\;\;x + \left(y \cdot z + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot a\right) \cdot b + \left(t \cdot a + \left(x + y \cdot z\right)\right)\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* (* z a) b) (+ (* t a) (+ x (* y z))))))
   (if (<= t_1 5e+304) t_1 (+ x (* z (+ y (* a (+ b (/ t z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * a) * b) + ((t * a) + (x + (y * z)));
	double tmp;
	if (t_1 <= 5e+304) {
		tmp = t_1;
	} else {
		tmp = x + (z * (y + (a * (b + (t / z)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((z * a) * b) + ((t * a) + (x + (y * z)))
    if (t_1 <= 5d+304) then
        tmp = t_1
    else
        tmp = x + (z * (y + (a * (b + (t / z)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * a) * b) + ((t * a) + (x + (y * z)));
	double tmp;
	if (t_1 <= 5e+304) {
		tmp = t_1;
	} else {
		tmp = x + (z * (y + (a * (b + (t / z)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((z * a) * b) + ((t * a) + (x + (y * z)))
	tmp = 0
	if t_1 <= 5e+304:
		tmp = t_1
	else:
		tmp = x + (z * (y + (a * (b + (t / z)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(z * a) * b) + Float64(Float64(t * a) + Float64(x + Float64(y * z))))
	tmp = 0.0
	if (t_1 <= 5e+304)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * Float64(b + Float64(t / z))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z * a) * b) + ((t * a) + (x + (y * z)));
	tmp = 0.0;
	if (t_1 <= 5e+304)
		tmp = t_1;
	else
		tmp = x + (z * (y + (a * (b + (t / z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+304], t$95$1, N[(x + N[(z * N[(y + N[(a * N[(b + N[(t / z), $MachinePrecision]), $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)) < 4.9999999999999997e304

   1. Initial program 98.6%

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

   if 4.9999999999999997e304 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 67.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. distribute-lft-in N/A

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

      5. *-commutative N/A

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

      6. associate-*l/ N/A

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

      7. associate-/l* N/A

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

      8. *-inverses N/A

         \[\leadsto z \cdot \left(\left(y + a \cdot b\right) + \frac{a \cdot t}{z}\right) + x \cdot 1 \]

      9. *-rgt-identity N/A

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

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(y + a \cdot b\right) + \frac{a \cdot t}{z}\right)\right), \color{blue}{x}\right) \]

   5. Simplified 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot a\right) \cdot b + \left(t \cdot a + \left(x + y \cdot z\right)\right) \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(t \cdot a + \left(x + y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + a \cdot b\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+113}:\\ \;\;\;\;\frac{z}{\frac{1}{t\_1}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-13}:\\ \;\;\;\;t \cdot a + \left(x + y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+186}:\\ \;\;\;\;x + \left(y \cdot z + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* a b))))
   (if (<= z -2.6e+113)
     (/ z (/ 1.0 t_1))
     (if (<= z 8.2e-13)
       (+ (* t a) (+ x (* y z)))
       (if (<= z 3.1e+186) (+ x (+ (* y z) (* a (* z b)))) (* z t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (a * b);
	double tmp;
	if (z <= -2.6e+113) {
		tmp = z / (1.0 / t_1);
	} else if (z <= 8.2e-13) {
		tmp = (t * a) + (x + (y * z));
	} else if (z <= 3.1e+186) {
		tmp = x + ((y * z) + (a * (z * b)));
	} else {
		tmp = z * 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 = y + (a * b)
    if (z <= (-2.6d+113)) then
        tmp = z / (1.0d0 / t_1)
    else if (z <= 8.2d-13) then
        tmp = (t * a) + (x + (y * z))
    else if (z <= 3.1d+186) then
        tmp = x + ((y * z) + (a * (z * b)))
    else
        tmp = z * 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 = y + (a * b);
	double tmp;
	if (z <= -2.6e+113) {
		tmp = z / (1.0 / t_1);
	} else if (z <= 8.2e-13) {
		tmp = (t * a) + (x + (y * z));
	} else if (z <= 3.1e+186) {
		tmp = x + ((y * z) + (a * (z * b)));
	} else {
		tmp = z * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (a * b)
	tmp = 0
	if z <= -2.6e+113:
		tmp = z / (1.0 / t_1)
	elif z <= 8.2e-13:
		tmp = (t * a) + (x + (y * z))
	elif z <= 3.1e+186:
		tmp = x + ((y * z) + (a * (z * b)))
	else:
		tmp = z * t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(a * b))
	tmp = 0.0
	if (z <= -2.6e+113)
		tmp = Float64(z / Float64(1.0 / t_1));
	elseif (z <= 8.2e-13)
		tmp = Float64(Float64(t * a) + Float64(x + Float64(y * z)));
	elseif (z <= 3.1e+186)
		tmp = Float64(x + Float64(Float64(y * z) + Float64(a * Float64(z * b))));
	else
		tmp = Float64(z * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (a * b);
	tmp = 0.0;
	if (z <= -2.6e+113)
		tmp = z / (1.0 / t_1);
	elseif (z <= 8.2e-13)
		tmp = (t * a) + (x + (y * z));
	elseif (z <= 3.1e+186)
		tmp = x + ((y * z) + (a * (z * b)));
	else
		tmp = z * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+113], N[(z / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-13], N[(N[(t * a), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+186], N[(x + N[(N[(y * z), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.5999999999999999e113

   1. Initial program 81.0%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(y + a \cdot b\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

      3. *-lowering-*.f64 87.4%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 87.4%

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

      1. flip-+ N/A

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

      2. clear-num N/A

         \[\leadsto z \cdot \frac{1}{\color{blue}{\frac{y - a \cdot b}{y \cdot y - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}}} \]

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{y - a \cdot b}{y \cdot y - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}\right)}\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(z, \left(\frac{1}{\color{blue}{\frac{y \cdot y - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}{y - a \cdot b}}}\right)\right) \]

      6. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(z, \left(\frac{1}{y + \color{blue}{a \cdot b}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(1, \color{blue}{\left(y + a \cdot b\right)}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(y, \color{blue}{\left(a \cdot b\right)}\right)\right)\right) \]

      9. *-lowering-*.f64 87.5%

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right)\right) \]

   7. Applied egg-rr 87.5%

      \[\leadsto \color{blue}{\frac{z}{\frac{1}{y + a \cdot b}}} \]

   if -2.5999999999999999e113 < z < 8.2000000000000004e-13

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0

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

   5. Simplified 92.0%

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

   if 8.2000000000000004e-13 < z < 3.1000000000000001e186

   1. Initial program 89.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t \cdot a + \left(a \cdot z\right) \cdot b\right) + y \cdot z\right), \color{blue}{x}\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(t \cdot a + \left(a \cdot z\right) \cdot b\right), \left(y \cdot z\right)\right), x\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t + \left(a \cdot z\right) \cdot b\right), \left(y \cdot z\right)\right), x\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(a \cdot t + a \cdot \left(z \cdot b\right)\right), \left(y \cdot z\right)\right), x\right) \]

      9. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(a \cdot \left(t + z \cdot b\right)\right), \left(y \cdot z\right)\right), x\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(t + z \cdot b\right)\right), \left(y \cdot z\right)\right), x\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \left(z \cdot b\right)\right)\right), \left(y \cdot z\right)\right), x\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(z, b\right)\right)\right), \left(y \cdot z\right)\right), x\right) \]

      13. *-lowering-*.f64 95.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(z, b\right)\right)\right), \mathsf{*.f64}\left(y, z\right)\right), x\right) \]

   4. Applied egg-rr 95.7%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot z\right)}\right), \mathsf{*.f64}\left(y, z\right)\right), x\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(z \cdot b\right)\right), \mathsf{*.f64}\left(y, z\right)\right), x\right) \]

      2. *-lowering-*.f64 89.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(z, b\right)\right), \mathsf{*.f64}\left(y, z\right)\right), x\right) \]

   7. Simplified 89.1%

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

   if 3.1000000000000001e186 < z

   1. Initial program 78.3%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(y + a \cdot b\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

      3. *-lowering-*.f64 95.9%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 95.9%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+113}:\\ \;\;\;\;\frac{z}{\frac{1}{y + a \cdot b}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-13}:\\ \;\;\;\;t \cdot a + \left(x + y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+186}:\\ \;\;\;\;x + \left(y \cdot z + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-28}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-289}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.2e-28)
   (* y z)
   (if (<= z -2.5e-141)
     x
     (if (<= z 5.4e-289) (* t a) (if (<= z 6.8e-110) x (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.2e-28) {
		tmp = y * z;
	} else if (z <= -2.5e-141) {
		tmp = x;
	} else if (z <= 5.4e-289) {
		tmp = t * a;
	} else if (z <= 6.8e-110) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.2d-28)) then
        tmp = y * z
    else if (z <= (-2.5d-141)) then
        tmp = x
    else if (z <= 5.4d-289) then
        tmp = t * a
    else if (z <= 6.8d-110) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.2e-28) {
		tmp = y * z;
	} else if (z <= -2.5e-141) {
		tmp = x;
	} else if (z <= 5.4e-289) {
		tmp = t * a;
	} else if (z <= 6.8e-110) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.2e-28:
		tmp = y * z
	elif z <= -2.5e-141:
		tmp = x
	elif z <= 5.4e-289:
		tmp = t * a
	elif z <= 6.8e-110:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.2e-28)
		tmp = Float64(y * z);
	elseif (z <= -2.5e-141)
		tmp = x;
	elseif (z <= 5.4e-289)
		tmp = Float64(t * a);
	elseif (z <= 6.8e-110)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.2e-28)
		tmp = y * z;
	elseif (z <= -2.5e-141)
		tmp = x;
	elseif (z <= 5.4e-289)
		tmp = t * a;
	elseif (z <= 6.8e-110)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.2e-28], N[(y * z), $MachinePrecision], If[LessEqual[z, -2.5e-141], x, If[LessEqual[z, 5.4e-289], N[(t * a), $MachinePrecision], If[LessEqual[z, 6.8e-110], x, N[(y * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.20000000000000013e-28 or 6.8000000000000002e-110 < z

   1. Initial program 87.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 46.6%

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{y}\right) \]

   5. Simplified 46.6%

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

   if -4.20000000000000013e-28 < z < -2.5e-141 or 5.4e-289 < z < 6.8000000000000002e-110

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 53.5%

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

   if -2.5e-141 < z < 5.4e-289

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 57.2%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{t}\right) \]

   5. Simplified 57.2%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-28}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-289}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-110}:\\ \;\;\;\;t \cdot a + \left(x + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (+ y (* a (+ b (/ t z))))))))
   (if (<= z -1.95e-90) t_1 (if (<= z 7e-110) (+ (* t a) (+ x (* y z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y + (a * (b + (t / z)))));
	double tmp;
	if (z <= -1.95e-90) {
		tmp = t_1;
	} else if (z <= 7e-110) {
		tmp = (t * a) + (x + (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 = x + (z * (y + (a * (b + (t / z)))))
    if (z <= (-1.95d-90)) then
        tmp = t_1
    else if (z <= 7d-110) then
        tmp = (t * a) + (x + (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 = x + (z * (y + (a * (b + (t / z)))));
	double tmp;
	if (z <= -1.95e-90) {
		tmp = t_1;
	} else if (z <= 7e-110) {
		tmp = (t * a) + (x + (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (y + (a * (b + (t / z)))))
	tmp = 0
	if z <= -1.95e-90:
		tmp = t_1
	elif z <= 7e-110:
		tmp = (t * a) + (x + (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(y + Float64(a * Float64(b + Float64(t / z))))))
	tmp = 0.0
	if (z <= -1.95e-90)
		tmp = t_1;
	elseif (z <= 7e-110)
		tmp = Float64(Float64(t * a) + Float64(x + Float64(y * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (y + (a * (b + (t / z)))));
	tmp = 0.0;
	if (z <= -1.95e-90)
		tmp = t_1;
	elseif (z <= 7e-110)
		tmp = (t * a) + (x + (y * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(y + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e-90], t$95$1, If[LessEqual[z, 7e-110], N[(N[(t * a), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95000000000000002e-90 or 6.99999999999999947e-110 < z

   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. Taylor expanded in z around inf

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. distribute-lft-in N/A

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

      5. *-commutative N/A

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

      6. associate-*l/ N/A

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

      7. associate-/l* N/A

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

      8. *-inverses N/A

         \[\leadsto z \cdot \left(\left(y + a \cdot b\right) + \frac{a \cdot t}{z}\right) + x \cdot 1 \]

      9. *-rgt-identity N/A

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

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(\left(y + a \cdot b\right) + \frac{a \cdot t}{z}\right)\right), \color{blue}{x}\right) \]

   5. Simplified 98.8%

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

   if -1.95000000000000002e-90 < z < 6.99999999999999947e-110

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

   5. Simplified 97.5%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-90}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-110}:\\ \;\;\;\;t \cdot a + \left(x + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+194}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-110}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))))
   (if (<= z -1.3e+194)
     (* z (* a b))
     (if (<= z -6.2e-28) t_1 (if (<= z 6.8e-110) (+ x (* t a)) t_1)))))

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 <= -1.3e+194) {
		tmp = z * (a * b);
	} else if (z <= -6.2e-28) {
		tmp = t_1;
	} else if (z <= 6.8e-110) {
		tmp = x + (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * z)
    if (z <= (-1.3d+194)) then
        tmp = z * (a * b)
    else if (z <= (-6.2d-28)) then
        tmp = t_1
    else if (z <= 6.8d-110) then
        tmp = x + (t * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if (z <= -1.3e+194) {
		tmp = z * (a * b);
	} else if (z <= -6.2e-28) {
		tmp = t_1;
	} else if (z <= 6.8e-110) {
		tmp = x + (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	tmp = 0
	if z <= -1.3e+194:
		tmp = z * (a * b)
	elif z <= -6.2e-28:
		tmp = t_1
	elif z <= 6.8e-110:
		tmp = x + (t * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	tmp = 0.0
	if (z <= -1.3e+194)
		tmp = Float64(z * Float64(a * b));
	elseif (z <= -6.2e-28)
		tmp = t_1;
	elseif (z <= 6.8e-110)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = t_1;
	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 <= -1.3e+194)
		tmp = z * (a * b);
	elseif (z <= -6.2e-28)
		tmp = t_1;
	elseif (z <= 6.8e-110)
		tmp = x + (t * a);
	else
		tmp = t_1;
	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, -1.3e+194], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-28], t$95$1, If[LessEqual[z, 6.8e-110], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2999999999999999e194

   1. Initial program 77.3%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot z\right)}\right) \]

      2. *-lowering-*.f64 36.0%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{z}\right)\right) \]

   5. Simplified 36.0%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot b\right), \color{blue}{z}\right) \]

      3. *-lowering-*.f64 54.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, b\right), z\right) \]

   7. Applied egg-rr 54.4%

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

   if -1.2999999999999999e194 < z < -6.19999999999999984e-28 or 6.8000000000000002e-110 < z

   1. Initial program 90.2%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot z\right), \color{blue}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot y\right), x\right) \]

      4. *-lowering-*.f64 65.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, y\right), x\right) \]

   5. Simplified 65.4%

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

   if -6.19999999999999984e-28 < z < 6.8000000000000002e-110

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot t\right), \color{blue}{x}\right) \]

      3. *-lowering-*.f64 86.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), x\right) \]

   5. Simplified 86.9%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+194}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-28}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-110}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+194}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-24}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+65}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.05e+194)
   (* z (* a b))
   (if (<= z -6.5e-24) (* y z) (if (<= z 4.5e+65) (+ x (* t a)) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.05e+194) {
		tmp = z * (a * b);
	} else if (z <= -6.5e-24) {
		tmp = y * z;
	} else if (z <= 4.5e+65) {
		tmp = x + (t * a);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.05d+194)) then
        tmp = z * (a * b)
    else if (z <= (-6.5d-24)) then
        tmp = y * z
    else if (z <= 4.5d+65) then
        tmp = x + (t * a)
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.05e+194) {
		tmp = z * (a * b);
	} else if (z <= -6.5e-24) {
		tmp = y * z;
	} else if (z <= 4.5e+65) {
		tmp = x + (t * a);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.05e+194:
		tmp = z * (a * b)
	elif z <= -6.5e-24:
		tmp = y * z
	elif z <= 4.5e+65:
		tmp = x + (t * a)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.05e+194)
		tmp = Float64(z * Float64(a * b));
	elseif (z <= -6.5e-24)
		tmp = Float64(y * z);
	elseif (z <= 4.5e+65)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.05e+194)
		tmp = z * (a * b);
	elseif (z <= -6.5e-24)
		tmp = y * z;
	elseif (z <= 4.5e+65)
		tmp = x + (t * a);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.05e+194], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.5e-24], N[(y * z), $MachinePrecision], If[LessEqual[z, 4.5e+65], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000008e194

   1. Initial program 77.3%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot z\right)}\right) \]

      2. *-lowering-*.f64 36.0%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{z}\right)\right) \]

   5. Simplified 36.0%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot b\right), \color{blue}{z}\right) \]

      3. *-lowering-*.f64 54.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, b\right), z\right) \]

   7. Applied egg-rr 54.4%

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

   if -1.05000000000000008e194 < z < -6.5e-24 or 4.5e65 < z

   1. Initial program 88.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 55.9%

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{y}\right) \]

   5. Simplified 55.9%

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

   if -6.5e-24 < z < 4.5e65

   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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot t\right), \color{blue}{x}\right) \]

      3. *-lowering-*.f64 74.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), x\right) \]

   5. Simplified 74.3%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+194}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-24}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+65}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + a \cdot b\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+113}:\\ \;\;\;\;\frac{z}{\frac{1}{t\_1}}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+91}:\\ \;\;\;\;t \cdot a + \left(x + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* a b))))
   (if (<= z -2.9e+113)
     (/ z (/ 1.0 t_1))
     (if (<= z 9.6e+91) (+ (* t a) (+ x (* y z))) (* z t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (a * b);
	double tmp;
	if (z <= -2.9e+113) {
		tmp = z / (1.0 / t_1);
	} else if (z <= 9.6e+91) {
		tmp = (t * a) + (x + (y * z));
	} else {
		tmp = z * 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 = y + (a * b)
    if (z <= (-2.9d+113)) then
        tmp = z / (1.0d0 / t_1)
    else if (z <= 9.6d+91) then
        tmp = (t * a) + (x + (y * z))
    else
        tmp = z * 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 = y + (a * b);
	double tmp;
	if (z <= -2.9e+113) {
		tmp = z / (1.0 / t_1);
	} else if (z <= 9.6e+91) {
		tmp = (t * a) + (x + (y * z));
	} else {
		tmp = z * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (a * b)
	tmp = 0
	if z <= -2.9e+113:
		tmp = z / (1.0 / t_1)
	elif z <= 9.6e+91:
		tmp = (t * a) + (x + (y * z))
	else:
		tmp = z * t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(a * b))
	tmp = 0.0
	if (z <= -2.9e+113)
		tmp = Float64(z / Float64(1.0 / t_1));
	elseif (z <= 9.6e+91)
		tmp = Float64(Float64(t * a) + Float64(x + Float64(y * z)));
	else
		tmp = Float64(z * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (a * b);
	tmp = 0.0;
	if (z <= -2.9e+113)
		tmp = z / (1.0 / t_1);
	elseif (z <= 9.6e+91)
		tmp = (t * a) + (x + (y * z));
	else
		tmp = z * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+113], N[(z / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e+91], N[(N[(t * a), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.89999999999999984e113

   1. Initial program 81.0%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(y + a \cdot b\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

      3. *-lowering-*.f64 87.4%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 87.4%

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

      1. flip-+ N/A

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

      2. clear-num N/A

         \[\leadsto z \cdot \frac{1}{\color{blue}{\frac{y - a \cdot b}{y \cdot y - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}}} \]

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{y - a \cdot b}{y \cdot y - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}\right)}\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(z, \left(\frac{1}{\color{blue}{\frac{y \cdot y - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}{y - a \cdot b}}}\right)\right) \]

      6. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(z, \left(\frac{1}{y + \color{blue}{a \cdot b}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(1, \color{blue}{\left(y + a \cdot b\right)}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(y, \color{blue}{\left(a \cdot b\right)}\right)\right)\right) \]

      9. *-lowering-*.f64 87.5%

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right)\right) \]

   7. Applied egg-rr 87.5%

      \[\leadsto \color{blue}{\frac{z}{\frac{1}{y + a \cdot b}}} \]

   if -2.89999999999999984e113 < z < 9.59999999999999932e91

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0

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

   5. Simplified 89.3%

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

   if 9.59999999999999932e91 < z

   1. Initial program 80.6%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(y + a \cdot b\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

      3. *-lowering-*.f64 88.2%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 88.2%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+113}:\\ \;\;\;\;\frac{z}{\frac{1}{y + a \cdot b}}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+91}:\\ \;\;\;\;t \cdot a + \left(x + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+88}:\\ \;\;\;\;t \cdot a + \left(x + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ y (* a b)))))
   (if (<= z -1.35e+115)
     t_1
     (if (<= z 1.2e+88) (+ (* t a) (+ x (* y z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + (a * b));
	double tmp;
	if (z <= -1.35e+115) {
		tmp = t_1;
	} else if (z <= 1.2e+88) {
		tmp = (t * a) + (x + (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 * (y + (a * b))
    if (z <= (-1.35d+115)) then
        tmp = t_1
    else if (z <= 1.2d+88) then
        tmp = (t * a) + (x + (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 * (y + (a * b));
	double tmp;
	if (z <= -1.35e+115) {
		tmp = t_1;
	} else if (z <= 1.2e+88) {
		tmp = (t * a) + (x + (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (y + (a * b))
	tmp = 0
	if z <= -1.35e+115:
		tmp = t_1
	elif z <= 1.2e+88:
		tmp = (t * a) + (x + (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (z <= -1.35e+115)
		tmp = t_1;
	elseif (z <= 1.2e+88)
		tmp = Float64(Float64(t * a) + Float64(x + 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 * (y + (a * b));
	tmp = 0.0;
	if (z <= -1.35e+115)
		tmp = t_1;
	elseif (z <= 1.2e+88)
		tmp = (t * a) + (x + (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[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+115], t$95$1, If[LessEqual[z, 1.2e+88], N[(N[(t * a), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35000000000000002e115 or 1.2e88 < z

   1. Initial program 80.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(y + a \cdot b\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

      3. *-lowering-*.f64 87.8%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 87.8%

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

   if -1.35000000000000002e115 < z < 1.2e88

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0

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

   5. Simplified 89.3%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+88}:\\ \;\;\;\;t \cdot a + \left(x + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-13}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ y (* a b)))))
   (if (<= z -1.3e-24) t_1 (if (<= z 8.5e-13) (+ x (* t a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + (a * b));
	double tmp;
	if (z <= -1.3e-24) {
		tmp = t_1;
	} else if (z <= 8.5e-13) {
		tmp = x + (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y + (a * b))
    if (z <= (-1.3d-24)) then
        tmp = t_1
    else if (z <= 8.5d-13) then
        tmp = x + (t * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + (a * b));
	double tmp;
	if (z <= -1.3e-24) {
		tmp = t_1;
	} else if (z <= 8.5e-13) {
		tmp = x + (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (y + (a * b))
	tmp = 0
	if z <= -1.3e-24:
		tmp = t_1
	elif z <= 8.5e-13:
		tmp = x + (t * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (z <= -1.3e-24)
		tmp = t_1;
	elseif (z <= 8.5e-13)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (y + (a * b));
	tmp = 0.0;
	if (z <= -1.3e-24)
		tmp = t_1;
	elseif (z <= 8.5e-13)
		tmp = x + (t * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e-24], t$95$1, If[LessEqual[z, 8.5e-13], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e-24 or 8.5000000000000001e-13 < z

   1. Initial program 86.0%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(y + a \cdot b\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

      3. *-lowering-*.f64 81.4%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 81.4%

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

   if -1.3e-24 < z < 8.5000000000000001e-13

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot t\right), \color{blue}{x}\right) \]

      3. *-lowering-*.f64 80.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, t\right), x\right) \]

   5. Simplified 80.3%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-13}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-40}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -1.3e+50) t_1 (if (<= a 6.8e-40) (+ x (* y z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double tmp;
	if (a <= -1.3e+50) {
		tmp = t_1;
	} else if (a <= 6.8e-40) {
		tmp = x + (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 * (t + (z * b))
    if (a <= (-1.3d+50)) then
        tmp = t_1
    else if (a <= 6.8d-40) then
        tmp = x + (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 * (t + (z * b));
	double tmp;
	if (a <= -1.3e+50) {
		tmp = t_1;
	} else if (a <= 6.8e-40) {
		tmp = x + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	tmp = 0
	if a <= -1.3e+50:
		tmp = t_1
	elif a <= 6.8e-40:
		tmp = x + (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + Float64(z * b)))
	tmp = 0.0
	if (a <= -1.3e+50)
		tmp = t_1;
	elseif (a <= 6.8e-40)
		tmp = Float64(x + 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 * (t + (z * b));
	tmp = 0.0;
	if (a <= -1.3e+50)
		tmp = t_1;
	elseif (a <= 6.8e-40)
		tmp = x + (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[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.3e+50], t$95$1, If[LessEqual[a, 6.8e-40], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3000000000000001e50 or 6.79999999999999968e-40 < a

   1. Initial program 86.8%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(t + b \cdot z\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \color{blue}{\left(b \cdot z\right)}\right)\right) \]

      3. *-lowering-*.f64 74.1%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(b, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 74.1%

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

   if -1.3000000000000001e50 < a < 6.79999999999999968e-40

   1. Initial program 97.0%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot z\right), \color{blue}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot y\right), x\right) \]

      4. *-lowering-*.f64 81.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, y\right), x\right) \]

   5. Simplified 81.3%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+50}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-40}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+30}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6.2e+49) (* z (* a b)) (if (<= a 4.1e+30) (* y z) (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.2e+49) {
		tmp = z * (a * b);
	} else if (a <= 4.1e+30) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-6.2d+49)) then
        tmp = z * (a * b)
    else if (a <= 4.1d+30) then
        tmp = y * z
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.2e+49) {
		tmp = z * (a * b);
	} else if (a <= 4.1e+30) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -6.2e+49:
		tmp = z * (a * b)
	elif a <= 4.1e+30:
		tmp = y * z
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6.2e+49)
		tmp = Float64(z * Float64(a * b));
	elseif (a <= 4.1e+30)
		tmp = Float64(y * z);
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -6.2e+49)
		tmp = z * (a * b);
	elseif (a <= 4.1e+30)
		tmp = y * z;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6.2e+49], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.1e+30], N[(y * z), $MachinePrecision], N[(t * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.19999999999999985e49

   1. Initial program 85.0%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot z\right)}\right) \]

      2. *-lowering-*.f64 49.3%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{z}\right)\right) \]

   5. Simplified 49.3%

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot b\right), \color{blue}{z}\right) \]

      3. *-lowering-*.f64 53.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, b\right), z\right) \]

   7. Applied egg-rr 53.5%

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

   if -6.19999999999999985e49 < a < 4.10000000000000005e30

   1. Initial program 96.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 44.6%

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{y}\right) \]

   5. Simplified 44.6%

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

   if 4.10000000000000005e30 < a

   1. Initial program 86.6%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 49.8%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{t}\right) \]

   5. Simplified 49.8%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+30}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+29}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -5.5e+49) (* a (* z b)) (if (<= a 1.45e+29) (* y z) (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.5e+49) {
		tmp = a * (z * b);
	} else if (a <= 1.45e+29) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-5.5d+49)) then
        tmp = a * (z * b)
    else if (a <= 1.45d+29) then
        tmp = y * z
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.5e+49) {
		tmp = a * (z * b);
	} else if (a <= 1.45e+29) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -5.5e+49:
		tmp = a * (z * b)
	elif a <= 1.45e+29:
		tmp = y * z
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5.5e+49)
		tmp = Float64(a * Float64(z * b));
	elseif (a <= 1.45e+29)
		tmp = Float64(y * z);
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -5.5e+49)
		tmp = a * (z * b);
	elseif (a <= 1.45e+29)
		tmp = y * z;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5.5e+49], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e+29], N[(y * z), $MachinePrecision], N[(t * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.50000000000000042e49

   1. Initial program 85.0%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot z\right)}\right) \]

      2. *-lowering-*.f64 49.3%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{z}\right)\right) \]

   5. Simplified 49.3%

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

   if -5.50000000000000042e49 < a < 1.45e29

   1. Initial program 96.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 44.6%

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{y}\right) \]

   5. Simplified 44.6%

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

   if 1.45e29 < a

   1. Initial program 86.6%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 49.8%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{t}\right) \]

   5. Simplified 49.8%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+29}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 38.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+121}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -5e+121) (* t a) (if (<= a 1.65e+15) x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5e+121) {
		tmp = t * a;
	} else if (a <= 1.65e+15) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-5d+121)) then
        tmp = t * a
    else if (a <= 1.65d+15) then
        tmp = x
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5e+121) {
		tmp = t * a;
	} else if (a <= 1.65e+15) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -5e+121:
		tmp = t * a
	elif a <= 1.65e+15:
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5e+121)
		tmp = Float64(t * a);
	elseif (a <= 1.65e+15)
		tmp = x;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -5e+121)
		tmp = t * a;
	elseif (a <= 1.65e+15)
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5e+121], N[(t * a), $MachinePrecision], If[LessEqual[a, 1.65e+15], x, N[(t * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.00000000000000007e121 or 1.65e15 < a

   1. Initial program 85.9%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 47.8%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{t}\right) \]

   5. Simplified 47.8%

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

   if -5.00000000000000007e121 < a < 1.65e15

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 34.3%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+121}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 26.3% 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 92.3%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 26.8%

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

Developer Target 1: 97.3% 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 2024191 
(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)))