Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.7% → 99.9%

Time: 7.6s

Alternatives: 9

Speedup: 0.8×

• 32.0% 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: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-13}:\\ \;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ y (+ (/ x z) (* a (+ b (/ t z))))))))
   (if (<= z -2e+30)
     t_1
     (if (<= z 1e-13) (+ (* y z) (+ x (* a (+ t (* z b))))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + ((x / z) + (a * (b + (t / z)))));
	double tmp;
	if (z <= -2e+30) {
		tmp = t_1;
	} else if (z <= 1e-13) {
		tmp = (y * z) + (x + (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 = z * (y + ((x / z) + (a * (b + (t / z)))))
    if (z <= (-2d+30)) then
        tmp = t_1
    else if (z <= 1d-13) then
        tmp = (y * z) + (x + (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 = z * (y + ((x / z) + (a * (b + (t / z)))));
	double tmp;
	if (z <= -2e+30) {
		tmp = t_1;
	} else if (z <= 1e-13) {
		tmp = (y * z) + (x + (a * (t + (z * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (y + ((x / z) + (a * (b + (t / z)))))
	tmp = 0
	if z <= -2e+30:
		tmp = t_1
	elif z <= 1e-13:
		tmp = (y * z) + (x + (a * (t + (z * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y + Float64(Float64(x / z) + Float64(a * Float64(b + Float64(t / z))))))
	tmp = 0.0
	if (z <= -2e+30)
		tmp = t_1;
	elseif (z <= 1e-13)
		tmp = Float64(Float64(y * z) + Float64(x + 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 = z * (y + ((x / z) + (a * (b + (t / z)))));
	tmp = 0.0;
	if (z <= -2e+30)
		tmp = t_1;
	elseif (z <= 1e-13)
		tmp = (y * z) + (x + (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[(z * N[(y + N[(N[(x / z), $MachinePrecision] + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+30], t$95$1, If[LessEqual[z, 1e-13], N[(N[(y * z), $MachinePrecision] + N[(x + 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 < -2e30 or 1e-13 < z

   1. Initial program 84.4%

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

      1. associate-+l+ 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

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in z around inf

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

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

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

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

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

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

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

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

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

      8. associate-/l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. /-lowering-/.f64 99.9%

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

   7. Simplified 99.9%

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

   if -2e30 < z < 1e-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. 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

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 100.0%

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

   3. Simplified 100.0%

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

Alternative 2: 97.8% accurate, 0.4× speedup

Math

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

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

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 = z * (y + ((x / z) + (a * (b + (t / z)))));
	}
	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 = z * (y + ((x / z) + (a * (b + (t / z)))));
	}
	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 = z * (y + ((x / z) + (a * (b + (t / z)))))
	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(z * Float64(y + Float64(Float64(x / z) + Float64(a * Float64(b + Float64(t / z))))));
	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 = z * (y + ((x / z) + (a * (b + (t / z)))));
	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[(z * N[(y + N[(N[(x / z), $MachinePrecision] + 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)) < +inf.0

   1. Initial program 98.8%

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

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 52.9%

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

   3. Simplified 52.9%

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

   5. Taylor expanded in z around inf

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

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

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

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

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

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

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

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

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

      8. associate-/l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. /-lowering-/.f64 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 98.8%

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

Alternative 3: 39.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+35}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-113}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.1e+35)
   (* t a)
   (if (<= t 3.3e-113) (* (* z a) b) (if (<= t 1.12e+40) x (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.1e+35) {
		tmp = t * a;
	} else if (t <= 3.3e-113) {
		tmp = (z * a) * b;
	} else if (t <= 1.12e+40) {
		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 (t <= (-2.1d+35)) then
        tmp = t * a
    else if (t <= 3.3d-113) then
        tmp = (z * a) * b
    else if (t <= 1.12d+40) 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 (t <= -2.1e+35) {
		tmp = t * a;
	} else if (t <= 3.3e-113) {
		tmp = (z * a) * b;
	} else if (t <= 1.12e+40) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.1e+35:
		tmp = t * a
	elif t <= 3.3e-113:
		tmp = (z * a) * b
	elif t <= 1.12e+40:
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.1e+35)
		tmp = Float64(t * a);
	elseif (t <= 3.3e-113)
		tmp = Float64(Float64(z * a) * b);
	elseif (t <= 1.12e+40)
		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 (t <= -2.1e+35)
		tmp = t * a;
	elseif (t <= 3.3e-113)
		tmp = (z * a) * b;
	elseif (t <= 1.12e+40)
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.1e+35], N[(t * a), $MachinePrecision], If[LessEqual[t, 3.3e-113], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 1.12e+40], x, N[(t * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0999999999999999e35 or 1.12000000000000001e40 < t

   1. Initial program 91.5%

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

      1. associate-+l+ 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

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 55.2%

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

   7. Simplified 55.2%

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

   if -2.0999999999999999e35 < t < 3.3000000000000002e-113

   1. Initial program 92.1%

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

      1. associate-+l+ 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

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in b around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot z \]

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 44.5%

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

   7. Simplified 44.5%

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

   if 3.3000000000000002e-113 < t < 1.12000000000000001e40

   1. Initial program 94.4%

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

      1. associate-+l+ 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

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 45.8%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+35}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-113}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-73}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 1.24 \cdot 10^{-293}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.1e-73)
   (* t a)
   (if (<= a 1.24e-293) (* y z) (if (<= a 2.55e-26) x (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.1e-73) {
		tmp = t * a;
	} else if (a <= 1.24e-293) {
		tmp = y * z;
	} else if (a <= 2.55e-26) {
		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 <= (-3.1d-73)) then
        tmp = t * a
    else if (a <= 1.24d-293) then
        tmp = y * z
    else if (a <= 2.55d-26) 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 <= -3.1e-73) {
		tmp = t * a;
	} else if (a <= 1.24e-293) {
		tmp = y * z;
	} else if (a <= 2.55e-26) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.1e-73:
		tmp = t * a
	elif a <= 1.24e-293:
		tmp = y * z
	elif a <= 2.55e-26:
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.1e-73)
		tmp = Float64(t * a);
	elseif (a <= 1.24e-293)
		tmp = Float64(y * z);
	elseif (a <= 2.55e-26)
		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 <= -3.1e-73)
		tmp = t * a;
	elseif (a <= 1.24e-293)
		tmp = y * z;
	elseif (a <= 2.55e-26)
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.1e-73], N[(t * a), $MachinePrecision], If[LessEqual[a, 1.24e-293], N[(y * z), $MachinePrecision], If[LessEqual[a, 2.55e-26], x, N[(t * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.09999999999999969e-73 or 2.54999999999999995e-26 < 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+ 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

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 41.2%

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

   7. Simplified 41.2%

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

   if -3.09999999999999969e-73 < a < 1.24000000000000001e-293

   1. Initial program 98.1%

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

      1. associate-+l+ 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

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 51.8%

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

   7. Simplified 51.8%

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

   if 1.24000000000000001e-293 < a < 2.54999999999999995e-26

   1. Initial program 98.3%

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

      1. associate-+l+ 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

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 50.7%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-73}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 1.24 \cdot 10^{-293}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.8 \cdot 10^{+260}:\\ \;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.8e+260)
   (+ (* y z) (+ x (* a (+ t (* z b)))))
   (+ x (* (* z a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.8e+260) {
		tmp = (y * z) + (x + (a * (t + (z * b))));
	} else {
		tmp = x + ((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 (b <= 2.8d+260) then
        tmp = (y * z) + (x + (a * (t + (z * b))))
    else
        tmp = x + ((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 (b <= 2.8e+260) {
		tmp = (y * z) + (x + (a * (t + (z * b))));
	} else {
		tmp = x + ((z * a) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.8e+260:
		tmp = (y * z) + (x + (a * (t + (z * b))))
	else:
		tmp = x + ((z * a) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.8e+260)
		tmp = Float64(Float64(y * z) + Float64(x + Float64(a * Float64(t + Float64(z * b)))));
	else
		tmp = Float64(x + Float64(Float64(z * a) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.8e+260)
		tmp = (y * z) + (x + (a * (t + (z * b))));
	else
		tmp = x + ((z * a) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.8e+260], N[(N[(y * z), $MachinePrecision] + N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.7999999999999998e260

   1. Initial program 91.8%

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

      1. associate-+l+ 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

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 95.1%

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

   3. Simplified 95.1%

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

   if 2.7999999999999998e260 < b

   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 x around inf

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

   5. Simplified 100.0%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.8 \cdot 10^{+260}:\\ \;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -7.6 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+25}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -7.6e-63) t_1 (if (<= a 7e+25) (+ 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 <= -7.6e-63) {
		tmp = t_1;
	} else if (a <= 7e+25) {
		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 <= (-7.6d-63)) then
        tmp = t_1
    else if (a <= 7d+25) 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 <= -7.6e-63) {
		tmp = t_1;
	} else if (a <= 7e+25) {
		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 <= -7.6e-63:
		tmp = t_1
	elif a <= 7e+25:
		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 <= -7.6e-63)
		tmp = t_1;
	elseif (a <= 7e+25)
		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 <= -7.6e-63)
		tmp = t_1;
	elseif (a <= 7e+25)
		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, -7.6e-63], t$95$1, If[LessEqual[a, 7e+25], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.60000000000000034e-63 or 6.99999999999999999e25 < a

   1. Initial program 87.0%

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

      1. associate-+l+ 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

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(t + b \cdot z\right)} \]
   6. 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 79.4%

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

   7. Simplified 79.4%

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

   if -7.60000000000000034e-63 < a < 6.99999999999999999e25

   1. Initial program 97.6%

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

      1. associate-+l+ 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

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 77.3%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+25}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;a \leq -9.6 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+201}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* z a) b)))
   (if (<= a -9.6e+89) t_1 (if (<= a 9e+201) (+ x (* 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 (a <= -9.6e+89) {
		tmp = t_1;
	} else if (a <= 9e+201) {
		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 = (z * a) * b
    if (a <= (-9.6d+89)) then
        tmp = t_1
    else if (a <= 9d+201) 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 = (z * a) * b;
	double tmp;
	if (a <= -9.6e+89) {
		tmp = t_1;
	} else if (a <= 9e+201) {
		tmp = x + (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 a <= -9.6e+89:
		tmp = t_1
	elif a <= 9e+201:
		tmp = x + (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 (a <= -9.6e+89)
		tmp = t_1;
	elseif (a <= 9e+201)
		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 = (z * a) * b;
	tmp = 0.0;
	if (a <= -9.6e+89)
		tmp = t_1;
	elseif (a <= 9e+201)
		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[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[a, -9.6e+89], t$95$1, If[LessEqual[a, 9e+201], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -9.60000000000000018e89 or 9.0000000000000002e201 < a

   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+ 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

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in b around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(b \cdot a\right) \cdot z \]

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 56.5%

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

   7. Simplified 56.5%

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

   if -9.60000000000000018e89 < a < 9.0000000000000002e201

   1. Initial program 95.5%

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

      1. associate-+l+ 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

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 66.0%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+89}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+201}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 39.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-63}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -8e-63) (* t a) (if (<= a 3e-24) x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -8e-63) {
		tmp = t * a;
	} else if (a <= 3e-24) {
		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 <= (-8d-63)) then
        tmp = t * a
    else if (a <= 3d-24) 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 <= -8e-63) {
		tmp = t * a;
	} else if (a <= 3e-24) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -8e-63:
		tmp = t * a
	elif a <= 3e-24:
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -8e-63)
		tmp = Float64(t * a);
	elseif (a <= 3e-24)
		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 <= -8e-63)
		tmp = t * a;
	elseif (a <= 3e-24)
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -8e-63], N[(t * a), $MachinePrecision], If[LessEqual[a, 3e-24], x, N[(t * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.00000000000000053e-63 or 2.99999999999999995e-24 < a

   1. Initial program 87.3%

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

      1. associate-+l+ 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

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 41.6%

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

   7. Simplified 41.6%

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

   if -8.00000000000000053e-63 < a < 2.99999999999999995e-24

   1. Initial program 98.3%

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

      1. associate-+l+ 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

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

      3. associate-+l+ N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. distribute-lft-out N/A

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

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

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

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

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

      12. *-lowering-*.f64 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 43.3%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-63}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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 92.2%

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

   1. associate-+l+ 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

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

   3. associate-+l+ N/A

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

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

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

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

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

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

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

   7. *-commutative N/A

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

   8. associate-*l* N/A

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

   9. distribute-lft-out N/A

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

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

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

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

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

   12. *-lowering-*.f64 93.5%

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

3. Simplified 93.5%

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

5. Taylor expanded in x around inf

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

7. Simplified 26.4%

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

Developer Target 1: 97.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024145 
(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)))