Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.0% → 96.2%

Time: 10.4s

Alternatives: 11

Speedup: 0.8×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.2% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(N[(t * a), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(y * z), $MachinePrecision] + N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y + N[(a * N[(b + N[(N[(t + N[(x / a), $MachinePrecision]), $MachinePrecision] / z), $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 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 98.3%

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

   3. Simplified 98.3%

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)} \]
   4. 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 42.1%

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

   3. Simplified 42.1%

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

   5. Taylor expanded in a around inf

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

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

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

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

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

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

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

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

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

      8. /-lowering-/.f64 42.1%

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

   7. Simplified 42.1%

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

   8. Taylor expanded in z around inf

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

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

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

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

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

      3. associate-/l* N/A

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

      4. distribute-lft-out N/A

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

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

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

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

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

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

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

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

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

      9. /-lowering-/.f64 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 98.5%

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

Alternative 2: 38.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-66}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-192}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* a b))))
   (if (<= z -5.8e+249)
     t_1
     (if (<= z -3.9e-66)
       (* y z)
       (if (<= z 1.35e-192) (* t a) (if (<= z 7.5e+49) x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double tmp;
	if (z <= -5.8e+249) {
		tmp = t_1;
	} else if (z <= -3.9e-66) {
		tmp = y * z;
	} else if (z <= 1.35e-192) {
		tmp = t * a;
	} else if (z <= 7.5e+49) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (a * b)
    if (z <= (-5.8d+249)) then
        tmp = t_1
    else if (z <= (-3.9d-66)) then
        tmp = y * z
    else if (z <= 1.35d-192) then
        tmp = t * a
    else if (z <= 7.5d+49) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double tmp;
	if (z <= -5.8e+249) {
		tmp = t_1;
	} else if (z <= -3.9e-66) {
		tmp = y * z;
	} else if (z <= 1.35e-192) {
		tmp = t * a;
	} else if (z <= 7.5e+49) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (a * b)
	tmp = 0
	if z <= -5.8e+249:
		tmp = t_1
	elif z <= -3.9e-66:
		tmp = y * z
	elif z <= 1.35e-192:
		tmp = t * a
	elif z <= 7.5e+49:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(a * b))
	tmp = 0.0
	if (z <= -5.8e+249)
		tmp = t_1;
	elseif (z <= -3.9e-66)
		tmp = Float64(y * z);
	elseif (z <= 1.35e-192)
		tmp = Float64(t * a);
	elseif (z <= 7.5e+49)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (a * b);
	tmp = 0.0;
	if (z <= -5.8e+249)
		tmp = t_1;
	elseif (z <= -3.9e-66)
		tmp = y * z;
	elseif (z <= 1.35e-192)
		tmp = t * a;
	elseif (z <= 7.5e+49)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+249], t$95$1, If[LessEqual[z, -3.9e-66], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.35e-192], N[(t * a), $MachinePrecision], If[LessEqual[z, 7.5e+49], x, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.80000000000000034e249 or 7.4999999999999995e49 < z

   1. Initial program 72.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in 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

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

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

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

      4. *-lowering-*.f64 56.5%

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

   7. Simplified 56.5%

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

   if -5.80000000000000034e249 < z < -3.89999999999999983e-66

   1. Initial program 81.5%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in 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 39.2%

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

   7. Simplified 39.2%

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

   if -3.89999999999999983e-66 < z < 1.34999999999999996e-192

   1. Initial program 99.9%

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

      1. associate-+l+ 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 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 49.0%

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

   7. Simplified 49.0%

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

   if 1.34999999999999996e-192 < z < 7.4999999999999995e49

   1. Initial program 100.0%

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

      1. associate-+l+ 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

   5. Taylor expanded in x around inf

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

   7. Simplified 46.9%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+249}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-66}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-192}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 39.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-25}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-113}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-286}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-14}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.4e-25)
   (* t a)
   (if (<= t -1.2e-113)
     (* y z)
     (if (<= t 4.1e-286) x (if (<= t 1.15e-14) (* y z) (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.4e-25) {
		tmp = t * a;
	} else if (t <= -1.2e-113) {
		tmp = y * z;
	} else if (t <= 4.1e-286) {
		tmp = x;
	} else if (t <= 1.15e-14) {
		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 (t <= (-1.4d-25)) then
        tmp = t * a
    else if (t <= (-1.2d-113)) then
        tmp = y * z
    else if (t <= 4.1d-286) then
        tmp = x
    else if (t <= 1.15d-14) 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 (t <= -1.4e-25) {
		tmp = t * a;
	} else if (t <= -1.2e-113) {
		tmp = y * z;
	} else if (t <= 4.1e-286) {
		tmp = x;
	} else if (t <= 1.15e-14) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.4e-25:
		tmp = t * a
	elif t <= -1.2e-113:
		tmp = y * z
	elif t <= 4.1e-286:
		tmp = x
	elif t <= 1.15e-14:
		tmp = y * z
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.4e-25)
		tmp = Float64(t * a);
	elseif (t <= -1.2e-113)
		tmp = Float64(y * z);
	elseif (t <= 4.1e-286)
		tmp = x;
	elseif (t <= 1.15e-14)
		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 (t <= -1.4e-25)
		tmp = t * a;
	elseif (t <= -1.2e-113)
		tmp = y * z;
	elseif (t <= 4.1e-286)
		tmp = x;
	elseif (t <= 1.15e-14)
		tmp = y * z;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.4e-25], N[(t * a), $MachinePrecision], If[LessEqual[t, -1.2e-113], N[(y * z), $MachinePrecision], If[LessEqual[t, 4.1e-286], x, If[LessEqual[t, 1.15e-14], N[(y * z), $MachinePrecision], N[(t * a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.39999999999999994e-25 or 1.14999999999999999e-14 < t

   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 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 51.7%

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

   7. Simplified 51.7%

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

   if -1.39999999999999994e-25 < t < -1.20000000000000006e-113 or 4.1e-286 < t < 1.14999999999999999e-14

   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 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 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 41.5%

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

   7. Simplified 41.5%

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

   if -1.20000000000000006e-113 < t < 4.1e-286

   1. Initial program 85.5%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 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 49.1%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-25}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-113}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-286}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-14}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + a \cdot b\right) + t \cdot a\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+39}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (+ y (* a b))) (* t a))))
   (if (<= z -4.6e-72) t_1 (if (<= z 1.2e+39) (+ 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))) + (t * a);
	double tmp;
	if (z <= -4.6e-72) {
		tmp = t_1;
	} else if (z <= 1.2e+39) {
		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))) + (t * a)
    if (z <= (-4.6d-72)) then
        tmp = t_1
    else if (z <= 1.2d+39) 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))) + (t * a);
	double tmp;
	if (z <= -4.6e-72) {
		tmp = t_1;
	} else if (z <= 1.2e+39) {
		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))) + (t * a)
	tmp = 0
	if z <= -4.6e-72:
		tmp = t_1
	elif z <= 1.2e+39:
		tmp = x + (t * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(y + Float64(a * b))) + Float64(t * a))
	tmp = 0.0
	if (z <= -4.6e-72)
		tmp = t_1;
	elseif (z <= 1.2e+39)
		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))) + (t * a);
	tmp = 0.0;
	if (z <= -4.6e-72)
		tmp = t_1;
	elseif (z <= 1.2e+39)
		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[(N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e-72], t$95$1, If[LessEqual[z, 1.2e+39], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.59999999999999989e-72 or 1.2e39 < z

   1. Initial program 77.1%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in x around 0

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

      1. distribute-lft-in N/A

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

      2. associate-+r+ N/A

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

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

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

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

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

      5. +-commutative N/A

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

      6. associate-*r* N/A

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

      7. distribute-rgt-in N/A

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

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

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

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

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

      10. *-lowering-*.f64 85.1%

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

   7. Simplified 85.1%

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

   if -4.59999999999999989e-72 < z < 1.2e39

   1. Initial program 99.9%

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

      1. associate-+l+ 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 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0

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

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

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

      2. *-lowering-*.f64 79.6%

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

   7. Simplified 79.6%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right) + t \cdot a\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+39}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right) + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-93}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+89}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* a b))))
   (if (<= z -6.5e+249)
     t_1
     (if (<= z -3.7e-93)
       (+ x (* y z))
       (if (<= z 4.7e+89) (+ x (* t a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double tmp;
	if (z <= -6.5e+249) {
		tmp = t_1;
	} else if (z <= -3.7e-93) {
		tmp = x + (y * z);
	} else if (z <= 4.7e+89) {
		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 * (a * b)
    if (z <= (-6.5d+249)) then
        tmp = t_1
    else if (z <= (-3.7d-93)) then
        tmp = x + (y * z)
    else if (z <= 4.7d+89) 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 * (a * b);
	double tmp;
	if (z <= -6.5e+249) {
		tmp = t_1;
	} else if (z <= -3.7e-93) {
		tmp = x + (y * z);
	} else if (z <= 4.7e+89) {
		tmp = x + (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (a * b)
	tmp = 0
	if z <= -6.5e+249:
		tmp = t_1
	elif z <= -3.7e-93:
		tmp = x + (y * z)
	elif z <= 4.7e+89:
		tmp = x + (t * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(a * b))
	tmp = 0.0
	if (z <= -6.5e+249)
		tmp = t_1;
	elseif (z <= -3.7e-93)
		tmp = Float64(x + Float64(y * z));
	elseif (z <= 4.7e+89)
		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 * (a * b);
	tmp = 0.0;
	if (z <= -6.5e+249)
		tmp = t_1;
	elseif (z <= -3.7e-93)
		tmp = x + (y * z);
	elseif (z <= 4.7e+89)
		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[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+249], t$95$1, If[LessEqual[z, -3.7e-93], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e+89], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.50000000000000028e249 or 4.70000000000000022e89 < z

   1. Initial program 70.8%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in 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

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

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

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

      4. *-lowering-*.f64 58.8%

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

   7. Simplified 58.8%

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

   if -6.50000000000000028e249 < z < -3.70000000000000002e-93

   1. Initial program 82.6%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 57.3%

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

   if -3.70000000000000002e-93 < z < 4.70000000000000022e89

   1. Initial program 99.2%

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

      1. associate-+l+ 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 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0

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

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

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

      2. *-lowering-*.f64 77.3%

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

   7. Simplified 77.3%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+249}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-93}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+89}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+110}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+91}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* a b))))
   (if (<= z -1.5e+250)
     t_1
     (if (<= z -7e+110) (* y z) (if (<= z 7.8e+91) (+ x (* t a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double tmp;
	if (z <= -1.5e+250) {
		tmp = t_1;
	} else if (z <= -7e+110) {
		tmp = y * z;
	} else if (z <= 7.8e+91) {
		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 * (a * b)
    if (z <= (-1.5d+250)) then
        tmp = t_1
    else if (z <= (-7d+110)) then
        tmp = y * z
    else if (z <= 7.8d+91) 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 * (a * b);
	double tmp;
	if (z <= -1.5e+250) {
		tmp = t_1;
	} else if (z <= -7e+110) {
		tmp = y * z;
	} else if (z <= 7.8e+91) {
		tmp = x + (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (a * b)
	tmp = 0
	if z <= -1.5e+250:
		tmp = t_1
	elif z <= -7e+110:
		tmp = y * z
	elif z <= 7.8e+91:
		tmp = x + (t * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(a * b))
	tmp = 0.0
	if (z <= -1.5e+250)
		tmp = t_1;
	elseif (z <= -7e+110)
		tmp = Float64(y * z);
	elseif (z <= 7.8e+91)
		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 * (a * b);
	tmp = 0.0;
	if (z <= -1.5e+250)
		tmp = t_1;
	elseif (z <= -7e+110)
		tmp = y * z;
	elseif (z <= 7.8e+91)
		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[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+250], t$95$1, If[LessEqual[z, -7e+110], N[(y * z), $MachinePrecision], If[LessEqual[z, 7.8e+91], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.49999999999999988e250 or 7.79999999999999935e91 < z

   1. Initial program 70.8%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 82.9%

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

   3. Simplified 82.9%

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

   5. Taylor expanded in 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

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

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

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

      4. *-lowering-*.f64 58.8%

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

   7. Simplified 58.8%

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

   if -1.49999999999999988e250 < z < -6.9999999999999998e110

   1. Initial program 68.3%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in 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 46.6%

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

   7. Simplified 46.6%

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

   if -6.9999999999999998e110 < z < 7.79999999999999935e91

   1. Initial program 98.2%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0

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

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

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

      2. *-lowering-*.f64 69.6%

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

   7. Simplified 69.6%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+250}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+110}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+91}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 94.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+237}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.35e+237)
   (* z (+ y (* a b)))
   (+ (* y z) (+ x (* a (+ t (* z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.35e+237) {
		tmp = z * (y + (a * b));
	} else {
		tmp = (y * z) + (x + (a * (t + (z * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.35d+237)) then
        tmp = z * (y + (a * b))
    else
        tmp = (y * z) + (x + (a * (t + (z * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.35e+237) {
		tmp = z * (y + (a * b));
	} else {
		tmp = (y * z) + (x + (a * (t + (z * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.35e+237:
		tmp = z * (y + (a * b))
	else:
		tmp = (y * z) + (x + (a * (t + (z * b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.35e+237)
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(Float64(y * z) + Float64(x + Float64(a * Float64(t + Float64(z * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.35e+237)
		tmp = z * (y + (a * b));
	else
		tmp = (y * z) + (x + (a * (t + (z * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.35e+237], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] + N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e237

   1. Initial program 38.9%

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

      1. associate-+l+ 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 53.8%

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

   3. Simplified 53.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(y + a \cdot b\right)} \]
   6. 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 92.4%

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

   7. Simplified 92.4%

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

   if -1.35e237 < z

   1. Initial program 91.1%

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

      1. associate-+l+ 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 96.3%

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

   3. Simplified 96.3%

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

Alternative 8: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -1.96 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+39}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ y (* a b)))))
   (if (<= z -1.96e-47) t_1 (if (<= z 1.2e+39) (+ 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 <= -1.96e-47) {
		tmp = t_1;
	} else if (z <= 1.2e+39) {
		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 <= (-1.96d-47)) then
        tmp = t_1
    else if (z <= 1.2d+39) 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 <= -1.96e-47) {
		tmp = t_1;
	} else if (z <= 1.2e+39) {
		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 <= -1.96e-47:
		tmp = t_1
	elif z <= 1.2e+39:
		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 <= -1.96e-47)
		tmp = t_1;
	elseif (z <= 1.2e+39)
		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 <= -1.96e-47)
		tmp = t_1;
	elseif (z <= 1.2e+39)
		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, -1.96e-47], t$95$1, If[LessEqual[z, 1.2e+39], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9600000000000001e-47 or 1.2e39 < z

   1. Initial program 76.6%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(y + a \cdot b\right)} \]
   6. 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 77.5%

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

   7. Simplified 77.5%

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

   if -1.9600000000000001e-47 < z < 1.2e39

   1. Initial program 99.9%

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

      1. associate-+l+ 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 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0

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

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

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

      2. *-lowering-*.f64 79.4%

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

   7. Simplified 79.4%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.96 \cdot 10^{-47}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+39}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+44}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -3.5e-66) t_1 (if (<= a 2e+44) (+ 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 <= -3.5e-66) {
		tmp = t_1;
	} else if (a <= 2e+44) {
		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 <= (-3.5d-66)) then
        tmp = t_1
    else if (a <= 2d+44) 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 <= -3.5e-66) {
		tmp = t_1;
	} else if (a <= 2e+44) {
		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 <= -3.5e-66:
		tmp = t_1
	elif a <= 2e+44:
		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 <= -3.5e-66)
		tmp = t_1;
	elseif (a <= 2e+44)
		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 <= -3.5e-66)
		tmp = t_1;
	elseif (a <= 2e+44)
		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, -3.5e-66], t$95$1, If[LessEqual[a, 2e+44], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.5e-66 or 2.0000000000000002e44 < a

   1. Initial program 77.9%

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

      1. associate-+l+ 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 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in 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 76.6%

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

   7. Simplified 76.6%

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

   if -3.5e-66 < a < 2.0000000000000002e44

   1. Initial program 99.2%

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

      1. associate-+l+ 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 x around inf

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

   7. Simplified 73.8%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-66}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+44}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-77}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.3e-77) (* t a) (if (<= t 6e+63) x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.3e-77) {
		tmp = t * a;
	} else if (t <= 6e+63) {
		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 <= (-1.3d-77)) then
        tmp = t * a
    else if (t <= 6d+63) 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 <= -1.3e-77) {
		tmp = t * a;
	} else if (t <= 6e+63) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.3e-77:
		tmp = t * a
	elif t <= 6e+63:
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.3e-77)
		tmp = Float64(t * a);
	elseif (t <= 6e+63)
		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 <= -1.3e-77)
		tmp = t * a;
	elseif (t <= 6e+63)
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.3e-77], N[(t * a), $MachinePrecision], If[LessEqual[t, 6e+63], x, N[(t * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3000000000000001e-77 or 5.99999999999999998e63 < t

   1. Initial program 87.4%

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

      1. associate-+l+ 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 50.7%

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

   7. Simplified 50.7%

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

   if -1.3000000000000001e-77 < t < 5.99999999999999998e63

   1. Initial program 89.3%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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 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 32.7%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-77}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 25.7% 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 88.5%

   \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
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 94.2%

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

3. Simplified 94.2%

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

5. Taylor expanded in x around inf

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

7. Simplified 25.5%

   \[\leadsto \color{blue}{x} \]
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 2024152 
(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)))