Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.2% → 96.7%

Time: 8.9s

Alternatives: 17

Speedup: 0.8×

• 33.7% 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: 92.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.7% accurate, 0.0× speedup

Math

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

FPCore

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

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 = fma((z * a), b, fma(a, t, fma(z, y, x)));
	} else {
		tmp = z * (y + (a * b));
	}
	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 = fma(Float64(z * a), b, fma(a, t, fma(z, y, x)));
	else
		tmp = Float64(z * Float64(y + Float64(a * b)));
	end
	return 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[(z * a), $MachinePrecision] * b + N[(a * t + N[(z * y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.8%

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

      1. associate-+l+ 98.8%

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

      2. associate-*l* 96.9%

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

   3. Simplified 96.9%

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

      1. associate-+r+ 96.9%

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

      2. +-commutative 96.9%

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

      3. associate-*r* 98.8%

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

      4. fma-def 98.8%

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

      5. +-commutative 98.8%

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

      6. *-commutative 98.8%

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

      7. fma-def 98.8%

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

      8. +-commutative 98.8%

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

      9. *-commutative 98.8%

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

      10. fma-def 98.8%

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

   5. Applied egg-rr 98.8%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. associate-*l* 11.1%

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

   3. Simplified 11.1%

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

   4. Taylor expanded in z around inf 88.9%

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

4. Final simplification 98.5%

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

Alternative 2: 96.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.8%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. associate-*l* 11.1%

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

   3. Simplified 11.1%

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

   4. Taylor expanded in z around inf 88.9%

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

4. Final simplification 98.4%

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

Alternative 3: 73.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -41000000000 \lor \neg \left(z \leq -2.05 \cdot 10^{-60}\right) \land \left(z \leq -5.4 \cdot 10^{-95} \lor \neg \left(z \leq 1.5 \cdot 10^{-55}\right) \land \left(z \leq 9.2 \cdot 10^{+34} \lor \neg \left(z \leq 2.35 \cdot 10^{+67}\right)\right)\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -41000000000.0)
         (and (not (<= z -2.05e-60))
              (or (<= z -5.4e-95)
                  (and (not (<= z 1.5e-55))
                       (or (<= z 9.2e+34) (not (<= z 2.35e+67)))))))
   (* z (+ y (* a b)))
   (+ x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -41000000000.0) || (!(z <= -2.05e-60) && ((z <= -5.4e-95) || (!(z <= 1.5e-55) && ((z <= 9.2e+34) || !(z <= 2.35e+67)))))) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-41000000000.0d0)) .or. (.not. (z <= (-2.05d-60))) .and. (z <= (-5.4d-95)) .or. (.not. (z <= 1.5d-55)) .and. (z <= 9.2d+34) .or. (.not. (z <= 2.35d+67))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -41000000000.0) || (!(z <= -2.05e-60) && ((z <= -5.4e-95) || (!(z <= 1.5e-55) && ((z <= 9.2e+34) || !(z <= 2.35e+67)))))) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -41000000000.0) or (not (z <= -2.05e-60) and ((z <= -5.4e-95) or (not (z <= 1.5e-55) and ((z <= 9.2e+34) or not (z <= 2.35e+67))))):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -41000000000.0) || (!(z <= -2.05e-60) && ((z <= -5.4e-95) || (!(z <= 1.5e-55) && ((z <= 9.2e+34) || !(z <= 2.35e+67))))))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -41000000000.0) || (~((z <= -2.05e-60)) && ((z <= -5.4e-95) || (~((z <= 1.5e-55)) && ((z <= 9.2e+34) || ~((z <= 2.35e+67)))))))
		tmp = z * (y + (a * b));
	else
		tmp = x + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -41000000000.0], And[N[Not[LessEqual[z, -2.05e-60]], $MachinePrecision], Or[LessEqual[z, -5.4e-95], And[N[Not[LessEqual[z, 1.5e-55]], $MachinePrecision], Or[LessEqual[z, 9.2e+34], N[Not[LessEqual[z, 2.35e+67]], $MachinePrecision]]]]]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1e10 or -2.05000000000000006e-60 < z < -5.4e-95 or 1.50000000000000008e-55 < z < 9.1999999999999993e34 or 2.35000000000000009e67 < 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+ 91.1%

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

      2. associate-*l* 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in z around inf 78.3%

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

   if -4.1e10 < z < -2.05000000000000006e-60 or -5.4e-95 < z < 1.50000000000000008e-55 or 9.1999999999999993e34 < z < 2.35000000000000009e67

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-*l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 84.4%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -41000000000 \lor \neg \left(z \leq -2.05 \cdot 10^{-60}\right) \land \left(z \leq -5.4 \cdot 10^{-95} \lor \neg \left(z \leq 1.5 \cdot 10^{-55}\right) \land \left(z \leq 9.2 \cdot 10^{+34} \lor \neg \left(z \leq 2.35 \cdot 10^{+67}\right)\right)\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]

Alternative 4: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -380000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-57}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+42}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(y \cdot z + t \cdot a\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+112}:\\ \;\;\;\;y \cdot z + \left(x + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (+ y (* a b))))))
   (if (<= z -380000000000.0)
     t_1
     (if (<= z 1.52e-57)
       (+ x (* a (+ t (* z b))))
       (if (<= z 5e+42)
         (+ (* (* z a) b) (+ (* y z) (* t a)))
         (if (<= z 1.15e+112) (+ (* y z) (+ x (* t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y + (a * b)));
	double tmp;
	if (z <= -380000000000.0) {
		tmp = t_1;
	} else if (z <= 1.52e-57) {
		tmp = x + (a * (t + (z * b)));
	} else if (z <= 5e+42) {
		tmp = ((z * a) * b) + ((y * z) + (t * a));
	} else if (z <= 1.15e+112) {
		tmp = (y * z) + (x + (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y + (a * b)))
    if (z <= (-380000000000.0d0)) then
        tmp = t_1
    else if (z <= 1.52d-57) then
        tmp = x + (a * (t + (z * b)))
    else if (z <= 5d+42) then
        tmp = ((z * a) * b) + ((y * z) + (t * a))
    else if (z <= 1.15d+112) then
        tmp = (y * z) + (x + (t * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y + (a * b)));
	double tmp;
	if (z <= -380000000000.0) {
		tmp = t_1;
	} else if (z <= 1.52e-57) {
		tmp = x + (a * (t + (z * b)));
	} else if (z <= 5e+42) {
		tmp = ((z * a) * b) + ((y * z) + (t * a));
	} else if (z <= 1.15e+112) {
		tmp = (y * z) + (x + (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (y + (a * b)))
	tmp = 0
	if z <= -380000000000.0:
		tmp = t_1
	elif z <= 1.52e-57:
		tmp = x + (a * (t + (z * b)))
	elif z <= 5e+42:
		tmp = ((z * a) * b) + ((y * z) + (t * a))
	elif z <= 1.15e+112:
		tmp = (y * z) + (x + (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(y + Float64(a * b))))
	tmp = 0.0
	if (z <= -380000000000.0)
		tmp = t_1;
	elseif (z <= 1.52e-57)
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	elseif (z <= 5e+42)
		tmp = Float64(Float64(Float64(z * a) * b) + Float64(Float64(y * z) + Float64(t * a)));
	elseif (z <= 1.15e+112)
		tmp = Float64(Float64(y * z) + Float64(x + Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (y + (a * b)));
	tmp = 0.0;
	if (z <= -380000000000.0)
		tmp = t_1;
	elseif (z <= 1.52e-57)
		tmp = x + (a * (t + (z * b)));
	elseif (z <= 5e+42)
		tmp = ((z * a) * b) + ((y * z) + (t * a));
	elseif (z <= 1.15e+112)
		tmp = (y * z) + (x + (t * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -380000000000.0], t$95$1, If[LessEqual[z, 1.52e-57], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+42], N[(N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+112], N[(N[(y * z), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.8e11 or 1.15e112 < z

   1. Initial program 88.1%

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

      1. +-commutative 88.1%

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

      2. +-commutative 88.1%

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

      3. associate-+l+ 88.1%

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

      4. associate-+r+ 88.1%

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

      5. *-commutative 88.1%

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

      6. associate-*l* 91.1%

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

      7. *-commutative 91.1%

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

      8. distribute-lft-out 95.5%

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

      9. fma-def 95.5%

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

      10. fma-def 95.5%

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

      11. +-commutative 95.5%

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

      12. fma-def 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around 0 92.4%

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

   if -3.8e11 < z < 1.5199999999999999e-57

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-*l* 99.9%

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

      5. distribute-lft-out 99.9%

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

      6. fma-def 99.9%

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

      7. +-commutative 99.9%

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

      8. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 91.9%

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

   if 1.5199999999999999e-57 < z < 5.00000000000000007e42

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 93.6%

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

   if 5.00000000000000007e42 < z < 1.15e112

   1. Initial program 95.2%

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

      1. associate-+l+ 95.2%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in b around 0 91.2%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -380000000000:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-57}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+42}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(y \cdot z + t \cdot a\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+112}:\\ \;\;\;\;y \cdot z + \left(x + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \]

Alternative 5: 95.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+93} \lor \neg \left(z \leq 2 \cdot 10^{+111}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(z \cdot b\right) + t \cdot a\right) + \left(x + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.2e+93) (not (<= z 2e+111)))
   (+ x (* z (+ y (* a b))))
   (+ (+ (* a (* z b)) (* t a)) (+ x (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.2e+93) || !(z <= 2e+111)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = ((a * (z * b)) + (t * a)) + (x + (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-9.2d+93)) .or. (.not. (z <= 2d+111))) then
        tmp = x + (z * (y + (a * b)))
    else
        tmp = ((a * (z * b)) + (t * a)) + (x + (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.2e+93) || !(z <= 2e+111)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = ((a * (z * b)) + (t * a)) + (x + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.2e+93) or not (z <= 2e+111):
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = ((a * (z * b)) + (t * a)) + (x + (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.2e+93) || !(z <= 2e+111))
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	else
		tmp = Float64(Float64(Float64(a * Float64(z * b)) + Float64(t * a)) + Float64(x + Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.2e+93) || ~((z <= 2e+111)))
		tmp = x + (z * (y + (a * b)));
	else
		tmp = ((a * (z * b)) + (t * a)) + (x + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.2e+93], N[Not[LessEqual[z, 2e+111]], $MachinePrecision]], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.2000000000000006e93 or 1.99999999999999991e111 < z

   1. Initial program 86.1%

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

      1. +-commutative 86.1%

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

      2. +-commutative 86.1%

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

      3. associate-+l+ 86.1%

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

      4. associate-+r+ 86.1%

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

      5. *-commutative 86.1%

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

      6. associate-*l* 89.6%

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

      7. *-commutative 89.6%

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

      8. distribute-lft-out 94.7%

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

      9. fma-def 94.8%

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

      10. fma-def 94.8%

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

      11. +-commutative 94.8%

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

      12. fma-def 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in t around 0 93.7%

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

   if -9.2000000000000006e93 < z < 1.99999999999999991e111

   1. Initial program 99.4%

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

      1. associate-+l+ 99.4%

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

      2. associate-*l* 99.4%

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

   3. Simplified 99.4%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+93} \lor \neg \left(z \leq 2 \cdot 10^{+111}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(z \cdot b\right) + t \cdot a\right) + \left(x + y \cdot z\right)\\ \end{array} \]

Alternative 6: 74.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.4 \cdot 10^{-27} \lor \neg \left(a \leq 2.45 \cdot 10^{-42}\right) \land \left(a \leq 5400000 \lor \neg \left(a \leq 1.2 \cdot 10^{+70}\right)\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -9.4e-27)
         (and (not (<= a 2.45e-42))
              (or (<= a 5400000.0) (not (<= a 1.2e+70)))))
   (* a (+ t (* z b)))
   (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -9.4e-27) || (!(a <= 2.45e-42) && ((a <= 5400000.0) || !(a <= 1.2e+70)))) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-9.4d-27)) .or. (.not. (a <= 2.45d-42)) .and. (a <= 5400000.0d0) .or. (.not. (a <= 1.2d+70))) then
        tmp = a * (t + (z * b))
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -9.4e-27) || (!(a <= 2.45e-42) && ((a <= 5400000.0) || !(a <= 1.2e+70)))) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -9.4e-27) or (not (a <= 2.45e-42) and ((a <= 5400000.0) or not (a <= 1.2e+70))):
		tmp = a * (t + (z * b))
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -9.4e-27) || (!(a <= 2.45e-42) && ((a <= 5400000.0) || !(a <= 1.2e+70))))
		tmp = Float64(a * Float64(t + Float64(z * b)));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -9.4e-27) || (~((a <= 2.45e-42)) && ((a <= 5400000.0) || ~((a <= 1.2e+70)))))
		tmp = a * (t + (z * b));
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -9.4e-27], And[N[Not[LessEqual[a, 2.45e-42]], $MachinePrecision], Or[LessEqual[a, 5400000.0], N[Not[LessEqual[a, 1.2e+70]], $MachinePrecision]]]], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.40000000000000065e-27 or 2.45e-42 < a < 5.4e6 or 1.19999999999999993e70 < a

   1. Initial program 92.1%

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

      1. associate-+l+ 92.1%

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

      2. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in a around inf 82.7%

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

   if -9.40000000000000065e-27 < a < 2.45e-42 or 5.4e6 < a < 1.19999999999999993e70

   1. Initial program 99.1%

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

      1. associate-+l+ 99.1%

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

      2. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in a around 0 76.7%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.4 \cdot 10^{-27} \lor \neg \left(a \leq 2.45 \cdot 10^{-42}\right) \land \left(a \leq 5400000 \lor \neg \left(a \leq 1.2 \cdot 10^{+70}\right)\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 7: 74.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ t_2 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -1.72 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 50000000:\\ \;\;\;\;y \cdot z + t \cdot a\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))) (t_2 (* a (+ t (* z b)))))
   (if (<= a -1.72e-38)
     t_2
     (if (<= a 1.4e-61)
       t_1
       (if (<= a 50000000.0)
         (+ (* y z) (* t a))
         (if (<= a 6.6e+69) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double t_2 = a * (t + (z * b));
	double tmp;
	if (a <= -1.72e-38) {
		tmp = t_2;
	} else if (a <= 1.4e-61) {
		tmp = t_1;
	} else if (a <= 50000000.0) {
		tmp = (y * z) + (t * a);
	} else if (a <= 6.6e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * z)
    t_2 = a * (t + (z * b))
    if (a <= (-1.72d-38)) then
        tmp = t_2
    else if (a <= 1.4d-61) then
        tmp = t_1
    else if (a <= 50000000.0d0) then
        tmp = (y * z) + (t * a)
    else if (a <= 6.6d+69) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double t_2 = a * (t + (z * b));
	double tmp;
	if (a <= -1.72e-38) {
		tmp = t_2;
	} else if (a <= 1.4e-61) {
		tmp = t_1;
	} else if (a <= 50000000.0) {
		tmp = (y * z) + (t * a);
	} else if (a <= 6.6e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	t_2 = a * (t + (z * b))
	tmp = 0
	if a <= -1.72e-38:
		tmp = t_2
	elif a <= 1.4e-61:
		tmp = t_1
	elif a <= 50000000.0:
		tmp = (y * z) + (t * a)
	elif a <= 6.6e+69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	t_2 = Float64(a * Float64(t + Float64(z * b)))
	tmp = 0.0
	if (a <= -1.72e-38)
		tmp = t_2;
	elseif (a <= 1.4e-61)
		tmp = t_1;
	elseif (a <= 50000000.0)
		tmp = Float64(Float64(y * z) + Float64(t * a));
	elseif (a <= 6.6e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * z);
	t_2 = a * (t + (z * b));
	tmp = 0.0;
	if (a <= -1.72e-38)
		tmp = t_2;
	elseif (a <= 1.4e-61)
		tmp = t_1;
	elseif (a <= 50000000.0)
		tmp = (y * z) + (t * a);
	elseif (a <= 6.6e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.72e-38], t$95$2, If[LessEqual[a, 1.4e-61], t$95$1, If[LessEqual[a, 50000000.0], N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.6e+69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.72e-38 or 6.5999999999999997e69 < a

   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+ 91.5%

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

      2. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in a around inf 83.2%

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

   if -1.72e-38 < a < 1.4000000000000001e-61 or 5e7 < a < 6.5999999999999997e69

   1. Initial program 99.1%

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

      1. associate-+l+ 99.1%

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

      2. associate-*l* 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in a around 0 77.7%

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

   if 1.4000000000000001e-61 < a < 5e7

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in b around 0 83.6%

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

   5. Taylor expanded in x around 0 72.9%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.72 \cdot 10^{-38}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 50000000:\\ \;\;\;\;y \cdot z + t \cdot a\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+69}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 8: 40.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+77}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-268}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-291}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+121}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.5e+77)
   (* t a)
   (if (<= t -4.5e-268)
     (* y z)
     (if (<= t 1.1e-291)
       x
       (if (<= t 1.7e-106) (* a (* z b)) (if (<= t 2.2e+121) x (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.5e+77) {
		tmp = t * a;
	} else if (t <= -4.5e-268) {
		tmp = y * z;
	} else if (t <= 1.1e-291) {
		tmp = x;
	} else if (t <= 1.7e-106) {
		tmp = a * (z * b);
	} else if (t <= 2.2e+121) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.5d+77)) then
        tmp = t * a
    else if (t <= (-4.5d-268)) then
        tmp = y * z
    else if (t <= 1.1d-291) then
        tmp = x
    else if (t <= 1.7d-106) then
        tmp = a * (z * b)
    else if (t <= 2.2d+121) then
        tmp = x
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.5e+77) {
		tmp = t * a;
	} else if (t <= -4.5e-268) {
		tmp = y * z;
	} else if (t <= 1.1e-291) {
		tmp = x;
	} else if (t <= 1.7e-106) {
		tmp = a * (z * b);
	} else if (t <= 2.2e+121) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.5e+77:
		tmp = t * a
	elif t <= -4.5e-268:
		tmp = y * z
	elif t <= 1.1e-291:
		tmp = x
	elif t <= 1.7e-106:
		tmp = a * (z * b)
	elif t <= 2.2e+121:
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.5e+77)
		tmp = Float64(t * a);
	elseif (t <= -4.5e-268)
		tmp = Float64(y * z);
	elseif (t <= 1.1e-291)
		tmp = x;
	elseif (t <= 1.7e-106)
		tmp = Float64(a * Float64(z * b));
	elseif (t <= 2.2e+121)
		tmp = x;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.5e+77)
		tmp = t * a;
	elseif (t <= -4.5e-268)
		tmp = y * z;
	elseif (t <= 1.1e-291)
		tmp = x;
	elseif (t <= 1.7e-106)
		tmp = a * (z * b);
	elseif (t <= 2.2e+121)
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.5e+77], N[(t * a), $MachinePrecision], If[LessEqual[t, -4.5e-268], N[(y * z), $MachinePrecision], If[LessEqual[t, 1.1e-291], x, If[LessEqual[t, 1.7e-106], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e+121], x, N[(t * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.50000000000000002e77 or 2.20000000000000001e121 < t

   1. Initial program 94.1%

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

      1. associate-+l+ 94.1%

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

      2. associate-*l* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around inf 63.5%

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

   if -2.50000000000000002e77 < t < -4.5000000000000001e-268

   1. Initial program 95.9%

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

      1. associate-+l+ 95.9%

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

      2. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in y around inf 37.5%

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

      1. *-commutative 37.5%

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

   6. Simplified 37.5%

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

   if -4.5000000000000001e-268 < t < 1.10000000000000001e-291 or 1.69999999999999991e-106 < t < 2.20000000000000001e121

   1. Initial program 97.9%

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

      1. associate-+l+ 97.9%

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

      2. associate-*l* 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in x around inf 44.2%

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

   if 1.10000000000000001e-291 < t < 1.69999999999999991e-106

   1. Initial program 93.7%

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

      1. associate-+l+ 93.7%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

      1. associate-+r+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-*r* 93.7%

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

      4. fma-def 93.7%

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

      5. +-commutative 93.7%

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

      6. *-commutative 93.7%

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

      7. fma-def 93.7%

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

      8. +-commutative 93.7%

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

      9. *-commutative 93.7%

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

      10. fma-def 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in b around inf 49.6%

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

      1. *-commutative 49.6%

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

   8. Simplified 49.6%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+77}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-268}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-291}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+121}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]

Alternative 9: 39.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+129}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-176}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-292}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-96}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.5e+129)
   (* t a)
   (if (<= t -6e-176)
     (* (* z a) b)
     (if (<= t 7.8e-292)
       x
       (if (<= t 6.5e-96) (* a (* z b)) (if (<= t 2.8e+120) x (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.5e+129) {
		tmp = t * a;
	} else if (t <= -6e-176) {
		tmp = (z * a) * b;
	} else if (t <= 7.8e-292) {
		tmp = x;
	} else if (t <= 6.5e-96) {
		tmp = a * (z * b);
	} else if (t <= 2.8e+120) {
		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 <= (-7.5d+129)) then
        tmp = t * a
    else if (t <= (-6d-176)) then
        tmp = (z * a) * b
    else if (t <= 7.8d-292) then
        tmp = x
    else if (t <= 6.5d-96) then
        tmp = a * (z * b)
    else if (t <= 2.8d+120) 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 <= -7.5e+129) {
		tmp = t * a;
	} else if (t <= -6e-176) {
		tmp = (z * a) * b;
	} else if (t <= 7.8e-292) {
		tmp = x;
	} else if (t <= 6.5e-96) {
		tmp = a * (z * b);
	} else if (t <= 2.8e+120) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.5e+129:
		tmp = t * a
	elif t <= -6e-176:
		tmp = (z * a) * b
	elif t <= 7.8e-292:
		tmp = x
	elif t <= 6.5e-96:
		tmp = a * (z * b)
	elif t <= 2.8e+120:
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.5e+129)
		tmp = Float64(t * a);
	elseif (t <= -6e-176)
		tmp = Float64(Float64(z * a) * b);
	elseif (t <= 7.8e-292)
		tmp = x;
	elseif (t <= 6.5e-96)
		tmp = Float64(a * Float64(z * b));
	elseif (t <= 2.8e+120)
		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 <= -7.5e+129)
		tmp = t * a;
	elseif (t <= -6e-176)
		tmp = (z * a) * b;
	elseif (t <= 7.8e-292)
		tmp = x;
	elseif (t <= 6.5e-96)
		tmp = a * (z * b);
	elseif (t <= 2.8e+120)
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.5e+129], N[(t * a), $MachinePrecision], If[LessEqual[t, -6e-176], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 7.8e-292], x, If[LessEqual[t, 6.5e-96], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+120], x, N[(t * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.4999999999999998e129 or 2.8000000000000001e120 < t

   1. Initial program 94.6%

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

      1. associate-+l+ 94.6%

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

      2. associate-*l* 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around inf 65.6%

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

   if -7.4999999999999998e129 < t < -6e-176

   1. Initial program 95.1%

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

      1. associate-+l+ 95.1%

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

      2. associate-*l* 90.7%

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

   3. Simplified 90.7%

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

      1. associate-+r+ 90.7%

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

      2. +-commutative 90.7%

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

      3. associate-*r* 95.1%

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

      4. fma-def 95.1%

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

      5. +-commutative 95.1%

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

      6. *-commutative 95.1%

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

      7. fma-def 95.1%

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

      8. +-commutative 95.1%

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

      9. *-commutative 95.1%

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

      10. fma-def 95.1%

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

   5. Applied egg-rr 95.1%

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

   6. Taylor expanded in b around inf 38.0%

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

      1. *-commutative 38.0%

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

   8. Simplified 38.0%

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

   9. Taylor expanded in b around 0 38.0%

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

       1. associate-*r* 39.1%

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

       2. *-commutative 39.1%

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

       3. associate-*r* 40.6%

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

   11. Simplified 40.6%

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

   if -6e-176 < t < 7.8e-292 or 6.50000000000000001e-96 < t < 2.8000000000000001e120

   1. Initial program 97.1%

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

      1. associate-+l+ 97.1%

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

      2. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in x around inf 40.8%

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

   if 7.8e-292 < t < 6.50000000000000001e-96

   1. Initial program 93.7%

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

      1. associate-+l+ 93.7%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

      1. associate-+r+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-*r* 93.7%

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

      4. fma-def 93.7%

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

      5. +-commutative 93.7%

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

      6. *-commutative 93.7%

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

      7. fma-def 93.7%

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

      8. +-commutative 93.7%

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

      9. *-commutative 93.7%

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

      10. fma-def 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in b around inf 49.6%

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

      1. *-commutative 49.6%

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

   8. Simplified 49.6%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+129}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-176}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-292}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-96}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]

Alternative 10: 61.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot a\\ t_2 := x + y \cdot z\\ \mathbf{if}\;z \leq -2700000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t a))) (t_2 (+ x (* y z))))
   (if (<= z -2700000000000.0)
     t_2
     (if (<= z -1.35e-59)
       t_1
       (if (<= z -9.5e-115) t_2 (if (<= z 2.2e+115) t_1 (* (* z a) b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double t_2 = x + (y * z);
	double tmp;
	if (z <= -2700000000000.0) {
		tmp = t_2;
	} else if (z <= -1.35e-59) {
		tmp = t_1;
	} else if (z <= -9.5e-115) {
		tmp = t_2;
	} else if (z <= 2.2e+115) {
		tmp = t_1;
	} else {
		tmp = (z * a) * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t * a)
    t_2 = x + (y * z)
    if (z <= (-2700000000000.0d0)) then
        tmp = t_2
    else if (z <= (-1.35d-59)) then
        tmp = t_1
    else if (z <= (-9.5d-115)) then
        tmp = t_2
    else if (z <= 2.2d+115) then
        tmp = t_1
    else
        tmp = (z * a) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double t_2 = x + (y * z);
	double tmp;
	if (z <= -2700000000000.0) {
		tmp = t_2;
	} else if (z <= -1.35e-59) {
		tmp = t_1;
	} else if (z <= -9.5e-115) {
		tmp = t_2;
	} else if (z <= 2.2e+115) {
		tmp = t_1;
	} else {
		tmp = (z * a) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * a)
	t_2 = x + (y * z)
	tmp = 0
	if z <= -2700000000000.0:
		tmp = t_2
	elif z <= -1.35e-59:
		tmp = t_1
	elif z <= -9.5e-115:
		tmp = t_2
	elif z <= 2.2e+115:
		tmp = t_1
	else:
		tmp = (z * a) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * a))
	t_2 = Float64(x + Float64(y * z))
	tmp = 0.0
	if (z <= -2700000000000.0)
		tmp = t_2;
	elseif (z <= -1.35e-59)
		tmp = t_1;
	elseif (z <= -9.5e-115)
		tmp = t_2;
	elseif (z <= 2.2e+115)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * a) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * a);
	t_2 = x + (y * z);
	tmp = 0.0;
	if (z <= -2700000000000.0)
		tmp = t_2;
	elseif (z <= -1.35e-59)
		tmp = t_1;
	elseif (z <= -9.5e-115)
		tmp = t_2;
	elseif (z <= 2.2e+115)
		tmp = t_1;
	else
		tmp = (z * a) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2700000000000.0], t$95$2, If[LessEqual[z, -1.35e-59], t$95$1, If[LessEqual[z, -9.5e-115], t$95$2, If[LessEqual[z, 2.2e+115], t$95$1, N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7e12 or -1.3499999999999999e-59 < z < -9.4999999999999996e-115

   1. Initial program 92.1%

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

      1. associate-+l+ 92.1%

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

      2. associate-*l* 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in a around 0 61.6%

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

   if -2.7e12 < z < -1.3499999999999999e-59 or -9.4999999999999996e-115 < z < 2.2e115

   1. Initial program 99.3%

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

      1. associate-+l+ 99.3%

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

      2. associate-*l* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 74.9%

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

   if 2.2e115 < z

   1. Initial program 84.1%

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

      1. associate-+l+ 84.1%

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

      2. associate-*l* 84.0%

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

   3. Simplified 84.0%

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

      1. associate-+r+ 84.0%

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

      2. +-commutative 84.0%

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

      3. associate-*r* 84.1%

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

      4. fma-def 84.1%

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

      5. +-commutative 84.1%

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

      6. *-commutative 84.1%

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

      7. fma-def 84.1%

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

      8. +-commutative 84.1%

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

      9. *-commutative 84.1%

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

      10. fma-def 84.1%

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

   5. Applied egg-rr 84.1%

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

   6. Taylor expanded in b around inf 50.3%

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

      1. *-commutative 50.3%

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

   8. Simplified 50.3%

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

   9. Taylor expanded in b around 0 50.3%

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

       1. associate-*r* 52.8%

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

       2. *-commutative 52.8%

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

       3. associate-*r* 55.7%

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

   11. Simplified 55.7%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2700000000000:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-59}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-115}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+115}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \]

Alternative 11: 87.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+38} \lor \neg \left(a \leq 6.6 \cdot 10^{+69}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -7.2e+38) (not (<= a 6.6e+69)))
   (+ x (* a (+ t (* z b))))
   (+ (* y z) (+ x (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7.2e+38) || !(a <= 6.6e+69)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (y * z) + (x + (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-7.2d+38)) .or. (.not. (a <= 6.6d+69))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = (y * z) + (x + (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7.2e+38) || !(a <= 6.6e+69)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (y * z) + (x + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -7.2e+38) or not (a <= 6.6e+69):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = (y * z) + (x + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -7.2e+38) || !(a <= 6.6e+69))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(Float64(y * z) + Float64(x + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -7.2e+38) || ~((a <= 6.6e+69)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = (y * z) + (x + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -7.2e+38], N[Not[LessEqual[a, 6.6e+69]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.19999999999999938e38 or 6.5999999999999997e69 < a

   1. Initial program 90.2%

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

      1. associate-+l+ 90.2%

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

      2. +-commutative 90.2%

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

      3. *-commutative 90.2%

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

      4. associate-*l* 93.7%

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

      5. distribute-lft-out 96.4%

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

      6. fma-def 97.3%

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

      7. +-commutative 97.3%

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

      8. fma-def 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in y around 0 92.4%

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

   if -7.19999999999999938e38 < a < 6.5999999999999997e69

   1. Initial program 99.3%

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

      1. associate-+l+ 99.3%

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

      2. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in b around 0 86.7%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+38} \lor \neg \left(a \leq 6.6 \cdot 10^{+69}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + t \cdot a\right)\\ \end{array} \]

Alternative 12: 87.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3600000000000 \lor \neg \left(z \leq 1.8 \cdot 10^{+57}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3600000000000.0) (not (<= z 1.8e+57)))
   (+ x (* z (+ y (* a b))))
   (+ x (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3600000000000.0) || !(z <= 1.8e+57)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3600000000000.0d0)) .or. (.not. (z <= 1.8d+57))) then
        tmp = x + (z * (y + (a * b)))
    else
        tmp = x + (a * (t + (z * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3600000000000.0) || !(z <= 1.8e+57)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3600000000000.0) or not (z <= 1.8e+57):
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3600000000000.0) || !(z <= 1.8e+57))
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	else
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3600000000000.0) || ~((z <= 1.8e+57)))
		tmp = x + (z * (y + (a * b)));
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3600000000000.0], N[Not[LessEqual[z, 1.8e+57]], $MachinePrecision]], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6e12 or 1.8000000000000001e57 < z

   1. Initial program 88.7%

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

      1. +-commutative 88.7%

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

      2. +-commutative 88.7%

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

      3. associate-+l+ 88.7%

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

      4. associate-+r+ 88.7%

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

      5. *-commutative 88.7%

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

      6. associate-*l* 92.3%

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

      7. *-commutative 92.3%

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

      8. distribute-lft-out 96.1%

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

      9. fma-def 96.1%

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

      10. fma-def 96.1%

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

      11. +-commutative 96.1%

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

      12. fma-def 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in t around 0 90.6%

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

   if -3.6e12 < z < 1.8000000000000001e57

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-*l* 99.3%

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

      5. distribute-lft-out 99.3%

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

      6. fma-def 99.3%

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

      7. +-commutative 99.3%

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

      8. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 89.1%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3600000000000 \lor \neg \left(z \leq 1.8 \cdot 10^{+57}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]

Alternative 13: 80.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+158}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+72}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.5e+158)
   (+ x (* y z))
   (if (<= y 1.65e+72) (+ x (* a (+ t (* z b)))) (+ (* y z) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.5e+158) {
		tmp = x + (y * z);
	} else if (y <= 1.65e+72) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (y * z) + (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 (y <= (-2.5d+158)) then
        tmp = x + (y * z)
    else if (y <= 1.65d+72) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = (y * z) + (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 (y <= -2.5e+158) {
		tmp = x + (y * z);
	} else if (y <= 1.65e+72) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (y * z) + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.5e+158:
		tmp = x + (y * z)
	elif y <= 1.65e+72:
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = (y * z) + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.5e+158)
		tmp = Float64(x + Float64(y * z));
	elseif (y <= 1.65e+72)
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(Float64(y * z) + Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.5e+158)
		tmp = x + (y * z);
	elseif (y <= 1.65e+72)
		tmp = x + (a * (t + (z * b)));
	else
		tmp = (y * z) + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.5e+158], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+72], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4999999999999998e158

   1. Initial program 94.0%

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

      1. associate-+l+ 94.0%

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

      2. associate-*l* 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in a around 0 82.9%

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

   if -2.4999999999999998e158 < y < 1.65e72

   1. Initial program 95.6%

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

      1. associate-+l+ 95.6%

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

      2. +-commutative 95.6%

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

      3. *-commutative 95.6%

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

      4. associate-*l* 94.1%

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

      5. distribute-lft-out 95.2%

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

      6. fma-def 95.2%

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

      7. +-commutative 95.2%

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

      8. fma-def 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in y around 0 87.1%

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

   if 1.65e72 < y

   1. Initial program 95.2%

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

      1. associate-+l+ 95.2%

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

      2. associate-*l* 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in b around 0 85.9%

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

   5. Taylor expanded in x around 0 77.0%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+158}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+72}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + t \cdot a\\ \end{array} \]

Alternative 14: 59.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2800000000000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+117}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2800000000000.0)
   (* y z)
   (if (<= z 1.7e+117) (+ x (* t a)) (* (* z a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2800000000000.0) {
		tmp = y * z;
	} else if (z <= 1.7e+117) {
		tmp = x + (t * a);
	} else {
		tmp = (z * a) * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2800000000000.0d0)) then
        tmp = y * z
    else if (z <= 1.7d+117) then
        tmp = x + (t * a)
    else
        tmp = (z * a) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2800000000000.0) {
		tmp = y * z;
	} else if (z <= 1.7e+117) {
		tmp = x + (t * a);
	} else {
		tmp = (z * a) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2800000000000.0:
		tmp = y * z
	elif z <= 1.7e+117:
		tmp = x + (t * a)
	else:
		tmp = (z * a) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2800000000000.0)
		tmp = Float64(y * z);
	elseif (z <= 1.7e+117)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = Float64(Float64(z * a) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2800000000000.0)
		tmp = y * z;
	elseif (z <= 1.7e+117)
		tmp = x + (t * a);
	else
		tmp = (z * a) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2800000000000.0], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.7e+117], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e12

   1. Initial program 90.8%

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

      1. associate-+l+ 90.8%

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

      2. associate-*l* 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in y around inf 49.7%

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

      1. *-commutative 49.7%

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

   6. Simplified 49.7%

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

   if -2.8e12 < z < 1.7e117

   1. Initial program 99.3%

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

      1. associate-+l+ 99.3%

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

      2. associate-*l* 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 72.1%

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

   if 1.7e117 < z

   1. Initial program 84.1%

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

      1. associate-+l+ 84.1%

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

      2. associate-*l* 84.0%

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

   3. Simplified 84.0%

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

      1. associate-+r+ 84.0%

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

      2. +-commutative 84.0%

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

      3. associate-*r* 84.1%

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

      4. fma-def 84.1%

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

      5. +-commutative 84.1%

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

      6. *-commutative 84.1%

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

      7. fma-def 84.1%

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

      8. +-commutative 84.1%

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

      9. *-commutative 84.1%

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

      10. fma-def 84.1%

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

   5. Applied egg-rr 84.1%

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

   6. Taylor expanded in b around inf 50.3%

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

      1. *-commutative 50.3%

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

   8. Simplified 50.3%

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

   9. Taylor expanded in b around 0 50.3%

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

       1. associate-*r* 52.8%

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

       2. *-commutative 52.8%

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

       3. associate-*r* 55.7%

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

   11. Simplified 55.7%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2800000000000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+117}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \]

Alternative 15: 38.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+119}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.5e+120) x (if (<= x 2.8e+119) (* t a) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.5e+120) {
		tmp = x;
	} else if (x <= 2.8e+119) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-9.5d+120)) then
        tmp = x
    else if (x <= 2.8d+119) then
        tmp = t * a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.5e+120) {
		tmp = x;
	} else if (x <= 2.8e+119) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.5e+120:
		tmp = x
	elif x <= 2.8e+119:
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.5e+120)
		tmp = x;
	elseif (x <= 2.8e+119)
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -9.5e+120)
		tmp = x;
	elseif (x <= 2.8e+119)
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.5e+120], x, If[LessEqual[x, 2.8e+119], N[(t * a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5e120 or 2.80000000000000013e119 < x

   1. Initial program 97.3%

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

      1. associate-+l+ 97.3%

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

      2. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in x around inf 58.4%

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

   if -9.5e120 < x < 2.80000000000000013e119

   1. Initial program 94.5%

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

      1. associate-+l+ 94.5%

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

      2. associate-*l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in t around inf 40.6%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+120}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+119}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 40.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+73}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+62}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.2e+73) (* y z) (if (<= y 6.2e+62) (* t a) (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.2e+73) {
		tmp = y * z;
	} else if (y <= 6.2e+62) {
		tmp = t * a;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.2d+73)) then
        tmp = y * z
    else if (y <= 6.2d+62) then
        tmp = t * a
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.2e+73) {
		tmp = y * z;
	} else if (y <= 6.2e+62) {
		tmp = t * a;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.2e+73:
		tmp = y * z
	elif y <= 6.2e+62:
		tmp = t * a
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.2e+73)
		tmp = Float64(y * z);
	elseif (y <= 6.2e+62)
		tmp = Float64(t * a);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.2e+73)
		tmp = y * z;
	elseif (y <= 6.2e+62)
		tmp = t * a;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.2e+73], N[(y * z), $MachinePrecision], If[LessEqual[y, 6.2e+62], N[(t * a), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e73 or 6.20000000000000029e62 < y

   1. Initial program 95.7%

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

      1. associate-+l+ 95.7%

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

      2. associate-*l* 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in y around inf 55.6%

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

      1. *-commutative 55.6%

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

   6. Simplified 55.6%

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

   if -2.2e73 < y < 6.20000000000000029e62

   1. Initial program 95.1%

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

      1. associate-+l+ 95.1%

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

      2. associate-*l* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in t around inf 41.3%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+73}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+62}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 17: 26.0% 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 95.3%

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

   1. associate-+l+ 95.3%

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

   2. associate-*l* 93.9%

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

3. Simplified 93.9%

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

4. Taylor expanded in x around inf 22.4%

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

5. Final simplification 22.4%

   \[\leadsto x \]

Developer target: 97.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023240 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (if (< z -11820553527347888000.0) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 4.7589743188364287e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

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