Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.7% → 94.5%

Time: 11.3s

Alternatives: 13

Speedup: 0.7×

• 32.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.26 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.26e+215) (+ (fma y z x) (* a (+ t (* z b)))) (* z (+ y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.26e+215) {
		tmp = fma(y, z, x) + (a * (t + (z * b)));
	} else {
		tmp = z * (y + (a * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.26e+215)
		tmp = Float64(fma(y, z, x) + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(z * Float64(y + Float64(a * b)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1.26e+215], N[(N[(y * z + x), $MachinePrecision] + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.26e215

   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. +-commutative 94.0%

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

      3. fma-define 94.0%

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

      4. associate-*l* 96.2%

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

      5. *-commutative 96.2%

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

      6. *-commutative 96.2%

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

      7. distribute-rgt-out 97.9%

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

      8. *-commutative 97.9%

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

   3. Simplified 97.9%

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

   if 1.26e215 < z

   1. Initial program 78.1%

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

      1. associate-+l+ 78.1%

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

      2. associate-*l* 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in z around inf 95.6%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.26 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.6% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* z y)) (* a t)) (* b (* z a)))))
   (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 = ((x + (z * y)) + (a * t)) + (b * (z * a));
	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 = ((x + (z * y)) + (a * t)) + (b * (z * a));
	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 = ((x + (z * y)) + (a * t)) + (b * (z * a))
	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(x + Float64(z * y)) + Float64(a * t)) + Float64(b * Float64(z * a)))
	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 = ((x + (z * y)) + (a * t)) + (b * (z * a));
	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[(x + N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b * N[(z * a), $MachinePrecision]), $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 97.6%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. associate-*l* 38.5%

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

   3. Simplified 38.5%

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

   5. Taylor expanded in z around inf 77.0%

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

4. Final simplification 96.5%

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

Alternative 3: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+39} \lor \neg \left(a \leq -0.00046 \lor \neg \left(a \leq -3 \cdot 10^{-92}\right) \land a \leq 1.5 \cdot 10^{-106}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -8.8e+39)
         (not (or (<= a -0.00046) (and (not (<= a -3e-92)) (<= a 1.5e-106)))))
   (+ x (* a (+ t (* z b))))
   (+ x (+ (* a t) (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -8.8e+39) || !((a <= -0.00046) || (!(a <= -3e-92) && (a <= 1.5e-106)))) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + ((a * t) + (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-8.8d+39)) .or. (.not. (a <= (-0.00046d0)) .or. (.not. (a <= (-3d-92))) .and. (a <= 1.5d-106))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = x + ((a * t) + (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -8.8e+39) || !((a <= -0.00046) || (!(a <= -3e-92) && (a <= 1.5e-106)))) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + ((a * t) + (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -8.8e+39) or not ((a <= -0.00046) or (not (a <= -3e-92) and (a <= 1.5e-106))):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = x + ((a * t) + (z * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -8.8e+39) || !((a <= -0.00046) || (!(a <= -3e-92) && (a <= 1.5e-106))))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -8.8e+39) || ~(((a <= -0.00046) || (~((a <= -3e-92)) && (a <= 1.5e-106)))))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = x + ((a * t) + (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -8.8e+39], N[Not[Or[LessEqual[a, -0.00046], And[N[Not[LessEqual[a, -3e-92]], $MachinePrecision], LessEqual[a, 1.5e-106]]]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.8000000000000006e39 or -4.6000000000000001e-4 < a < -3.00000000000000013e-92 or 1.50000000000000009e-106 < a

   1. Initial program 88.6%

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

      1. associate-+l+ 88.6%

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

      2. +-commutative 88.6%

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

      3. fma-define 88.6%

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

      4. associate-*l* 94.5%

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

      5. *-commutative 94.5%

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

      6. *-commutative 94.5%

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

      7. distribute-rgt-out 97.0%

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

      8. *-commutative 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in y around 0 92.0%

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

   if -8.8000000000000006e39 < a < -4.6000000000000001e-4 or -3.00000000000000013e-92 < a < 1.50000000000000009e-106

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in b around 0 97.2%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+39} \lor \neg \left(a \leq -0.00046 \lor \neg \left(a \leq -3 \cdot 10^{-92}\right) \land a \leq 1.5 \cdot 10^{-106}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ t_2 := x + a \cdot t\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-280}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))) (t_2 (+ x (* a t))))
   (if (<= x -4.5e+61)
     t_2
     (if (<= x 8.5e-300)
       t_1
       (if (<= x 6.2e-280) (* z y) (if (<= x 4.3e+86) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double t_2 = x + (a * t);
	double tmp;
	if (x <= -4.5e+61) {
		tmp = t_2;
	} else if (x <= 8.5e-300) {
		tmp = t_1;
	} else if (x <= 6.2e-280) {
		tmp = z * y;
	} else if (x <= 4.3e+86) {
		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 = a * (t + (z * b))
    t_2 = x + (a * t)
    if (x <= (-4.5d+61)) then
        tmp = t_2
    else if (x <= 8.5d-300) then
        tmp = t_1
    else if (x <= 6.2d-280) then
        tmp = z * y
    else if (x <= 4.3d+86) 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 = a * (t + (z * b));
	double t_2 = x + (a * t);
	double tmp;
	if (x <= -4.5e+61) {
		tmp = t_2;
	} else if (x <= 8.5e-300) {
		tmp = t_1;
	} else if (x <= 6.2e-280) {
		tmp = z * y;
	} else if (x <= 4.3e+86) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	t_2 = x + (a * t)
	tmp = 0
	if x <= -4.5e+61:
		tmp = t_2
	elif x <= 8.5e-300:
		tmp = t_1
	elif x <= 6.2e-280:
		tmp = z * y
	elif x <= 4.3e+86:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + Float64(z * b)))
	t_2 = Float64(x + Float64(a * t))
	tmp = 0.0
	if (x <= -4.5e+61)
		tmp = t_2;
	elseif (x <= 8.5e-300)
		tmp = t_1;
	elseif (x <= 6.2e-280)
		tmp = Float64(z * y);
	elseif (x <= 4.3e+86)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + (z * b));
	t_2 = x + (a * t);
	tmp = 0.0;
	if (x <= -4.5e+61)
		tmp = t_2;
	elseif (x <= 8.5e-300)
		tmp = t_1;
	elseif (x <= 6.2e-280)
		tmp = z * y;
	elseif (x <= 4.3e+86)
		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[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+61], t$95$2, If[LessEqual[x, 8.5e-300], t$95$1, If[LessEqual[x, 6.2e-280], N[(z * y), $MachinePrecision], If[LessEqual[x, 4.3e+86], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5e61 or 4.3000000000000002e86 < x

   1. Initial program 92.3%

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

      1. associate-+l+ 92.3%

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

      2. associate-*l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in z around 0 71.0%

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

      1. +-commutative 71.0%

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

   7. Simplified 71.0%

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

   if -4.5e61 < x < 8.4999999999999995e-300 or 6.20000000000000042e-280 < x < 4.3000000000000002e86

   1. Initial program 92.4%

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

      1. associate-+l+ 92.4%

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

      2. associate-*l* 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in a around inf 72.3%

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

   if 8.4999999999999995e-300 < x < 6.20000000000000042e-280

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in y around inf 78.1%

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

      1. *-commutative 78.1%

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

   7. Simplified 78.1%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+61}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-300}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-280}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+86}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-38}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+56}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+85}:\\ \;\;\;\;a \cdot t + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ y (* a b)))))
   (if (<= z -2.6e+40)
     t_1
     (if (<= z 1.2e-38)
       (+ x (* a t))
       (if (<= z 1.45e+56)
         (* a (+ t (* z b)))
         (if (<= z 5.6e+85) (+ (* a t) (* z y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + (a * b));
	double tmp;
	if (z <= -2.6e+40) {
		tmp = t_1;
	} else if (z <= 1.2e-38) {
		tmp = x + (a * t);
	} else if (z <= 1.45e+56) {
		tmp = a * (t + (z * b));
	} else if (z <= 5.6e+85) {
		tmp = (a * t) + (z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y + (a * b))
    if (z <= (-2.6d+40)) then
        tmp = t_1
    else if (z <= 1.2d-38) then
        tmp = x + (a * t)
    else if (z <= 1.45d+56) then
        tmp = a * (t + (z * b))
    else if (z <= 5.6d+85) then
        tmp = (a * t) + (z * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + (a * b));
	double tmp;
	if (z <= -2.6e+40) {
		tmp = t_1;
	} else if (z <= 1.2e-38) {
		tmp = x + (a * t);
	} else if (z <= 1.45e+56) {
		tmp = a * (t + (z * b));
	} else if (z <= 5.6e+85) {
		tmp = (a * t) + (z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (y + (a * b))
	tmp = 0
	if z <= -2.6e+40:
		tmp = t_1
	elif z <= 1.2e-38:
		tmp = x + (a * t)
	elif z <= 1.45e+56:
		tmp = a * (t + (z * b))
	elif z <= 5.6e+85:
		tmp = (a * t) + (z * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (z <= -2.6e+40)
		tmp = t_1;
	elseif (z <= 1.2e-38)
		tmp = Float64(x + Float64(a * t));
	elseif (z <= 1.45e+56)
		tmp = Float64(a * Float64(t + Float64(z * b)));
	elseif (z <= 5.6e+85)
		tmp = Float64(Float64(a * t) + Float64(z * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (y + (a * b));
	tmp = 0.0;
	if (z <= -2.6e+40)
		tmp = t_1;
	elseif (z <= 1.2e-38)
		tmp = x + (a * t);
	elseif (z <= 1.45e+56)
		tmp = a * (t + (z * b));
	elseif (z <= 5.6e+85)
		tmp = (a * t) + (z * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+40], t$95$1, If[LessEqual[z, 1.2e-38], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+56], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+85], N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6000000000000001e40 or 5.5999999999999998e85 < z

   1. Initial program 85.4%

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

      1. associate-+l+ 85.4%

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

      2. associate-*l* 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in z around inf 79.8%

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

   if -2.6000000000000001e40 < z < 1.20000000000000011e-38

   1. Initial program 99.1%

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

      1. associate-+l+ 99.1%

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

      2. associate-*l* 99.9%

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

   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. Add Preprocessing

   5. Taylor expanded in z around 0 78.0%

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

      1. +-commutative 78.0%

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

   7. Simplified 78.0%

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

   if 1.20000000000000011e-38 < z < 1.45000000000000004e56

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 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. Add Preprocessing

   5. Taylor expanded in a around inf 82.3%

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

   if 1.45000000000000004e56 < z < 5.5999999999999998e85

   1. Initial program 77.8%

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

      1. associate-+l+ 77.8%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in b around 0 100.0%

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

   6. Taylor expanded in x around 0 89.0%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-38}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+56}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+85}:\\ \;\;\;\;a \cdot t + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-301}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-157}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+52}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.2e+72)
   x
   (if (<= x 4.2e-301)
     (* a t)
     (if (<= x 7.2e-157) (* z y) (if (<= x 1.02e+52) (* a t) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.2e+72) {
		tmp = x;
	} else if (x <= 4.2e-301) {
		tmp = a * t;
	} else if (x <= 7.2e-157) {
		tmp = z * y;
	} else if (x <= 1.02e+52) {
		tmp = a * t;
	} 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 <= (-6.2d+72)) then
        tmp = x
    else if (x <= 4.2d-301) then
        tmp = a * t
    else if (x <= 7.2d-157) then
        tmp = z * y
    else if (x <= 1.02d+52) then
        tmp = a * t
    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 <= -6.2e+72) {
		tmp = x;
	} else if (x <= 4.2e-301) {
		tmp = a * t;
	} else if (x <= 7.2e-157) {
		tmp = z * y;
	} else if (x <= 1.02e+52) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.2e+72:
		tmp = x
	elif x <= 4.2e-301:
		tmp = a * t
	elif x <= 7.2e-157:
		tmp = z * y
	elif x <= 1.02e+52:
		tmp = a * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.2e+72)
		tmp = x;
	elseif (x <= 4.2e-301)
		tmp = Float64(a * t);
	elseif (x <= 7.2e-157)
		tmp = Float64(z * y);
	elseif (x <= 1.02e+52)
		tmp = Float64(a * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.2e+72)
		tmp = x;
	elseif (x <= 4.2e-301)
		tmp = a * t;
	elseif (x <= 7.2e-157)
		tmp = z * y;
	elseif (x <= 1.02e+52)
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.2e+72], x, If[LessEqual[x, 4.2e-301], N[(a * t), $MachinePrecision], If[LessEqual[x, 7.2e-157], N[(z * y), $MachinePrecision], If[LessEqual[x, 1.02e+52], N[(a * t), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.19999999999999977e72 or 1.02000000000000002e52 < x

   1. Initial program 91.6%

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

      1. associate-+l+ 91.6%

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

      2. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in x around inf 56.8%

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

   if -6.19999999999999977e72 < x < 4.1999999999999997e-301 or 7.2e-157 < x < 1.02000000000000002e52

   1. Initial program 92.4%

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

      1. associate-+l+ 92.4%

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

      2. associate-*l* 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. Add Preprocessing

   5. Taylor expanded in t around inf 43.0%

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

   if 4.1999999999999997e-301 < x < 7.2e-157

   1. Initial program 96.9%

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

      1. associate-+l+ 96.9%

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

      2. associate-*l* 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in y around inf 54.4%

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

      1. *-commutative 54.4%

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

   7. Simplified 54.4%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-301}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-157}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+52}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-301}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-157}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+50}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9e+50)
   x
   (if (<= x 3.2e-301)
     (* a (* z b))
     (if (<= x 9.5e-157) (* z y) (if (<= x 7e+50) (* a t) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9e+50) {
		tmp = x;
	} else if (x <= 3.2e-301) {
		tmp = a * (z * b);
	} else if (x <= 9.5e-157) {
		tmp = z * y;
	} else if (x <= 7e+50) {
		tmp = a * t;
	} 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 <= (-9d+50)) then
        tmp = x
    else if (x <= 3.2d-301) then
        tmp = a * (z * b)
    else if (x <= 9.5d-157) then
        tmp = z * y
    else if (x <= 7d+50) then
        tmp = a * t
    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 <= -9e+50) {
		tmp = x;
	} else if (x <= 3.2e-301) {
		tmp = a * (z * b);
	} else if (x <= 9.5e-157) {
		tmp = z * y;
	} else if (x <= 7e+50) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9e+50:
		tmp = x
	elif x <= 3.2e-301:
		tmp = a * (z * b)
	elif x <= 9.5e-157:
		tmp = z * y
	elif x <= 7e+50:
		tmp = a * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9e+50)
		tmp = x;
	elseif (x <= 3.2e-301)
		tmp = Float64(a * Float64(z * b));
	elseif (x <= 9.5e-157)
		tmp = Float64(z * y);
	elseif (x <= 7e+50)
		tmp = Float64(a * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -9e+50)
		tmp = x;
	elseif (x <= 3.2e-301)
		tmp = a * (z * b);
	elseif (x <= 9.5e-157)
		tmp = z * y;
	elseif (x <= 7e+50)
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9e+50], x, If[LessEqual[x, 3.2e-301], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e-157], N[(z * y), $MachinePrecision], If[LessEqual[x, 7e+50], N[(a * t), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.00000000000000027e50 or 7.00000000000000012e50 < x

   1. Initial program 92.0%

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

      1. associate-+l+ 92.0%

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

      2. associate-*l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in x around inf 55.2%

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

   if -9.00000000000000027e50 < x < 3.1999999999999999e-301

   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* 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in a around inf 76.6%

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

   6. Taylor expanded in t around 0 42.4%

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

   if 3.1999999999999999e-301 < x < 9.50000000000000019e-157

   1. Initial program 96.9%

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

      1. associate-+l+ 96.9%

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

      2. associate-*l* 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in y around inf 54.4%

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

      1. *-commutative 54.4%

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

   7. Simplified 54.4%

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

   if 9.50000000000000019e-157 < x < 7.00000000000000012e50

   1. Initial program 93.3%

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

      1. associate-+l+ 93.3%

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

      2. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in t around inf 50.4%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-301}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-157}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+50}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+158}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+278}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= z -2.9e+40)
     t_1
     (if (<= z 7.8e+158) (+ x (* a t)) (if (<= z 8.2e+278) t_1 (* z y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (z <= -2.9e+40) {
		tmp = t_1;
	} else if (z <= 7.8e+158) {
		tmp = x + (a * t);
	} else if (z <= 8.2e+278) {
		tmp = t_1;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (z <= (-2.9d+40)) then
        tmp = t_1
    else if (z <= 7.8d+158) then
        tmp = x + (a * t)
    else if (z <= 8.2d+278) then
        tmp = t_1
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (z <= -2.9e+40) {
		tmp = t_1;
	} else if (z <= 7.8e+158) {
		tmp = x + (a * t);
	} else if (z <= 8.2e+278) {
		tmp = t_1;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if z <= -2.9e+40:
		tmp = t_1
	elif z <= 7.8e+158:
		tmp = x + (a * t)
	elif z <= 8.2e+278:
		tmp = t_1
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (z <= -2.9e+40)
		tmp = t_1;
	elseif (z <= 7.8e+158)
		tmp = Float64(x + Float64(a * t));
	elseif (z <= 8.2e+278)
		tmp = t_1;
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (z <= -2.9e+40)
		tmp = t_1;
	elseif (z <= 7.8e+158)
		tmp = x + (a * t);
	elseif (z <= 8.2e+278)
		tmp = t_1;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+40], t$95$1, If[LessEqual[z, 7.8e+158], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+278], t$95$1, N[(z * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.90000000000000017e40 or 7.8e158 < z < 8.2000000000000003e278

   1. Initial program 86.9%

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

      1. associate-+l+ 86.9%

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

      2. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in a around inf 60.2%

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

   6. Taylor expanded in t around 0 51.4%

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

   if -2.90000000000000017e40 < z < 7.8e158

   1. Initial program 96.3%

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

      1. associate-+l+ 96.3%

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

      2. associate-*l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in z around 0 70.9%

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

      1. +-commutative 70.9%

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

   7. Simplified 70.9%

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

   if 8.2000000000000003e278 < z

   1. Initial program 78.6%

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

      1. associate-+l+ 78.6%

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

      2. associate-*l* 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in y around inf 89.5%

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

      1. *-commutative 89.5%

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

   7. Simplified 89.5%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+158}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+278}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 9.5 \cdot 10^{+214}:\\ \;\;\;\;\left(x + z \cdot y\right) + \left(a \cdot t + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 9.5e+214)
   (+ (+ x (* z y)) (+ (* a t) (* a (* z b))))
   (* z (+ y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 9.5e+214) {
		tmp = (x + (z * y)) + ((a * t) + (a * (z * b)));
	} else {
		tmp = z * (y + (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 <= 9.5d+214) then
        tmp = (x + (z * y)) + ((a * t) + (a * (z * b)))
    else
        tmp = z * (y + (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 <= 9.5e+214) {
		tmp = (x + (z * y)) + ((a * t) + (a * (z * b)));
	} else {
		tmp = z * (y + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 9.5e+214:
		tmp = (x + (z * y)) + ((a * t) + (a * (z * b)))
	else:
		tmp = z * (y + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 9.5e+214)
		tmp = Float64(Float64(x + Float64(z * y)) + Float64(Float64(a * t) + Float64(a * Float64(z * b))));
	else
		tmp = Float64(z * Float64(y + Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 9.5e+214)
		tmp = (x + (z * y)) + ((a * t) + (a * (z * b)));
	else
		tmp = z * (y + (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 9.5e+214], N[(N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 9.49999999999999921e214

   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* 96.2%

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

   3. Simplified 96.2%

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

   if 9.49999999999999921e214 < z

   1. Initial program 78.1%

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

      1. associate-+l+ 78.1%

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

      2. associate-*l* 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in z around inf 95.6%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 9.5 \cdot 10^{+214}:\\ \;\;\;\;\left(x + z \cdot y\right) + \left(a \cdot t + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+98} \lor \neg \left(z \leq 1.05 \cdot 10^{+174}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.35e+98) (not (<= z 1.05e+174)))
   (* 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 <= -2.35e+98) || !(z <= 1.05e+174)) {
		tmp = 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 <= (-2.35d+98)) .or. (.not. (z <= 1.05d+174))) then
        tmp = 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 <= -2.35e+98) || !(z <= 1.05e+174)) {
		tmp = 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 <= -2.35e+98) or not (z <= 1.05e+174):
		tmp = 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 <= -2.35e+98) || !(z <= 1.05e+174))
		tmp = 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 <= -2.35e+98) || ~((z <= 1.05e+174)))
		tmp = 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, -2.35e+98], N[Not[LessEqual[z, 1.05e+174]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $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 < -2.34999999999999985e98 or 1.05000000000000008e174 < z

   1. Initial program 84.0%

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

      1. associate-+l+ 84.0%

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

      2. associate-*l* 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in z around inf 86.5%

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

   if -2.34999999999999985e98 < z < 1.05000000000000008e174

   1. Initial program 96.6%

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

      1. associate-+l+ 96.6%

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

      2. +-commutative 96.6%

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

      3. fma-define 96.6%

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

      4. associate-*l* 97.7%

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

      5. *-commutative 97.7%

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

      6. *-commutative 97.7%

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

      7. distribute-rgt-out 98.3%

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

      8. *-commutative 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in y around 0 88.2%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+98} \lor \neg \left(z \leq 1.05 \cdot 10^{+174}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+40} \lor \neg \left(z \leq 5.4 \cdot 10^{+26}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.85e+40) (not (<= z 5.4e+26)))
   (* z (+ y (* a b)))
   (+ x (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.85e+40) || !(z <= 5.4e+26)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.85d+40)) .or. (.not. (z <= 5.4d+26))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + (a * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.85e+40) || !(z <= 5.4e+26)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.85e+40) or not (z <= 5.4e+26):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (a * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.85e+40) || !(z <= 5.4e+26))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(a * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.85e+40) || ~((z <= 5.4e+26)))
		tmp = z * (y + (a * b));
	else
		tmp = x + (a * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.85e+40], N[Not[LessEqual[z, 5.4e+26]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85e40 or 5.4e26 < z

   1. Initial program 85.4%

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

      1. associate-+l+ 85.4%

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

      2. associate-*l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in z around inf 76.9%

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

   if -1.85e40 < z < 5.4e26

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 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. Add Preprocessing

   5. Taylor expanded in z around 0 77.3%

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

      1. +-commutative 77.3%

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

   7. Simplified 77.3%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+40} \lor \neg \left(z \leq 5.4 \cdot 10^{+26}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+49}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.5e+72) x (if (<= x 6e+49) (* a t) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.5e+72) {
		tmp = x;
	} else if (x <= 6e+49) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-4.5d+72)) then
        tmp = x
    else if (x <= 6d+49) then
        tmp = a * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.5e+72) {
		tmp = x;
	} else if (x <= 6e+49) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.5e+72:
		tmp = x
	elif x <= 6e+49:
		tmp = a * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.5e+72)
		tmp = x;
	elseif (x <= 6e+49)
		tmp = Float64(a * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.5e+72)
		tmp = x;
	elseif (x <= 6e+49)
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.5e+72], x, If[LessEqual[x, 6e+49], N[(a * t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.4999999999999998e72 or 6.0000000000000005e49 < x

   1. Initial program 91.6%

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

      1. associate-+l+ 91.6%

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

      2. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in x around inf 56.8%

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

   if -4.4999999999999998e72 < x < 6.0000000000000005e49

   1. Initial program 93.2%

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

      1. associate-+l+ 93.2%

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

      2. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in t around inf 38.5%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+49}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 26.1% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 92.6%

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

   1. associate-+l+ 92.6%

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

   2. associate-*l* 94.2%

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

3. Simplified 94.2%

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

5. Taylor expanded in x around inf 25.9%

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

6. Final simplification 25.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.7% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024047 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (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)))