Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.5% → 99.3%

Time: 12.5s

Alternatives: 15

Speedup: 0.6×

• 32.4% 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: 92.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+21} \lor \neg \left(z \leq 5 \cdot 10^{+34}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(z \cdot b\right) + t \cdot a\right) + \left(x + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7e+21) (not (<= z 5e+34)))
   (* z (+ y (+ (/ x z) (* a (+ b (/ t z))))))
   (+ (+ (* 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 <= -7e+21) || !(z <= 5e+34)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} 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 <= (-7d+21)) .or. (.not. (z <= 5d+34))) then
        tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
    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 <= -7e+21) || !(z <= 5e+34)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} 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 <= -7e+21) or not (z <= 5e+34):
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
	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 <= -7e+21) || !(z <= 5e+34))
		tmp = Float64(z * Float64(y + Float64(Float64(x / z) + Float64(a * Float64(b + Float64(t / z))))));
	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 <= -7e+21) || ~((z <= 5e+34)))
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	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, -7e+21], N[Not[LessEqual[z, 5e+34]], $MachinePrecision]], N[(z * N[(y + N[(N[(x / z), $MachinePrecision] + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $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 < -7e21 or 4.9999999999999998e34 < z

   1. Initial program 76.2%

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

      1. associate-+l+ 76.2%

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

      2. associate-*l* 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in z around inf 95.7%

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

      1. +-commutative 95.7%

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

      2. associate-+l+ 95.7%

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

      3. +-commutative 95.7%

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

      4. associate-/l* 99.0%

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

      5. distribute-lft-out 99.9%

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

   7. Simplified 99.9%

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

   if -7e21 < z < 4.9999999999999998e34

   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* 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
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+21} \lor \neg \left(z \leq 5 \cdot 10^{+34}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(z \cdot b\right) + t \cdot a\right) + \left(x + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot a + \left(x + y \cdot z\right)\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (* t a) (+ x (* y z))) (* (* z a) b))))
   (if (<= t_1 2e+304) t_1 (* z (+ y (+ (/ x z) (* a (+ b (/ t z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t * a) + (x + (y * z))) + ((z * a) * b);
	double tmp;
	if (t_1 <= 2e+304) {
		tmp = t_1;
	} else {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t * a) + (x + (y * z))) + ((z * a) * b)
    if (t_1 <= 2d+304) then
        tmp = t_1
    else
        tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t * a) + (x + (y * z))) + ((z * a) * b);
	double tmp;
	if (t_1 <= 2e+304) {
		tmp = t_1;
	} else {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t * a) + (x + (y * z))) + ((z * a) * b)
	tmp = 0
	if t_1 <= 2e+304:
		tmp = t_1
	else:
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t * a) + Float64(x + Float64(y * z))) + Float64(Float64(z * a) * b))
	tmp = 0.0
	if (t_1 <= 2e+304)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(y + Float64(Float64(x / z) + Float64(a * Float64(b + Float64(t / z))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t * a) + (x + (y * z))) + ((z * a) * b);
	tmp = 0.0;
	if (t_1 <= 2e+304)
		tmp = t_1;
	else
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t * a), $MachinePrecision] + N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+304], t$95$1, N[(z * N[(y + N[(N[(x / z), $MachinePrecision] + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < 1.9999999999999999e304

   1. Initial program 98.6%

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

   if 1.9999999999999999e304 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 48.4%

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

      1. associate-+l+ 48.4%

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

      2. associate-*l* 66.0%

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

   3. Simplified 66.0%

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

   5. Taylor expanded in z around inf 90.0%

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

      1. +-commutative 90.0%

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

      2. associate-+l+ 90.0%

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

      3. +-commutative 90.0%

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

      4. associate-/l* 98.0%

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

      5. distribute-lft-out 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t \cdot a + \left(x + y \cdot z\right)\right) + \left(z \cdot a\right) \cdot b \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\left(t \cdot a + \left(x + y \cdot z\right)\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 39.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{+63}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -0.01:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-225}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 260:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.85e+63)
   (* t a)
   (if (<= a -0.01)
     x
     (if (<= a -9.8e-225)
       (* y z)
       (if (<= a 7.4e-56) x (if (<= a 260.0) (* a (* z b)) (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.85e+63) {
		tmp = t * a;
	} else if (a <= -0.01) {
		tmp = x;
	} else if (a <= -9.8e-225) {
		tmp = y * z;
	} else if (a <= 7.4e-56) {
		tmp = x;
	} else if (a <= 260.0) {
		tmp = a * (z * b);
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.85d+63)) then
        tmp = t * a
    else if (a <= (-0.01d0)) then
        tmp = x
    else if (a <= (-9.8d-225)) then
        tmp = y * z
    else if (a <= 7.4d-56) then
        tmp = x
    else if (a <= 260.0d0) then
        tmp = a * (z * b)
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.85e+63) {
		tmp = t * a;
	} else if (a <= -0.01) {
		tmp = x;
	} else if (a <= -9.8e-225) {
		tmp = y * z;
	} else if (a <= 7.4e-56) {
		tmp = x;
	} else if (a <= 260.0) {
		tmp = a * (z * b);
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.85e+63:
		tmp = t * a
	elif a <= -0.01:
		tmp = x
	elif a <= -9.8e-225:
		tmp = y * z
	elif a <= 7.4e-56:
		tmp = x
	elif a <= 260.0:
		tmp = a * (z * b)
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.85e+63)
		tmp = Float64(t * a);
	elseif (a <= -0.01)
		tmp = x;
	elseif (a <= -9.8e-225)
		tmp = Float64(y * z);
	elseif (a <= 7.4e-56)
		tmp = x;
	elseif (a <= 260.0)
		tmp = Float64(a * Float64(z * b));
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.85e+63)
		tmp = t * a;
	elseif (a <= -0.01)
		tmp = x;
	elseif (a <= -9.8e-225)
		tmp = y * z;
	elseif (a <= 7.4e-56)
		tmp = x;
	elseif (a <= 260.0)
		tmp = a * (z * b);
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.85e+63], N[(t * a), $MachinePrecision], If[LessEqual[a, -0.01], x, If[LessEqual[a, -9.8e-225], N[(y * z), $MachinePrecision], If[LessEqual[a, 7.4e-56], x, If[LessEqual[a, 260.0], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], N[(t * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.8500000000000001e63 or 260 < a

   1. Initial program 78.0%

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

      1. associate-+l+ 78.0%

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

      2. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in z around 0 60.9%

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

   6. Taylor expanded in x around 0 51.1%

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

   if -2.8500000000000001e63 < a < -0.0100000000000000002 or -9.79999999999999942e-225 < a < 7.4000000000000004e-56

   1. Initial program 97.5%

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

      1. associate-+l+ 97.5%

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

      2. associate-*l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in z around 0 59.4%

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

   6. Taylor expanded in x around inf 49.7%

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

   if -0.0100000000000000002 < a < -9.79999999999999942e-225

   1. Initial program 98.0%

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

      1. add-cube-cbrt 97.7%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(\sqrt[3]{a \cdot z} \cdot \sqrt[3]{a \cdot z}\right) \cdot \sqrt[3]{a \cdot z}\right)} \cdot b \]

      2. pow3 97.7%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(\sqrt[3]{a \cdot z}\right)}^{3}} \cdot b \]

      3. *-commutative 97.7%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + {\left(\sqrt[3]{\color{blue}{z \cdot a}}\right)}^{3} \cdot b \]

   4. Applied egg-rr 97.7%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(\sqrt[3]{z \cdot a}\right)}^{3}} \cdot b \]

   5. Taylor expanded in z around inf 63.7%

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

      1. +-commutative 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in a around 0 45.2%

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

      1. *-commutative 45.2%

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

   10. Simplified 45.2%

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

   if 7.4000000000000004e-56 < a < 260

   1. Initial program 91.5%

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

      1. add-cube-cbrt 91.1%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(\sqrt[3]{a \cdot z} \cdot \sqrt[3]{a \cdot z}\right) \cdot \sqrt[3]{a \cdot z}\right)} \cdot b \]

      2. pow3 91.1%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(\sqrt[3]{a \cdot z}\right)}^{3}} \cdot b \]

      3. *-commutative 91.1%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + {\left(\sqrt[3]{\color{blue}{z \cdot a}}\right)}^{3} \cdot b \]

   4. Applied egg-rr 91.1%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(\sqrt[3]{z \cdot a}\right)}^{3}} \cdot b \]

   5. Taylor expanded in z around inf 92.0%

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

      1. +-commutative 92.0%

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

   7. Simplified 92.0%

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

   8. Taylor expanded in a around inf 50.9%

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

      1. *-commutative 50.9%

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

   10. Simplified 50.9%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{+63}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -0.01:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-225}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 260:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+63}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -14.5:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-226}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-9}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -8.5e+63)
   (* t a)
   (if (<= a -14.5)
     x
     (if (<= a -1.02e-226)
       (* y z)
       (if (<= a 6.6e-104) x (if (<= a 1.5e-9) (* y z) (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -8.5e+63) {
		tmp = t * a;
	} else if (a <= -14.5) {
		tmp = x;
	} else if (a <= -1.02e-226) {
		tmp = y * z;
	} else if (a <= 6.6e-104) {
		tmp = x;
	} else if (a <= 1.5e-9) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-8.5d+63)) then
        tmp = t * a
    else if (a <= (-14.5d0)) then
        tmp = x
    else if (a <= (-1.02d-226)) then
        tmp = y * z
    else if (a <= 6.6d-104) then
        tmp = x
    else if (a <= 1.5d-9) then
        tmp = y * z
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -8.5e+63) {
		tmp = t * a;
	} else if (a <= -14.5) {
		tmp = x;
	} else if (a <= -1.02e-226) {
		tmp = y * z;
	} else if (a <= 6.6e-104) {
		tmp = x;
	} else if (a <= 1.5e-9) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -8.5e+63:
		tmp = t * a
	elif a <= -14.5:
		tmp = x
	elif a <= -1.02e-226:
		tmp = y * z
	elif a <= 6.6e-104:
		tmp = x
	elif a <= 1.5e-9:
		tmp = y * z
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -8.5e+63)
		tmp = Float64(t * a);
	elseif (a <= -14.5)
		tmp = x;
	elseif (a <= -1.02e-226)
		tmp = Float64(y * z);
	elseif (a <= 6.6e-104)
		tmp = x;
	elseif (a <= 1.5e-9)
		tmp = Float64(y * z);
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -8.5e+63)
		tmp = t * a;
	elseif (a <= -14.5)
		tmp = x;
	elseif (a <= -1.02e-226)
		tmp = y * z;
	elseif (a <= 6.6e-104)
		tmp = x;
	elseif (a <= 1.5e-9)
		tmp = y * z;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -8.5e+63], N[(t * a), $MachinePrecision], If[LessEqual[a, -14.5], x, If[LessEqual[a, -1.02e-226], N[(y * z), $MachinePrecision], If[LessEqual[a, 6.6e-104], x, If[LessEqual[a, 1.5e-9], N[(y * z), $MachinePrecision], N[(t * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.5000000000000004e63 or 1.49999999999999999e-9 < a

   1. Initial program 78.2%

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

      1. associate-+l+ 78.2%

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

      2. associate-*l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in z around 0 60.3%

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

   6. Taylor expanded in x around 0 50.6%

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

   if -8.5000000000000004e63 < a < -14.5 or -1.01999999999999998e-226 < a < 6.60000000000000004e-104

   1. Initial program 98.6%

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

      1. associate-+l+ 98.6%

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

      2. associate-*l* 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. Add Preprocessing

   5. Taylor expanded in z around 0 60.6%

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

   6. Taylor expanded in x around inf 52.4%

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

   if -14.5 < a < -1.01999999999999998e-226 or 6.60000000000000004e-104 < a < 1.49999999999999999e-9

   1. Initial program 95.7%

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

      1. add-cube-cbrt 95.4%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(\sqrt[3]{a \cdot z} \cdot \sqrt[3]{a \cdot z}\right) \cdot \sqrt[3]{a \cdot z}\right)} \cdot b \]

      2. pow3 95.4%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(\sqrt[3]{a \cdot z}\right)}^{3}} \cdot b \]

      3. *-commutative 95.4%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + {\left(\sqrt[3]{\color{blue}{z \cdot a}}\right)}^{3} \cdot b \]

   4. Applied egg-rr 95.4%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(\sqrt[3]{z \cdot a}\right)}^{3}} \cdot b \]

   5. Taylor expanded in z around inf 65.7%

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

      1. +-commutative 65.7%

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

   7. Simplified 65.7%

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

   8. Taylor expanded in a around 0 44.2%

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

      1. *-commutative 44.2%

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

   10. Simplified 44.2%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+63}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -14.5:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-226}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-9}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-109} \lor \neg \left(z \leq 1.15 \cdot 10^{-57}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6e-109) (not (<= z 1.15e-57)))
   (* z (+ y (+ (/ x z) (* a (+ b (/ t z))))))
   (+ x (+ (* t a) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6e-109) || !(z <= 1.15e-57)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} else {
		tmp = x + ((t * a) + (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 <= (-6d-109)) .or. (.not. (z <= 1.15d-57))) then
        tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
    else
        tmp = x + ((t * a) + (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 <= -6e-109) || !(z <= 1.15e-57)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} else {
		tmp = x + ((t * a) + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6e-109) or not (z <= 1.15e-57):
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
	else:
		tmp = x + ((t * a) + (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6e-109) || !(z <= 1.15e-57))
		tmp = Float64(z * Float64(y + Float64(Float64(x / z) + Float64(a * Float64(b + Float64(t / z))))));
	else
		tmp = Float64(x + Float64(Float64(t * a) + Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6e-109) || ~((z <= 1.15e-57)))
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	else
		tmp = x + ((t * a) + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6e-109], N[Not[LessEqual[z, 1.15e-57]], $MachinePrecision]], N[(z * N[(y + N[(N[(x / z), $MachinePrecision] + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000043e-109 or 1.15e-57 < z

   1. Initial program 81.4%

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

      1. associate-+l+ 81.4%

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

      2. associate-*l* 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. Add Preprocessing

   5. Taylor expanded in z around inf 95.5%

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

      1. +-commutative 95.5%

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

      2. associate-+l+ 95.5%

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

      3. +-commutative 95.5%

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

      4. associate-/l* 98.1%

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

      5. distribute-lft-out 98.7%

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

   7. Simplified 98.7%

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

   if -6.00000000000000043e-109 < z < 1.15e-57

   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* 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 93.2%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-109} \lor \neg \left(z \leq 1.15 \cdot 10^{-57}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+42}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+86}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))))
   (if (<= z -2.9e+136)
     t_1
     (if (<= z -7e+42) (* z (* a b)) (if (<= z 1.25e+86) (+ x (* t a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if (z <= -2.9e+136) {
		tmp = t_1;
	} else if (z <= -7e+42) {
		tmp = z * (a * b);
	} else if (z <= 1.25e+86) {
		tmp = x + (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * z)
    if (z <= (-2.9d+136)) then
        tmp = t_1
    else if (z <= (-7d+42)) then
        tmp = z * (a * b)
    else if (z <= 1.25d+86) then
        tmp = x + (t * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if (z <= -2.9e+136) {
		tmp = t_1;
	} else if (z <= -7e+42) {
		tmp = z * (a * b);
	} else if (z <= 1.25e+86) {
		tmp = x + (t * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	tmp = 0
	if z <= -2.9e+136:
		tmp = t_1
	elif z <= -7e+42:
		tmp = z * (a * b)
	elif z <= 1.25e+86:
		tmp = x + (t * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	tmp = 0.0
	if (z <= -2.9e+136)
		tmp = t_1;
	elseif (z <= -7e+42)
		tmp = Float64(z * Float64(a * b));
	elseif (z <= 1.25e+86)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * z);
	tmp = 0.0;
	if (z <= -2.9e+136)
		tmp = t_1;
	elseif (z <= -7e+42)
		tmp = z * (a * b);
	elseif (z <= 1.25e+86)
		tmp = x + (t * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+136], t$95$1, If[LessEqual[z, -7e+42], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+86], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.89999999999999974e136 or 1.2499999999999999e86 < z

   1. Initial program 71.5%

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

      1. associate-+l+ 71.5%

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

      2. associate-*l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in b around 0 74.1%

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

   6. Taylor expanded in a around 0 59.6%

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

      1. *-commutative 59.6%

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

   8. Simplified 59.6%

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

   if -2.89999999999999974e136 < z < -7.00000000000000047e42

   1. Initial program 87.2%

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

      1. add-cube-cbrt 86.9%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(\sqrt[3]{a \cdot z} \cdot \sqrt[3]{a \cdot z}\right) \cdot \sqrt[3]{a \cdot z}\right)} \cdot b \]

      2. pow3 86.9%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(\sqrt[3]{a \cdot z}\right)}^{3}} \cdot b \]

      3. *-commutative 86.9%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + {\left(\sqrt[3]{\color{blue}{z \cdot a}}\right)}^{3} \cdot b \]

   4. Applied egg-rr 86.9%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(\sqrt[3]{z \cdot a}\right)}^{3}} \cdot b \]

   5. Taylor expanded in z around inf 83.5%

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

      1. +-commutative 83.5%

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

   7. Simplified 83.5%

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

   8. Taylor expanded in a around inf 51.5%

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

      1. associate-*r* 59.4%

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

      2. *-commutative 59.4%

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

   10. Simplified 59.4%

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

   if -7.00000000000000047e42 < z < 1.2499999999999999e86

   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. Add Preprocessing

   5. Taylor expanded in z around 0 76.3%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+136}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+42}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+86}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+138}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+140}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.9e+138)
   (* y z)
   (if (<= z -1.22e+36)
     (* z (* a b))
     (if (<= z 5e+140) (+ x (* t a)) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.9e+138) {
		tmp = y * z;
	} else if (z <= -1.22e+36) {
		tmp = z * (a * b);
	} else if (z <= 5e+140) {
		tmp = x + (t * a);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.9d+138)) then
        tmp = y * z
    else if (z <= (-1.22d+36)) then
        tmp = z * (a * b)
    else if (z <= 5d+140) then
        tmp = x + (t * a)
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.9e+138) {
		tmp = y * z;
	} else if (z <= -1.22e+36) {
		tmp = z * (a * b);
	} else if (z <= 5e+140) {
		tmp = x + (t * a);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.9e+138:
		tmp = y * z
	elif z <= -1.22e+36:
		tmp = z * (a * b)
	elif z <= 5e+140:
		tmp = x + (t * a)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.9e+138)
		tmp = Float64(y * z);
	elseif (z <= -1.22e+36)
		tmp = Float64(z * Float64(a * b));
	elseif (z <= 5e+140)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.9e+138)
		tmp = y * z;
	elseif (z <= -1.22e+36)
		tmp = z * (a * b);
	elseif (z <= 5e+140)
		tmp = x + (t * a);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.9e+138], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.22e+36], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+140], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9000000000000001e138 or 5.00000000000000008e140 < z

   1. Initial program 69.5%

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

      1. add-cube-cbrt 69.4%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(\sqrt[3]{a \cdot z} \cdot \sqrt[3]{a \cdot z}\right) \cdot \sqrt[3]{a \cdot z}\right)} \cdot b \]

      2. pow3 69.4%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(\sqrt[3]{a \cdot z}\right)}^{3}} \cdot b \]

      3. *-commutative 69.4%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + {\left(\sqrt[3]{\color{blue}{z \cdot a}}\right)}^{3} \cdot b \]

   4. Applied egg-rr 69.4%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(\sqrt[3]{z \cdot a}\right)}^{3}} \cdot b \]

   5. Taylor expanded in z around inf 83.0%

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

      1. +-commutative 83.0%

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

   7. Simplified 83.0%

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

   8. Taylor expanded in a around 0 58.0%

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

      1. *-commutative 58.0%

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

   10. Simplified 58.0%

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

   if -2.9000000000000001e138 < z < -1.21999999999999995e36

   1. Initial program 87.2%

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

      1. add-cube-cbrt 86.9%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(\sqrt[3]{a \cdot z} \cdot \sqrt[3]{a \cdot z}\right) \cdot \sqrt[3]{a \cdot z}\right)} \cdot b \]

      2. pow3 86.9%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(\sqrt[3]{a \cdot z}\right)}^{3}} \cdot b \]

      3. *-commutative 86.9%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + {\left(\sqrt[3]{\color{blue}{z \cdot a}}\right)}^{3} \cdot b \]

   4. Applied egg-rr 86.9%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(\sqrt[3]{z \cdot a}\right)}^{3}} \cdot b \]

   5. Taylor expanded in z around inf 83.5%

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

      1. +-commutative 83.5%

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

   7. Simplified 83.5%

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

   8. Taylor expanded in a around inf 51.5%

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

      1. associate-*r* 59.4%

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

      2. *-commutative 59.4%

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

   10. Simplified 59.4%

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

   if -1.21999999999999995e36 < z < 5.00000000000000008e140

   1. Initial program 98.1%

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

      1. associate-+l+ 98.1%

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

      2. associate-*l* 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. Add Preprocessing

   5. Taylor expanded in z around 0 73.7%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+138}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+140}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+19} \lor \neg \left(z \leq 1.5 \cdot 10^{-14}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.5e+19) (not (<= z 1.5e-14)))
   (+ 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 <= -6.5e+19) || !(z <= 1.5e-14)) {
		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 <= (-6.5d+19)) .or. (.not. (z <= 1.5d-14))) 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 <= -6.5e+19) || !(z <= 1.5e-14)) {
		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 <= -6.5e+19) or not (z <= 1.5e-14):
		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 <= -6.5e+19) || !(z <= 1.5e-14))
		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 <= -6.5e+19) || ~((z <= 1.5e-14)))
		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, -6.5e+19], N[Not[LessEqual[z, 1.5e-14]], $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 < -6.5e19 or 1.4999999999999999e-14 < z

   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* 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in t around 0 71.8%

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

      1. +-commutative 71.8%

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

      2. associate-*r* 77.7%

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

      3. distribute-rgt-in 85.4%

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

   7. Simplified 85.4%

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

   if -6.5e19 < z < 1.4999999999999999e-14

   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. +-commutative 100.0%

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

      3. fma-define 100.0%

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

      4. associate-*l* 100.0%

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

      5. *-commutative 100.0%

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

      6. *-commutative 100.0%

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

      7. distribute-rgt-out 100.0%

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

      8. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 88.7%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+19} \lor \neg \left(z \leq 1.5 \cdot 10^{-14}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+29} \lor \neg \left(z \leq 1.35 \cdot 10^{+140}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.2e+29) (not (<= z 1.35e+140)))
   (* 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 <= -1.2e+29) || !(z <= 1.35e+140)) {
		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 <= (-1.2d+29)) .or. (.not. (z <= 1.35d+140))) 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 <= -1.2e+29) || !(z <= 1.35e+140)) {
		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 <= -1.2e+29) or not (z <= 1.35e+140):
		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 <= -1.2e+29) || !(z <= 1.35e+140))
		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 <= -1.2e+29) || ~((z <= 1.35e+140)))
		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, -1.2e+29], N[Not[LessEqual[z, 1.35e+140]], $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 < -1.2e29 or 1.35000000000000009e140 < z

   1. Initial program 74.1%

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

      1. associate-+l+ 74.1%

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

      2. associate-*l* 79.1%

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

   3. Simplified 79.1%

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

   5. Taylor expanded in z around inf 83.3%

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

   if -1.2e29 < z < 1.35000000000000009e140

   1. Initial program 98.1%

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

      1. associate-+l+ 98.1%

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

      2. +-commutative 98.1%

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

      3. fma-define 98.1%

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

      4. associate-*l* 97.4%

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

      5. *-commutative 97.4%

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

      6. *-commutative 97.4%

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

      7. distribute-rgt-out 98.7%

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

      8. *-commutative 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around 0 85.5%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+29} \lor \neg \left(z \leq 1.35 \cdot 10^{+140}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+107}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+17}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.8e+107)
   (+ x (* a (+ t (* z b))))
   (if (<= b 8.5e+17) (+ x (+ (* t a) (* y z))) (+ x (* z (+ y (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.8e+107) {
		tmp = x + (a * (t + (z * b)));
	} else if (b <= 8.5e+17) {
		tmp = x + ((t * a) + (y * z));
	} else {
		tmp = x + (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 (b <= (-2.8d+107)) then
        tmp = x + (a * (t + (z * b)))
    else if (b <= 8.5d+17) then
        tmp = x + ((t * a) + (y * z))
    else
        tmp = x + (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 (b <= -2.8e+107) {
		tmp = x + (a * (t + (z * b)));
	} else if (b <= 8.5e+17) {
		tmp = x + ((t * a) + (y * z));
	} else {
		tmp = x + (z * (y + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.8e+107:
		tmp = x + (a * (t + (z * b)))
	elif b <= 8.5e+17:
		tmp = x + ((t * a) + (y * z))
	else:
		tmp = x + (z * (y + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.8e+107)
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	elseif (b <= 8.5e+17)
		tmp = Float64(x + Float64(Float64(t * a) + Float64(y * z)));
	else
		tmp = Float64(x + 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 (b <= -2.8e+107)
		tmp = x + (a * (t + (z * b)));
	elseif (b <= 8.5e+17)
		tmp = x + ((t * a) + (y * z));
	else
		tmp = x + (z * (y + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.8e+107], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e+17], N[(x + N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.79999999999999985e107

   1. Initial program 87.4%

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

      1. associate-+l+ 87.4%

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

      2. +-commutative 87.4%

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

      3. fma-define 87.4%

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

      4. associate-*l* 78.1%

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

      5. *-commutative 78.1%

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

      6. *-commutative 78.1%

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

      7. distribute-rgt-out 83.1%

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

      8. *-commutative 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in y around 0 80.7%

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

   if -2.79999999999999985e107 < b < 8.5e17

   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. associate-+l+ 88.7%

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

      2. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in b around 0 93.1%

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

   if 8.5e17 < b

   1. Initial program 89.8%

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

      1. associate-+l+ 89.8%

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

      2. associate-*l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in t around 0 75.9%

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

      1. +-commutative 75.9%

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

      2. associate-*r* 82.5%

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

      3. distribute-rgt-in 88.3%

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

   7. Simplified 88.3%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+107}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+17}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 40.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+140}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-49}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.05e+140)
   (* y z)
   (if (<= z -1.65e-49) (* z (* a b)) (if (<= z 1.55e-13) x (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.05e+140) {
		tmp = y * z;
	} else if (z <= -1.65e-49) {
		tmp = z * (a * b);
	} else if (z <= 1.55e-13) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.05d+140)) then
        tmp = y * z
    else if (z <= (-1.65d-49)) then
        tmp = z * (a * b)
    else if (z <= 1.55d-13) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.05e+140) {
		tmp = y * z;
	} else if (z <= -1.65e-49) {
		tmp = z * (a * b);
	} else if (z <= 1.55e-13) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.05e+140:
		tmp = y * z
	elif z <= -1.65e-49:
		tmp = z * (a * b)
	elif z <= 1.55e-13:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.05e+140)
		tmp = Float64(y * z);
	elseif (z <= -1.65e-49)
		tmp = Float64(z * Float64(a * b));
	elseif (z <= 1.55e-13)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.05e+140)
		tmp = y * z;
	elseif (z <= -1.65e-49)
		tmp = z * (a * b);
	elseif (z <= 1.55e-13)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.05e+140], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.65e-49], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-13], x, N[(y * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0499999999999999e140 or 1.55e-13 < z

   1. Initial program 75.2%

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

      1. add-cube-cbrt 75.0%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(\sqrt[3]{a \cdot z} \cdot \sqrt[3]{a \cdot z}\right) \cdot \sqrt[3]{a \cdot z}\right)} \cdot b \]

      2. pow3 75.0%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(\sqrt[3]{a \cdot z}\right)}^{3}} \cdot b \]

      3. *-commutative 75.0%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + {\left(\sqrt[3]{\color{blue}{z \cdot a}}\right)}^{3} \cdot b \]

   4. Applied egg-rr 75.0%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(\sqrt[3]{z \cdot a}\right)}^{3}} \cdot b \]

   5. Taylor expanded in z around inf 76.5%

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

      1. +-commutative 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in a around 0 50.1%

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

      1. *-commutative 50.1%

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

   10. Simplified 50.1%

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

   if -2.0499999999999999e140 < z < -1.65e-49

   1. Initial program 89.4%

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

      1. add-cube-cbrt 89.1%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(\sqrt[3]{a \cdot z} \cdot \sqrt[3]{a \cdot z}\right) \cdot \sqrt[3]{a \cdot z}\right)} \cdot b \]

      2. pow3 89.2%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(\sqrt[3]{a \cdot z}\right)}^{3}} \cdot b \]

      3. *-commutative 89.2%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + {\left(\sqrt[3]{\color{blue}{z \cdot a}}\right)}^{3} \cdot b \]

   4. Applied egg-rr 89.2%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{{\left(\sqrt[3]{z \cdot a}\right)}^{3}} \cdot b \]

   5. Taylor expanded in z around inf 76.5%

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

      1. +-commutative 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in a around inf 46.7%

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

      1. associate-*r* 53.2%

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

      2. *-commutative 53.2%

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

   10. Simplified 53.2%

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

   if -1.65e-49 < z < 1.55e-13

   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* 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 z around 0 81.2%

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

   6. Taylor expanded in x around inf 42.9%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+140}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-49}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+38} \lor \neg \left(z \leq 3.1 \cdot 10^{+41}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.8e+38) (not (<= z 3.1e+41)))
   (* 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 <= -3.8e+38) || !(z <= 3.1e+41)) {
		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 <= (-3.8d+38)) .or. (.not. (z <= 3.1d+41))) 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 <= -3.8e+38) || !(z <= 3.1e+41)) {
		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 <= -3.8e+38) or not (z <= 3.1e+41):
		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 <= -3.8e+38) || !(z <= 3.1e+41))
		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 <= -3.8e+38) || ~((z <= 3.1e+41)))
		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, -3.8e+38], N[Not[LessEqual[z, 3.1e+41]], $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 < -3.7999999999999998e38 or 3.1e41 < z

   1. Initial program 76.2%

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

      1. associate-+l+ 76.2%

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

      2. associate-*l* 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in z around inf 79.7%

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

   if -3.7999999999999998e38 < z < 3.1e41

   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* 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 z around 0 79.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+38} \lor \neg \left(z \leq 3.1 \cdot 10^{+41}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+76} \lor \neg \left(a \leq 5 \cdot 10^{-13}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.15e+76) (not (<= a 5e-13)))
   (* 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 <= -1.15e+76) || !(a <= 5e-13)) {
		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 <= (-1.15d+76)) .or. (.not. (a <= 5d-13))) 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 <= -1.15e+76) || !(a <= 5e-13)) {
		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 <= -1.15e+76) or not (a <= 5e-13):
		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 <= -1.15e+76) || !(a <= 5e-13))
		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 <= -1.15e+76) || ~((a <= 5e-13)))
		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, -1.15e+76], N[Not[LessEqual[a, 5e-13]], $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 < -1.15000000000000001e76 or 4.9999999999999999e-13 < a

   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. +-commutative 78.6%

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

      3. fma-define 78.6%

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

      4. associate-*l* 88.7%

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

      5. *-commutative 88.7%

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

      6. *-commutative 88.7%

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

      7. distribute-rgt-out 94.7%

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

      8. *-commutative 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in y around 0 85.0%

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

   6. Taylor expanded in x around 0 75.2%

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

   if -1.15000000000000001e76 < a < 4.9999999999999999e-13

   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* 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in b around 0 84.2%

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

   6. Taylor expanded in a around 0 72.6%

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

      1. *-commutative 72.6%

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

   8. Simplified 72.6%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+76} \lor \neg \left(a \leq 5 \cdot 10^{-13}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 38.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+62} \lor \neg \left(a \leq 8.5 \cdot 10^{-56}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1e+62) (not (<= a 8.5e-56))) (* t a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1e+62) || !(a <= 8.5e-56)) {
		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 ((a <= (-1d+62)) .or. (.not. (a <= 8.5d-56))) 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 ((a <= -1e+62) || !(a <= 8.5e-56)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1e+62) or not (a <= 8.5e-56):
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1e+62) || !(a <= 8.5e-56))
		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 ((a <= -1e+62) || ~((a <= 8.5e-56)))
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1e+62], N[Not[LessEqual[a, 8.5e-56]], $MachinePrecision]], N[(t * a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.00000000000000004e62 or 8.49999999999999932e-56 < a

   1. Initial program 79.3%

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

      1. associate-+l+ 79.3%

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

      2. associate-*l* 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in z around 0 56.0%

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

   6. Taylor expanded in x around 0 47.1%

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

   if -1.00000000000000004e62 < a < 8.49999999999999932e-56

   1. Initial program 97.7%

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

      1. associate-+l+ 97.7%

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

      2. associate-*l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in z around 0 50.2%

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

   6. Taylor expanded in x around inf 39.2%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+62} \lor \neg \left(a \leq 8.5 \cdot 10^{-56}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 26.8% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.8%

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

   1. associate-+l+ 88.8%

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

   2. associate-*l* 90.4%

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

3. Simplified 90.4%

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

5. Taylor expanded in z around 0 53.0%

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

6. Taylor expanded in x around inf 25.2%

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

Developer Target 1: 97.6% 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 2024146 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -11820553527347888000) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 47589743188364287/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a))))))

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