Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.0% → 96.5%
Time: 3.9s
Alternatives: 11
Speedup: 0.5×

Specification

?
\[\begin{array}{l} \\ \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))
double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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

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);
}

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

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

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

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]

\begin{array}{l}

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

Sampling outcomes in binary64 precision:

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Accuracy vs Speed?

Herbie found 11 alternatives:

AlternativeAccuracySpeedup
The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Initial Program: 92.0% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))
double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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

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);
}

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

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

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

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]

\begin{array}{l}

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

Alternative 1: 96.5% accurate, 0.5× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y\right) \cdot z\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b))))
   (if (<= t_1 INFINITY) t_1 (* (fma b a y) z))))
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (y * z)) + (t * a)) + ((a * z) * b);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(b, a, y) * z;
	}
	return tmp;
}

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

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

\begin{array}{l}

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

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(b, a, y\right) \cdot z\\


\end{array}
\end{array}
Derivation
  1. Split input into 2 regimes

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

    1. Initial program 94.7%

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

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

    1. Initial program 0.0%

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

    3. Taylor expanded in z around inf

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

      1. *-commutativeN/A

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

      2. lower-*.f64N/A

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

      3. +-commutativeN/A

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

      4. *-commutativeN/A

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

      5. lower-fma.f6494.4

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

    5. Applied rewrites94.4%

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

Alternative 2: 60.7% accurate, 0.9× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+200}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-15}:\\ \;\;\;\;\left(b \cdot z\right) \cdot a\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+212}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot z\right) \cdot b\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.55e+200)
   (fma a t x)
   (if (<= a -1.85e-15)
     (* (* b z) a)
     (if (<= a 2.5e+75)
       (fma z y x)
       (if (<= a 3.8e+212) (fma a t x) (* (* a z) b))))))
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.55e+200) {
		tmp = fma(a, t, x);
	} else if (a <= -1.85e-15) {
		tmp = (b * z) * a;
	} else if (a <= 2.5e+75) {
		tmp = fma(z, y, x);
	} else if (a <= 3.8e+212) {
		tmp = fma(a, t, x);
	} else {
		tmp = (a * z) * b;
	}
	return tmp;
}

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.55e+200)
		tmp = fma(a, t, x);
	elseif (a <= -1.85e-15)
		tmp = Float64(Float64(b * z) * a);
	elseif (a <= 2.5e+75)
		tmp = fma(z, y, x);
	elseif (a <= 3.8e+212)
		tmp = fma(a, t, x);
	else
		tmp = Float64(Float64(a * z) * b);
	end
	return tmp
end

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.55e+200], N[(a * t + x), $MachinePrecision], If[LessEqual[a, -1.85e-15], N[(N[(b * z), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[a, 2.5e+75], N[(z * y + x), $MachinePrecision], If[LessEqual[a, 3.8e+212], N[(a * t + x), $MachinePrecision], N[(N[(a * z), $MachinePrecision] * b), $MachinePrecision]]]]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;a \leq -1.55 \cdot 10^{+200}:\\
\;\;\;\;\mathsf{fma}\left(a, t, x\right)\\

\mathbf{elif}\;a \leq -1.85 \cdot 10^{-15}:\\
\;\;\;\;\left(b \cdot z\right) \cdot a\\

\mathbf{elif}\;a \leq 2.5 \cdot 10^{+75}:\\
\;\;\;\;\mathsf{fma}\left(z, y, x\right)\\

\mathbf{elif}\;a \leq 3.8 \cdot 10^{+212}:\\
\;\;\;\;\mathsf{fma}\left(a, t, x\right)\\

\mathbf{else}:\\
\;\;\;\;\left(a \cdot z\right) \cdot b\\


\end{array}
\end{array}
Derivation
  1. Split input into 4 regimes

  2. if a < -1.54999999999999997e200 or 2.5000000000000001e75 < a < 3.79999999999999988e212

    1. Initial program 81.8%

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

    3. Taylor expanded in z around 0

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

      1. +-commutativeN/A

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

      2. lower-fma.f6469.7

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

    5. Applied rewrites69.7%

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

    if -1.54999999999999997e200 < a < -1.85000000000000008e-15

    1. Initial program 74.1%

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

    3. Taylor expanded in b around inf

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

      1. *-commutativeN/A

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

      2. lower-*.f64N/A

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

      3. lower-*.f6453.5

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

    5. Applied rewrites53.5%

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

    if -1.85000000000000008e-15 < a < 2.5000000000000001e75

    1. Initial program 98.5%

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

    3. Taylor expanded in a around 0

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

      1. +-commutativeN/A

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

      2. *-commutativeN/A

        \[\leadsto z \cdot y + x \]

      3. lower-fma.f6474.3

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

    5. Applied rewrites74.3%

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

    if 3.79999999999999988e212 < a

    1. Initial program 68.7%

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

    3. Taylor expanded in b around inf

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

      1. *-commutativeN/A

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

      2. lower-*.f64N/A

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

      3. lower-*.f6462.1

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

    5. Applied rewrites62.1%

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

      1. lift-*.f64N/A

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

      2. lift-*.f64N/A

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

      3. *-commutativeN/A

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

      4. *-commutativeN/A

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

      5. associate-*l*N/A

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

      6. lower-*.f64N/A

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

      7. lower-*.f6465.6

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

    7. Applied rewrites65.6%

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

Alternative 3: 60.7% accurate, 0.9× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot z\right) \cdot b\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+200}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+212}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a z) b)))
   (if (<= a -1.55e+200)
     (fma a t x)
     (if (<= a -1.85e-15)
       t_1
       (if (<= a 2.5e+75) (fma z y x) (if (<= a 3.8e+212) (fma a t x) t_1))))))
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * z) * b;
	double tmp;
	if (a <= -1.55e+200) {
		tmp = fma(a, t, x);
	} else if (a <= -1.85e-15) {
		tmp = t_1;
	} else if (a <= 2.5e+75) {
		tmp = fma(z, y, x);
	} else if (a <= 3.8e+212) {
		tmp = fma(a, t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * z) * b)
	tmp = 0.0
	if (a <= -1.55e+200)
		tmp = fma(a, t, x);
	elseif (a <= -1.85e-15)
		tmp = t_1;
	elseif (a <= 2.5e+75)
		tmp = fma(z, y, x);
	elseif (a <= 3.8e+212)
		tmp = fma(a, t, x);
	else
		tmp = t_1;
	end
	return tmp
end

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * z), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[a, -1.55e+200], N[(a * t + x), $MachinePrecision], If[LessEqual[a, -1.85e-15], t$95$1, If[LessEqual[a, 2.5e+75], N[(z * y + x), $MachinePrecision], If[LessEqual[a, 3.8e+212], N[(a * t + x), $MachinePrecision], t$95$1]]]]]

\begin{array}{l}

\\
\begin{array}{l}
t_1 := \left(a \cdot z\right) \cdot b\\
\mathbf{if}\;a \leq -1.55 \cdot 10^{+200}:\\
\;\;\;\;\mathsf{fma}\left(a, t, x\right)\\

\mathbf{elif}\;a \leq -1.85 \cdot 10^{-15}:\\
\;\;\;\;t\_1\\

\mathbf{elif}\;a \leq 2.5 \cdot 10^{+75}:\\
\;\;\;\;\mathsf{fma}\left(z, y, x\right)\\

\mathbf{elif}\;a \leq 3.8 \cdot 10^{+212}:\\
\;\;\;\;\mathsf{fma}\left(a, t, x\right)\\

\mathbf{else}:\\
\;\;\;\;t\_1\\


\end{array}
\end{array}
Derivation
  1. Split input into 3 regimes

  2. if a < -1.54999999999999997e200 or 2.5000000000000001e75 < a < 3.79999999999999988e212

    1. Initial program 81.8%

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

    3. Taylor expanded in z around 0

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

      1. +-commutativeN/A

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

      2. lower-fma.f6469.7

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

    5. Applied rewrites69.7%

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

    if -1.54999999999999997e200 < a < -1.85000000000000008e-15 or 3.79999999999999988e212 < a

    1. Initial program 72.1%

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

    3. Taylor expanded in b around inf

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

      1. *-commutativeN/A

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

      2. lower-*.f64N/A

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

      3. lower-*.f6456.7

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

    5. Applied rewrites56.7%

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

      1. lift-*.f64N/A

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

      2. lift-*.f64N/A

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

      3. *-commutativeN/A

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

      4. *-commutativeN/A

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

      5. associate-*l*N/A

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

      6. lower-*.f64N/A

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

      7. lower-*.f6457.7

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

    7. Applied rewrites57.7%

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

    if -1.85000000000000008e-15 < a < 2.5000000000000001e75

    1. Initial program 98.5%

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

    3. Taylor expanded in a around 0

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

      1. +-commutativeN/A

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

      2. *-commutativeN/A

        \[\leadsto z \cdot y + x \]

      3. lower-fma.f6474.3

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

    5. Applied rewrites74.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, x\right)} \]
  3. Recombined 3 regimes into one program.
  4. Add Preprocessing

Alternative 4: 86.7% accurate, 1.2× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{+95} \lor \neg \left(b \leq 8.2 \cdot 10^{+67}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(b, z, t\right), a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.9e+95) (not (<= b 8.2e+67)))
   (fma (fma b z t) a x)
   (fma a t (fma z y x))))
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.9e+95) || !(b <= 8.2e+67)) {
		tmp = fma(fma(b, z, t), a, x);
	} else {
		tmp = fma(a, t, fma(z, y, x));
	}
	return tmp;
}

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.9e+95) || !(b <= 8.2e+67))
		tmp = fma(fma(b, z, t), a, x);
	else
		tmp = fma(a, t, fma(z, y, x));
	end
	return tmp
end

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.9e+95], N[Not[LessEqual[b, 8.2e+67]], $MachinePrecision]], N[(N[(b * z + t), $MachinePrecision] * a + x), $MachinePrecision], N[(a * t + N[(z * y + x), $MachinePrecision]), $MachinePrecision]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;b \leq -3.9 \cdot 10^{+95} \lor \neg \left(b \leq 8.2 \cdot 10^{+67}\right):\\
\;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(b, z, t\right), a, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\\


\end{array}
\end{array}
Derivation
  1. Split input into 2 regimes

  2. if b < -3.8999999999999997e95 or 8.19999999999999959e67 < b

    1. Initial program 88.1%

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

    3. Taylor expanded in y around 0

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

      1. distribute-lft-inN/A

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

      2. +-commutativeN/A

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

      3. *-commutativeN/A

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

      4. lower-fma.f64N/A

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

      5. +-commutativeN/A

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

      6. lower-fma.f6487.5

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

    5. Applied rewrites87.5%

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

    if -3.8999999999999997e95 < b < 8.19999999999999959e67

    1. Initial program 88.0%

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

    3. Taylor expanded in b around 0

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

      1. +-commutativeN/A

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

      2. *-commutativeN/A

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

      3. lift-*.f64N/A

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

      4. associate-+l+N/A

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

      5. +-commutativeN/A

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

      6. lift-*.f64N/A

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

      7. *-commutativeN/A

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

      8. lower-fma.f64N/A

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

      9. +-commutativeN/A

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

      10. *-commutativeN/A

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

      11. lower-fma.f6488.8

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

    5. Applied rewrites88.8%

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

  4. Final simplification88.3%

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{+95} \lor \neg \left(b \leq 8.2 \cdot 10^{+67}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(b, z, t\right), a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\\ \end{array} \]
  5. Add Preprocessing

Alternative 5: 82.6% accurate, 1.2× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{+141}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot z, b, x\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+134}:\\ \;\;\;\;\mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y\right) \cdot z\\ \end{array} \end{array} \]
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.8e+141)
   (fma (* a z) b x)
   (if (<= b 4.8e+134) (fma a t (fma z y x)) (* (fma b a y) z))))
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.8e+141) {
		tmp = fma((a * z), b, x);
	} else if (b <= 4.8e+134) {
		tmp = fma(a, t, fma(z, y, x));
	} else {
		tmp = fma(b, a, y) * z;
	}
	return tmp;
}

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.8e+141)
		tmp = fma(Float64(a * z), b, x);
	elseif (b <= 4.8e+134)
		tmp = fma(a, t, fma(z, y, x));
	else
		tmp = Float64(fma(b, a, y) * z);
	end
	return tmp
end

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.8e+141], N[(N[(a * z), $MachinePrecision] * b + x), $MachinePrecision], If[LessEqual[b, 4.8e+134], N[(a * t + N[(z * y + x), $MachinePrecision]), $MachinePrecision], N[(N[(b * a + y), $MachinePrecision] * z), $MachinePrecision]]]

\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;b \leq -9.8 \cdot 10^{+141}:\\
\;\;\;\;\mathsf{fma}\left(a \cdot z, b, x\right)\\

\mathbf{elif}\;b \leq 4.8 \cdot 10^{+134}:\\
\;\;\;\;\mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(b, a, y\right) \cdot z\\


\end{array}
\end{array}
Derivation
  1. Split input into 3 regimes

  2. if b < -9.8000000000000002e141

    1. Initial program 87.7%

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

    3. Taylor expanded in x around inf

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

      1. Applied rewrites80.9%

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

        1. lift-+.f64N/A

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

        2. lift-*.f64N/A

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

        3. lift-*.f64N/A

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

        4. +-commutativeN/A

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

        5. lower-fma.f64N/A

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

        6. lift-*.f6480.9

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

      3. Applied rewrites80.9%

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

      if -9.8000000000000002e141 < b < 4.80000000000000011e134

      1. Initial program 88.8%

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

      3. Taylor expanded in b around 0

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

        1. +-commutativeN/A

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

        2. *-commutativeN/A

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

        3. lift-*.f64N/A

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

        4. associate-+l+N/A

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

        5. +-commutativeN/A

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

        6. lift-*.f64N/A

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

        7. *-commutativeN/A

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

        8. lower-fma.f64N/A

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

        9. +-commutativeN/A

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

        10. *-commutativeN/A

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

        11. lower-fma.f6488.4

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

      5. Applied rewrites88.4%

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

      if 4.80000000000000011e134 < b

      1. Initial program 85.0%

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

      3. Taylor expanded in z around inf

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

        1. *-commutativeN/A

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

        2. lower-*.f64N/A

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

        3. +-commutativeN/A

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

        4. *-commutativeN/A

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

        5. lower-fma.f6482.1

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

      5. Applied rewrites82.1%

        \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, y\right) \cdot z} \]
    5. Recombined 3 regimes into one program.
    6. Add Preprocessing

    Alternative 6: 74.5% accurate, 1.2× speedup?

    \[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+17} \lor \neg \left(z \leq 1.6 \cdot 10^{-68}\right):\\ \;\;\;\;\mathsf{fma}\left(b, a, y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \end{array} \end{array} \]
    (FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.5e+17) (not (<= z 1.6e-68))) (* (fma b a y) z) (fma a t x)))
    double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.5e+17) || !(z <= 1.6e-68)) {
		tmp = fma(b, a, y) * z;
	} else {
		tmp = fma(a, t, x);
	}
	return tmp;
}

    function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.5e+17) || !(z <= 1.6e-68))
		tmp = Float64(fma(b, a, y) * z);
	else
		tmp = fma(a, t, x);
	end
	return tmp
end

    code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.5e+17], N[Not[LessEqual[z, 1.6e-68]], $MachinePrecision]], N[(N[(b * a + y), $MachinePrecision] * z), $MachinePrecision], N[(a * t + x), $MachinePrecision]]

    \begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -8.5 \cdot 10^{+17} \lor \neg \left(z \leq 1.6 \cdot 10^{-68}\right):\\
\;\;\;\;\mathsf{fma}\left(b, a, y\right) \cdot z\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(a, t, x\right)\\


\end{array}
\end{array}
    Derivation
    1. Split input into 2 regimes

    2. if z < -8.5e17 or 1.5999999999999999e-68 < z

      1. Initial program 81.3%

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

      3. Taylor expanded in z around inf

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

        1. *-commutativeN/A

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

        2. lower-*.f64N/A

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

        3. +-commutativeN/A

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

        4. *-commutativeN/A

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

        5. lower-fma.f6482.5

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

      5. Applied rewrites82.5%

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

      if -8.5e17 < z < 1.5999999999999999e-68

      1. Initial program 98.1%

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

      3. Taylor expanded in z around 0

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

        1. +-commutativeN/A

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

        2. lower-fma.f6482.6

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

      5. Applied rewrites82.6%

        \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]
    3. Recombined 2 regimes into one program.

    4. Final simplification82.5%

      \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+17} \lor \neg \left(z \leq 1.6 \cdot 10^{-68}\right):\\ \;\;\;\;\mathsf{fma}\left(b, a, y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \end{array} \]
    5. Add Preprocessing

    Alternative 7: 40.1% accurate, 1.2× speedup?

    \[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+17}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-218}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-68}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]
    (FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8.5e+17)
   (* z y)
   (if (<= z 7.5e-218) x (if (<= z 1.6e-68) (* a t) (* z y)))))
    double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.5e+17) {
		tmp = z * y;
	} else if (z <= 7.5e-218) {
		tmp = x;
	} else if (z <= 1.6e-68) {
		tmp = a * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

    module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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 <= (-8.5d+17)) then
        tmp = z * y
    else if (z <= 7.5d-218) then
        tmp = x
    else if (z <= 1.6d-68) then
        tmp = a * t
    else
        tmp = z * y
    end if
    code = tmp
end function

    public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.5e+17) {
		tmp = z * y;
	} else if (z <= 7.5e-218) {
		tmp = x;
	} else if (z <= 1.6e-68) {
		tmp = a * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

    def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8.5e+17:
		tmp = z * y
	elif z <= 7.5e-218:
		tmp = x
	elif z <= 1.6e-68:
		tmp = a * t
	else:
		tmp = z * y
	return tmp

    function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.5e+17)
		tmp = Float64(z * y);
	elseif (z <= 7.5e-218)
		tmp = x;
	elseif (z <= 1.6e-68)
		tmp = Float64(a * t);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

    function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8.5e+17)
		tmp = z * y;
	elseif (z <= 7.5e-218)
		tmp = x;
	elseif (z <= 1.6e-68)
		tmp = a * t;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

    code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8.5e+17], N[(z * y), $MachinePrecision], If[LessEqual[z, 7.5e-218], x, If[LessEqual[z, 1.6e-68], N[(a * t), $MachinePrecision], N[(z * y), $MachinePrecision]]]]

    \begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -8.5 \cdot 10^{+17}:\\
\;\;\;\;z \cdot y\\

\mathbf{elif}\;z \leq 7.5 \cdot 10^{-218}:\\
\;\;\;\;x\\

\mathbf{elif}\;z \leq 1.6 \cdot 10^{-68}:\\
\;\;\;\;a \cdot t\\

\mathbf{else}:\\
\;\;\;\;z \cdot y\\


\end{array}
\end{array}
    Derivation
    1. Split input into 3 regimes

    2. if z < -8.5e17 or 1.5999999999999999e-68 < z

      1. Initial program 81.3%

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

      3. Taylor expanded in y around inf

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

        1. *-commutativeN/A

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

        2. lower-*.f6444.9

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

      5. Applied rewrites44.9%

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

      if -8.5e17 < z < 7.50000000000000011e-218

      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

      3. Taylor expanded in x around inf

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

        1. Applied rewrites47.8%

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

        if 7.50000000000000011e-218 < z < 1.5999999999999999e-68

        1. Initial program 97.0%

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

        3. Taylor expanded in t around inf

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

          1. lower-*.f6447.8

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

        5. Applied rewrites47.8%

          \[\leadsto \color{blue}{a \cdot t} \]
      5. Recombined 3 regimes into one program.
      6. Add Preprocessing

      Alternative 8: 64.0% accurate, 1.6× speedup?

      \[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-45} \lor \neg \left(z \leq 2.2 \cdot 10^{-69}\right):\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \end{array} \end{array} \]
      (FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.3e-45) (not (<= z 2.2e-69))) (fma z y x) (fma a t x)))
      double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.3e-45) || !(z <= 2.2e-69)) {
		tmp = fma(z, y, x);
	} else {
		tmp = fma(a, t, x);
	}
	return tmp;
}

      function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.3e-45) || !(z <= 2.2e-69))
		tmp = fma(z, y, x);
	else
		tmp = fma(a, t, x);
	end
	return tmp
end

      code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.3e-45], N[Not[LessEqual[z, 2.2e-69]], $MachinePrecision]], N[(z * y + x), $MachinePrecision], N[(a * t + x), $MachinePrecision]]

      \begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -2.3 \cdot 10^{-45} \lor \neg \left(z \leq 2.2 \cdot 10^{-69}\right):\\
\;\;\;\;\mathsf{fma}\left(z, y, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(a, t, x\right)\\


\end{array}
\end{array}
      Derivation
      1. Split input into 2 regimes

      2. if z < -2.29999999999999992e-45 or 2.2e-69 < z

        1. Initial program 81.9%

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

        3. Taylor expanded in a around 0

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

          1. +-commutativeN/A

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

          2. *-commutativeN/A

            \[\leadsto z \cdot y + x \]

          3. lower-fma.f6453.9

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

        5. Applied rewrites53.9%

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

        if -2.29999999999999992e-45 < z < 2.2e-69

        1. Initial program 98.9%

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

        3. Taylor expanded in z around 0

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

          1. +-commutativeN/A

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

          2. lower-fma.f6484.8

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

        5. Applied rewrites84.8%

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]
      3. Recombined 2 regimes into one program.

      4. Final simplification65.1%

        \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-45} \lor \neg \left(z \leq 2.2 \cdot 10^{-69}\right):\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \end{array} \]
      5. Add Preprocessing

      Alternative 9: 58.7% accurate, 1.6× speedup?

      \[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+96} \lor \neg \left(z \leq 1.05 \cdot 10^{-26}\right):\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \end{array} \end{array} \]
      (FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.6e+96) (not (<= z 1.05e-26))) (* z y) (fma a t x)))
      double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.6e+96) || !(z <= 1.05e-26)) {
		tmp = z * y;
	} else {
		tmp = fma(a, t, x);
	}
	return tmp;
}

      function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.6e+96) || !(z <= 1.05e-26))
		tmp = Float64(z * y);
	else
		tmp = fma(a, t, x);
	end
	return tmp
end

      code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.6e+96], N[Not[LessEqual[z, 1.05e-26]], $MachinePrecision]], N[(z * y), $MachinePrecision], N[(a * t + x), $MachinePrecision]]

      \begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;z \leq -2.6 \cdot 10^{+96} \lor \neg \left(z \leq 1.05 \cdot 10^{-26}\right):\\
\;\;\;\;z \cdot y\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(a, t, x\right)\\


\end{array}
\end{array}
      Derivation
      1. Split input into 2 regimes

      2. if z < -2.6e96 or 1.05000000000000004e-26 < z

        1. Initial program 77.9%

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

        3. Taylor expanded in y around inf

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

          1. *-commutativeN/A

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

          2. lower-*.f6448.8

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

        5. Applied rewrites48.8%

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

        if -2.6e96 < z < 1.05000000000000004e-26

        1. Initial program 97.1%

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

        3. Taylor expanded in z around 0

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

          1. +-commutativeN/A

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

          2. lower-fma.f6470.6

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

        5. Applied rewrites70.6%

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]
      3. Recombined 2 regimes into one program.

      4. Final simplification60.3%

        \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+96} \lor \neg \left(z \leq 1.05 \cdot 10^{-26}\right):\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \end{array} \]
      5. Add Preprocessing

      Alternative 10: 39.3% accurate, 1.7× speedup?

      \[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{-48} \lor \neg \left(a \leq 1.18 \cdot 10^{-60}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]
      (FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.25e-48) (not (<= a 1.18e-60))) (* a t) x))
      double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.25e-48) || !(a <= 1.18e-60)) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

      module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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 <= (-2.25d-48)) .or. (.not. (a <= 1.18d-60))) then
        tmp = a * t
    else
        tmp = x
    end if
    code = tmp
end function

      public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.25e-48) || !(a <= 1.18e-60)) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

      def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.25e-48) or not (a <= 1.18e-60):
		tmp = a * t
	else:
		tmp = x
	return tmp

      function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.25e-48) || !(a <= 1.18e-60))
		tmp = Float64(a * t);
	else
		tmp = x;
	end
	return tmp
end

      function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.25e-48) || ~((a <= 1.18e-60)))
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

      code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.25e-48], N[Not[LessEqual[a, 1.18e-60]], $MachinePrecision]], N[(a * t), $MachinePrecision], x]

      \begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;a \leq -2.25 \cdot 10^{-48} \lor \neg \left(a \leq 1.18 \cdot 10^{-60}\right):\\
\;\;\;\;a \cdot t\\

\mathbf{else}:\\
\;\;\;\;x\\


\end{array}
\end{array}
      Derivation
      1. Split input into 2 regimes

      2. if a < -2.24999999999999994e-48 or 1.17999999999999994e-60 < a

        1. Initial program 81.1%

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

        3. Taylor expanded in t around inf

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

          1. lower-*.f6439.9

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

        5. Applied rewrites39.9%

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

        if -2.24999999999999994e-48 < a < 1.17999999999999994e-60

        1. Initial program 98.1%

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

        3. Taylor expanded in x around inf

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

          1. Applied rewrites39.2%

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

        6. Final simplification39.7%

          \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{-48} \lor \neg \left(a \leq 1.18 \cdot 10^{-60}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
        7. Add Preprocessing

        Alternative 11: 26.9% accurate, 30.0× speedup?

        \[\begin{array}{l} \\ x \end{array} \]
        (FPCore (x y z t a b) :precision binary64 x)
        double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

        module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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

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

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

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

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

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

        \begin{array}{l}

\\
x
\end{array}
        Derivation

        1. Initial program 88.1%

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

        3. Taylor expanded in x around inf

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

          1. Applied rewrites23.3%

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

          Developer Target 1: 97.2% accurate, 0.8× speedup?

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

          module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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

          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;
}

          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

          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

          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

          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]]]

          \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}

          Reproduce

          ?
          herbie shell --seed 2025079 
(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)))