Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.2% → 96.5%

Time: 3.5s

Alternatives: 12

Speedup: 0.3×

• 31.8% 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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(b, z, t\right), a, z \cdot y\right)\\ t_2 := \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 6 \cdot 10^{+304}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (fma b z t) a (* z y)))
        (t_2 (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b))))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 6e+304) t_2 t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(fma(b, z, t), a, (z * y));
	double t_2 = ((x + (y * z)) + (t * a)) + ((a * z) * b);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 6e+304) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(fma(b, z, t), a, Float64(z * y))
	t_2 = Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(a * z) * b))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 6e+304)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * z + t), $MachinePrecision] * a + N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 6e+304], t$95$2, t$95$1]]]]

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 or 5.9999999999999996e304 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 78.1%

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

   2. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. distribute-lft-in N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 90.6

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

   4. Applied rewrites 90.6%

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

   if -inf.0 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < 5.9999999999999996e304

   1. Initial program 99.5%

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

Alternative 2: 88.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(b, z, t\right), a, z \cdot y\right)\\ t_2 := \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ t_3 := \mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+92}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2.5 \cdot 10^{+97}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(b, a, y\right), z, x\right)}{t} + a\right) \cdot t\\ \mathbf{elif}\;t\_2 \leq 6 \cdot 10^{+304}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (fma b z t) a (* z y)))
        (t_2 (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))
        (t_3 (fma a t (fma z y x))))
   (if (<= t_2 -2e+304)
     t_1
     (if (<= t_2 -1e+92)
       t_3
       (if (<= t_2 2.5e+97)
         (* (+ (/ (fma (fma b a y) z x) t) a) t)
         (if (<= t_2 6e+304) t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(fma(b, z, t), a, (z * y));
	double t_2 = ((x + (y * z)) + (t * a)) + ((a * z) * b);
	double t_3 = fma(a, t, fma(z, y, x));
	double tmp;
	if (t_2 <= -2e+304) {
		tmp = t_1;
	} else if (t_2 <= -1e+92) {
		tmp = t_3;
	} else if (t_2 <= 2.5e+97) {
		tmp = ((fma(fma(b, a, y), z, x) / t) + a) * t;
	} else if (t_2 <= 6e+304) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(fma(b, z, t), a, Float64(z * y))
	t_2 = Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(a * z) * b))
	t_3 = fma(a, t, fma(z, y, x))
	tmp = 0.0
	if (t_2 <= -2e+304)
		tmp = t_1;
	elseif (t_2 <= -1e+92)
		tmp = t_3;
	elseif (t_2 <= 2.5e+97)
		tmp = Float64(Float64(Float64(fma(fma(b, a, y), z, x) / t) + a) * t);
	elseif (t_2 <= 6e+304)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * z + t), $MachinePrecision] * a + N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(a * z), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * t + N[(z * y + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+304], t$95$1, If[LessEqual[t$95$2, -1e+92], t$95$3, If[LessEqual[t$95$2, 2.5e+97], N[(N[(N[(N[(N[(b * a + y), $MachinePrecision] * z + x), $MachinePrecision] / t), $MachinePrecision] + a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$2, 6e+304], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < -1.9999999999999999e304 or 5.9999999999999996e304 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 78.4%

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

   2. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. distribute-lft-in N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 90.2

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

   4. Applied rewrites 90.2%

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

   if -1.9999999999999999e304 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < -1e92 or 2.49999999999999999e97 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < 5.9999999999999996e304

   1. Initial program 99.9%

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

   2. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 84.5

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

   4. Applied rewrites 84.5%

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

   if -1e92 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < 2.49999999999999999e97

   1. Initial program 98.7%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. div-add-rev N/A

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

      3. div-add N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 94.7%

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

Alternative 3: 87.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(b, z, t\right), a, z \cdot y\right)\\ t_2 := \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 6 \cdot 10^{+304}:\\ \;\;\;\;\mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (fma b z t) a (* z y)))
        (t_2 (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b))))
   (if (<= t_2 -2e+304) t_1 (if (<= t_2 6e+304) (fma a t (fma z y x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(fma(b, z, t), a, (z * y));
	double t_2 = ((x + (y * z)) + (t * a)) + ((a * z) * b);
	double tmp;
	if (t_2 <= -2e+304) {
		tmp = t_1;
	} else if (t_2 <= 6e+304) {
		tmp = fma(a, t, fma(z, y, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(fma(b, z, t), a, Float64(z * y))
	t_2 = Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(a * z) * b))
	tmp = 0.0
	if (t_2 <= -2e+304)
		tmp = t_1;
	elseif (t_2 <= 6e+304)
		tmp = fma(a, t, fma(z, y, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * z + t), $MachinePrecision] * a + N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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$2, -2e+304], t$95$1, If[LessEqual[t$95$2, 6e+304], N[(a * t + N[(z * y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

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 or 5.9999999999999996e304 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 78.4%

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

   2. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. distribute-lft-in N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 90.2

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

   4. Applied rewrites 90.2%

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

   if -1.9999999999999999e304 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < 5.9999999999999996e304

   1. Initial program 99.5%

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

   2. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 85.4

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

   4. Applied rewrites 85.4%

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

Alternative 4: 82.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, a, y\right) \cdot z\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (fma b a y) z)))
   (if (<= z -9.8e+20) t_1 (if (<= z 1.35e+112) (fma a t (fma z y x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(b, a, y) * z;
	double tmp;
	if (z <= -9.8e+20) {
		tmp = t_1;
	} else if (z <= 1.35e+112) {
		tmp = fma(a, t, fma(z, y, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(b, a, y) * z)
	tmp = 0.0
	if (z <= -9.8e+20)
		tmp = t_1;
	elseif (z <= 1.35e+112)
		tmp = fma(a, t, fma(z, y, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * a + y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -9.8e+20], t$95$1, If[LessEqual[z, 1.35e+112], N[(a * t + N[(z * y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.8e20 or 1.3500000000000001e112 < z

   1. Initial program 83.6%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 79.2

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

   4. Applied rewrites 79.2%

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

   if -9.8e20 < z < 1.3500000000000001e112

   1. Initial program 97.8%

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

   2. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 85.2

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

   4. Applied rewrites 85.2%

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

Alternative 5: 72.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, a, y\right) \cdot z\\ \mathbf{if}\;z \leq -760000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-151}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (fma b a y) z)))
   (if (<= z -760000000.0)
     t_1
     (if (<= z 3.9e-151) (fma a t x) (if (<= z 6e+85) (fma z y x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(b, a, y) * z;
	double tmp;
	if (z <= -760000000.0) {
		tmp = t_1;
	} else if (z <= 3.9e-151) {
		tmp = fma(a, t, x);
	} else if (z <= 6e+85) {
		tmp = fma(z, y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(b, a, y) * z)
	tmp = 0.0
	if (z <= -760000000.0)
		tmp = t_1;
	elseif (z <= 3.9e-151)
		tmp = fma(a, t, x);
	elseif (z <= 6e+85)
		tmp = fma(z, y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * a + y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -760000000.0], t$95$1, If[LessEqual[z, 3.9e-151], N[(a * t + x), $MachinePrecision], If[LessEqual[z, 6e+85], N[(z * y + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.6e8 or 6.0000000000000001e85 < z

   1. Initial program 84.5%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 77.9

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

   4. Applied rewrites 77.9%

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

   if -7.6e8 < z < 3.90000000000000007e-151

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 77.5

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

   4. Applied rewrites 77.5%

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

   if 3.90000000000000007e-151 < z < 6.0000000000000001e85

   1. Initial program 96.5%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 51.1

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

   4. Applied rewrites 51.1%

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

Alternative 6: 64.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-20}:\\ \;\;\;\;\left(a \cdot z\right) \cdot b\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.6e+78)
   (fma a t x)
   (if (<= t -6.5e+16)
     (fma z y x)
     (if (<= t -8e-20)
       (* (* a z) b)
       (if (<= t 2.55e+75) (fma z y x) (fma a t x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.6e+78) {
		tmp = fma(a, t, x);
	} else if (t <= -6.5e+16) {
		tmp = fma(z, y, x);
	} else if (t <= -8e-20) {
		tmp = (a * z) * b;
	} else if (t <= 2.55e+75) {
		tmp = fma(z, y, x);
	} else {
		tmp = fma(a, t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.6e+78)
		tmp = fma(a, t, x);
	elseif (t <= -6.5e+16)
		tmp = fma(z, y, x);
	elseif (t <= -8e-20)
		tmp = Float64(Float64(a * z) * b);
	elseif (t <= 2.55e+75)
		tmp = fma(z, y, x);
	else
		tmp = fma(a, t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.6e+78], N[(a * t + x), $MachinePrecision], If[LessEqual[t, -6.5e+16], N[(z * y + x), $MachinePrecision], If[LessEqual[t, -8e-20], N[(N[(a * z), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 2.55e+75], N[(z * y + x), $MachinePrecision], N[(a * t + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.5999999999999998e78 or 2.55000000000000018e75 < t

   1. Initial program 90.0%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 69.7

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

   4. Applied rewrites 69.7%

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

   if -7.5999999999999998e78 < t < -6.5e16 or -7.99999999999999956e-20 < t < 2.55000000000000018e75

   1. Initial program 93.6%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 61.8

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

   4. Applied rewrites 61.8%

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

   if -6.5e16 < t < -7.99999999999999956e-20

   1. Initial program 94.3%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 28.1

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

   4. Applied rewrites 28.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 28.9

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

   6. Applied rewrites 28.9%

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

Alternative 7: 63.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-20}:\\ \;\;\;\;\left(b \cdot a\right) \cdot z\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.6e+78)
   (fma a t x)
   (if (<= t -6.5e+16)
     (fma z y x)
     (if (<= t -8e-20)
       (* (* b a) z)
       (if (<= t 2.55e+75) (fma z y x) (fma a t x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.6e+78) {
		tmp = fma(a, t, x);
	} else if (t <= -6.5e+16) {
		tmp = fma(z, y, x);
	} else if (t <= -8e-20) {
		tmp = (b * a) * z;
	} else if (t <= 2.55e+75) {
		tmp = fma(z, y, x);
	} else {
		tmp = fma(a, t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.6e+78)
		tmp = fma(a, t, x);
	elseif (t <= -6.5e+16)
		tmp = fma(z, y, x);
	elseif (t <= -8e-20)
		tmp = Float64(Float64(b * a) * z);
	elseif (t <= 2.55e+75)
		tmp = fma(z, y, x);
	else
		tmp = fma(a, t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.6e+78], N[(a * t + x), $MachinePrecision], If[LessEqual[t, -6.5e+16], N[(z * y + x), $MachinePrecision], If[LessEqual[t, -8e-20], N[(N[(b * a), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t, 2.55e+75], N[(z * y + x), $MachinePrecision], N[(a * t + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.5999999999999998e78 or 2.55000000000000018e75 < t

   1. Initial program 90.0%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 69.7

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

   4. Applied rewrites 69.7%

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

   if -7.5999999999999998e78 < t < -6.5e16 or -7.99999999999999956e-20 < t < 2.55000000000000018e75

   1. Initial program 93.6%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 61.8

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

   4. Applied rewrites 61.8%

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

   if -6.5e16 < t < -7.99999999999999956e-20

   1. Initial program 94.3%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 53.5

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

   4. Applied rewrites 53.5%

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

   5. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 27.1

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

   7. Applied rewrites 27.1%

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

Alternative 8: 63.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.6e+86) (fma a t x) (if (<= t 2.55e+75) (fma z y x) (fma a t x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.6e+86) {
		tmp = fma(a, t, x);
	} else if (t <= 2.55e+75) {
		tmp = fma(z, y, x);
	} else {
		tmp = fma(a, t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.6e+86)
		tmp = fma(a, t, x);
	elseif (t <= 2.55e+75)
		tmp = fma(z, y, x);
	else
		tmp = fma(a, t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.6e+86], N[(a * t + x), $MachinePrecision], If[LessEqual[t, 2.55e+75], N[(z * y + x), $MachinePrecision], N[(a * t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5999999999999998e86 or 2.55000000000000018e75 < t

   1. Initial program 89.9%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 69.9

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

   4. Applied rewrites 69.9%

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

   if -2.5999999999999998e86 < t < 2.55000000000000018e75

   1. Initial program 93.6%

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

   2. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 61.5

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

   4. Applied rewrites 61.5%

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

Alternative 9: 59.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+57}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+163}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.8e+57) (* z y) (if (<= z 8.5e+163) (fma a t x) (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.8e+57) {
		tmp = z * y;
	} else if (z <= 8.5e+163) {
		tmp = fma(a, t, x);
	} else {
		tmp = z * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.8e+57)
		tmp = Float64(z * y);
	elseif (z <= 8.5e+163)
		tmp = fma(a, t, x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.8e+57], N[(z * y), $MachinePrecision], If[LessEqual[z, 8.5e+163], N[(a * t + x), $MachinePrecision], N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8000000000000003e57 or 8.5000000000000003e163 < 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. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 45.9

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

   4. Applied rewrites 45.9%

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

   if -5.8000000000000003e57 < z < 8.5000000000000003e163

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.9

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

   4. Applied rewrites 65.9%

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

Alternative 10: 40.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+78}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-17}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-81}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+75}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.6e+78)
   (* a t)
   (if (<= t -8.8e-17)
     (* z y)
     (if (<= t 8.2e-81) x (if (<= t 2.55e+75) (* z y) (* a t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.6e+78) {
		tmp = a * t;
	} else if (t <= -8.8e-17) {
		tmp = z * y;
	} else if (t <= 8.2e-81) {
		tmp = x;
	} else if (t <= 2.55e+75) {
		tmp = z * y;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

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 (t <= (-7.6d+78)) then
        tmp = a * t
    else if (t <= (-8.8d-17)) then
        tmp = z * y
    else if (t <= 8.2d-81) then
        tmp = x
    else if (t <= 2.55d+75) then
        tmp = z * y
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.6e+78) {
		tmp = a * t;
	} else if (t <= -8.8e-17) {
		tmp = z * y;
	} else if (t <= 8.2e-81) {
		tmp = x;
	} else if (t <= 2.55e+75) {
		tmp = z * y;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.6e+78:
		tmp = a * t
	elif t <= -8.8e-17:
		tmp = z * y
	elif t <= 8.2e-81:
		tmp = x
	elif t <= 2.55e+75:
		tmp = z * y
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.6e+78)
		tmp = Float64(a * t);
	elseif (t <= -8.8e-17)
		tmp = Float64(z * y);
	elseif (t <= 8.2e-81)
		tmp = x;
	elseif (t <= 2.55e+75)
		tmp = Float64(z * y);
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.6e+78)
		tmp = a * t;
	elseif (t <= -8.8e-17)
		tmp = z * y;
	elseif (t <= 8.2e-81)
		tmp = x;
	elseif (t <= 2.55e+75)
		tmp = z * y;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.6e+78], N[(a * t), $MachinePrecision], If[LessEqual[t, -8.8e-17], N[(z * y), $MachinePrecision], If[LessEqual[t, 8.2e-81], x, If[LessEqual[t, 2.55e+75], N[(z * y), $MachinePrecision], N[(a * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.5999999999999998e78 or 2.55000000000000018e75 < t

   1. Initial program 90.0%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 53.3

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

   4. Applied rewrites 53.3%

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

   if -7.5999999999999998e78 < t < -8.8e-17 or 8.19999999999999968e-81 < t < 2.55000000000000018e75

   1. Initial program 93.2%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 30.5

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

   4. Applied rewrites 30.5%

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

   if -8.8e-17 < t < 8.19999999999999968e-81

   1. Initial program 93.8%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 34.5%

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

Alternative 11: 40.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3900000000000:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3900000000000.0) (* a t) (if (<= t 3.3e+74) x (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3900000000000.0) {
		tmp = a * t;
	} else if (t <= 3.3e+74) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

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 (t <= (-3900000000000.0d0)) then
        tmp = a * t
    else if (t <= 3.3d+74) then
        tmp = x
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3900000000000.0) {
		tmp = a * t;
	} else if (t <= 3.3e+74) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3900000000000.0:
		tmp = a * t
	elif t <= 3.3e+74:
		tmp = x
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3900000000000.0)
		tmp = Float64(a * t);
	elseif (t <= 3.3e+74)
		tmp = x;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3900000000000.0)
		tmp = a * t;
	elseif (t <= 3.3e+74)
		tmp = x;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3900000000000.0], N[(a * t), $MachinePrecision], If[LessEqual[t, 3.3e+74], x, N[(a * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.9e12 or 3.3000000000000002e74 < t

   1. Initial program 90.3%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 50.0

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

   4. Applied rewrites 50.0%

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

   if -3.9e12 < t < 3.3000000000000002e74

   1. Initial program 93.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 32.5%

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

Alternative 12: 26.8% accurate, 21.0× 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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 26.8%

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

Reproduce

herbie shell --seed 2025115 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64
  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))