Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B

Percentage Accurate: 99.9% → 99.9%

Time: 7.8s

Alternatives: 13

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x + \cos y\right) - z \cdot \sin y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ x (cos y)) (* z (sin y))))

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(y));
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + cos(y)) - (z * sin(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.cos(y)) - (z * Math.sin(y));
}

Python

def code(x, y, z):
	return (x + math.cos(y)) - (z * math.sin(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + cos(y)) - (z * sin(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + \cos y\right) - z \cdot \sin y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ x (cos y)) (* z (sin y))))

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(y));
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + cos(y)) - (z * sin(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.cos(y)) - (z * Math.sin(y));
}

Python

def code(x, y, z):
	return (x + math.cos(y)) - (z * math.sin(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + cos(y)) - (z * sin(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-z, \sin y, \cos y\right) + x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (fma (- z) (sin y) (cos y)) x))

C

double code(double x, double y, double z) {
	return fma(-z, sin(y), cos(y)) + x;
}

Julia

function code(x, y, z)
	return Float64(fma(Float64(-z), sin(y), cos(y)) + x)
end

Wolfram

code[x_, y_, z_] := N[(N[((-z) * N[Sin[y], $MachinePrecision] + N[Cos[y], $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. lift--.f64 N/A

      \[\leadsto \color{blue}{\left(x + \cos y\right) - z \cdot \sin y} \]

   2. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(x + \cos y\right)} - z \cdot \sin y \]

   3. associate--l+ N/A

      \[\leadsto \color{blue}{x + \left(\cos y - z \cdot \sin y\right)} \]

   4. +-commutative N/A

      \[\leadsto \color{blue}{\left(\cos y - z \cdot \sin y\right) + x} \]

   5. lower-+.f64 N/A

      \[\leadsto \color{blue}{\left(\cos y - z \cdot \sin y\right) + x} \]

   6. lift-*.f64 N/A

      \[\leadsto \left(\cos y - \color{blue}{z \cdot \sin y}\right) + x \]

   7. fp-cancel-sub-sign-inv N/A

      \[\leadsto \color{blue}{\left(\cos y + \left(\mathsf{neg}\left(z\right)\right) \cdot \sin y\right)} + x \]

   8. +-commutative N/A

      \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \sin y + \cos y\right)} + x \]

   9. lower-fma.f64 N/A

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

   10. lower-neg.f64 99.9

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

4. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-z, \sin y, \cos y\right) + x} \]
5. Add Preprocessing

Alternative 2: 99.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -4 \cdot 10^{-10} \lor \neg \left(x \leq 1.4 \cdot 10^{-24}\right):\\ \;\;\;\;\left(x + 1\right) - t\_0\\ \mathbf{else}:\\ \;\;\;\;\cos y - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -4e-10) (not (<= x 1.4e-24)))
     (- (+ x 1.0) t_0)
     (- (cos y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double tmp;
	if ((x <= -4e-10) || !(x <= 1.4e-24)) {
		tmp = (x + 1.0) - t_0;
	} else {
		tmp = cos(y) - t_0;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * sin(y)
    if ((x <= (-4d-10)) .or. (.not. (x <= 1.4d-24))) then
        tmp = (x + 1.0d0) - t_0
    else
        tmp = cos(y) - t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double tmp;
	if ((x <= -4e-10) || !(x <= 1.4e-24)) {
		tmp = (x + 1.0) - t_0;
	} else {
		tmp = Math.cos(y) - t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	tmp = 0
	if (x <= -4e-10) or not (x <= 1.4e-24):
		tmp = (x + 1.0) - t_0
	else:
		tmp = math.cos(y) - t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	tmp = 0.0
	if ((x <= -4e-10) || !(x <= 1.4e-24))
		tmp = Float64(Float64(x + 1.0) - t_0);
	else
		tmp = Float64(cos(y) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	tmp = 0.0;
	if ((x <= -4e-10) || ~((x <= 1.4e-24)))
		tmp = (x + 1.0) - t_0;
	else
		tmp = cos(y) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -4e-10], N[Not[LessEqual[x, 1.4e-24]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000015e-10 or 1.4000000000000001e-24 < x

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \left(x + \color{blue}{1}\right) - z \cdot \sin y \]
   4. Step-by-step derivation

   5. Applied rewrites 98.1%

      \[\leadsto \left(x + \color{blue}{1}\right) - z \cdot \sin y \]

   if -4.00000000000000015e-10 < x < 1.4000000000000001e-24

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower-cos.f64 99.9

         \[\leadsto \color{blue}{\cos y} - z \cdot \sin y \]

   5. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\cos y} - z \cdot \sin y \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-10} \lor \neg \left(x \leq 1.4 \cdot 10^{-24}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+234}:\\ \;\;\;\;x - \mathsf{fma}\left(y, z, -1\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+120} \lor \neg \left(z \leq 1.06 \cdot 10^{+65}\right):\\ \;\;\;\;\left(-z\right) \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.6e+234)
   (- x (fma y z -1.0))
   (if (or (<= z -4.6e+120) (not (<= z 1.06e+65)))
     (* (- z) (sin y))
     (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.6e+234) {
		tmp = x - fma(y, z, -1.0);
	} else if ((z <= -4.6e+120) || !(z <= 1.06e+65)) {
		tmp = -z * sin(y);
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.6e+234)
		tmp = Float64(x - fma(y, z, -1.0));
	elseif ((z <= -4.6e+120) || !(z <= 1.06e+65))
		tmp = Float64(Float64(-z) * sin(y));
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.6e+234], N[(x - N[(y * z + -1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -4.6e+120], N[Not[LessEqual[z, 1.06e+65]], $MachinePrecision]], N[((-z) * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.6000000000000001e234

   1. Initial program 99.6%

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

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x + \cos y\right) - z \cdot \sin y} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x + \cos y\right)} - z \cdot \sin y \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{x + \left(\cos y - z \cdot \sin y\right)} \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\cos y - z \cdot \sin y\right) + x} \]

      5. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(\cos y - z \cdot \sin y\right) + x} \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\cos y - \color{blue}{z \cdot \sin y}\right) + x \]

      7. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(\cos y + \left(\mathsf{neg}\left(z\right)\right) \cdot \sin y\right)} + x \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \sin y + \cos y\right)} + x \]

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + -1 \cdot \left(y \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(y \cdot z\right)\right) + 1} \]

      2. associate-*r* N/A

         \[\leadsto \left(x + \color{blue}{\left(-1 \cdot y\right) \cdot z}\right) + 1 \]

      3. mul-1-neg N/A

         \[\leadsto \left(x + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot z\right) + 1 \]

      4. fp-cancel-sub-sign N/A

         \[\leadsto \color{blue}{\left(x - y \cdot z\right)} + 1 \]

      5. associate-+l- N/A

         \[\leadsto \color{blue}{x - \left(y \cdot z - 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto x - \left(y \cdot z - \color{blue}{1 \cdot 1}\right) \]

      7. fp-cancel-sub-sign N/A

         \[\leadsto x - \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(1\right)\right) \cdot 1\right)} \]

      8. metadata-eval N/A

         \[\leadsto x - \left(y \cdot z + \color{blue}{-1} \cdot 1\right) \]

      9. metadata-eval N/A

         \[\leadsto x - \left(y \cdot z + \color{blue}{-1}\right) \]

      10. lower--.f64 N/A

          \[\leadsto \color{blue}{x - \left(y \cdot z + -1\right)} \]

      11. lower-fma.f64 85.7

          \[\leadsto x - \color{blue}{\mathsf{fma}\left(y, z, -1\right)} \]

   7. Applied rewrites 85.7%

      \[\leadsto \color{blue}{x - \mathsf{fma}\left(y, z, -1\right)} \]

   if -7.6000000000000001e234 < z < -4.59999999999999985e120 or 1.06e65 < z

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \sin y\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \sin y\right)} \]

      2. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot \sin y} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot \sin y} \]

      4. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(-z\right)} \cdot \sin y \]

      5. lower-sin.f64 67.5

         \[\leadsto \left(-z\right) \cdot \color{blue}{\sin y} \]

   5. Applied rewrites 67.5%

      \[\leadsto \color{blue}{\left(-z\right) \cdot \sin y} \]

   if -4.59999999999999985e120 < z < 1.06e65

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. lower-+.f64 78.7

         \[\leadsto \color{blue}{1 + x} \]

   5. Applied rewrites 78.7%

      \[\leadsto \color{blue}{1 + x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+234}:\\ \;\;\;\;x - \mathsf{fma}\left(y, z, -1\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+120} \lor \neg \left(z \leq 1.06 \cdot 10^{+65}\right):\\ \;\;\;\;\left(-z\right) \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-99} \lor \neg \left(z \leq 5.2 \cdot 10^{-123}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \cos y\right) - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.8e-99) (not (<= z 5.2e-123)))
   (- (+ x 1.0) (* z (sin y)))
   (- (+ x (cos y)) (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.8e-99) || !(z <= 5.2e-123)) {
		tmp = (x + 1.0) - (z * sin(y));
	} else {
		tmp = (x + cos(y)) - (z * y);
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-8.8d-99)) .or. (.not. (z <= 5.2d-123))) then
        tmp = (x + 1.0d0) - (z * sin(y))
    else
        tmp = (x + cos(y)) - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.8e-99) || !(z <= 5.2e-123)) {
		tmp = (x + 1.0) - (z * Math.sin(y));
	} else {
		tmp = (x + Math.cos(y)) - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.8e-99) or not (z <= 5.2e-123):
		tmp = (x + 1.0) - (z * math.sin(y))
	else:
		tmp = (x + math.cos(y)) - (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.8e-99) || !(z <= 5.2e-123))
		tmp = Float64(Float64(x + 1.0) - Float64(z * sin(y)));
	else
		tmp = Float64(Float64(x + cos(y)) - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.8e-99) || ~((z <= 5.2e-123)))
		tmp = (x + 1.0) - (z * sin(y));
	else
		tmp = (x + cos(y)) - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.8e-99], N[Not[LessEqual[z, 5.2e-123]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.80000000000000018e-99 or 5.1999999999999999e-123 < z

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \left(x + \color{blue}{1}\right) - z \cdot \sin y \]
   4. Step-by-step derivation

   5. Applied rewrites 91.2%

      \[\leadsto \left(x + \color{blue}{1}\right) - z \cdot \sin y \]

   if -8.80000000000000018e-99 < z < 5.1999999999999999e-123

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 91.9

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

   5. Applied rewrites 91.9%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-99} \lor \neg \left(z \leq 5.2 \cdot 10^{-123}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \cos y\right) - z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \left(x + 1\right) - z \cdot \sin y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ x 1.0) (* z (sin y))))

C

double code(double x, double y, double z) {
	return (x + 1.0) - (z * sin(y));
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + 1.0d0) - (z * sin(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + 1.0) - (z * Math.sin(y));
}

Python

def code(x, y, z):
	return (x + 1.0) - (z * math.sin(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + 1.0) - Float64(z * sin(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + 1.0) - (z * sin(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x + \cos y\right) - z \cdot \sin y \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \left(x + \color{blue}{1}\right) - z \cdot \sin y \]
4. Step-by-step derivation

5. Applied rewrites 87.9%

   \[\leadsto \left(x + \color{blue}{1}\right) - z \cdot \sin y \]
6. Add Preprocessing

Alternative 6: 69.9% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+17} \lor \neg \left(y \leq 3.2\right):\\ \;\;\;\;1 + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - \mathsf{fma}\left(\mathsf{fma}\left(0.008333333333333333, y \cdot y, -0.16666666666666666\right) \cdot z, y \cdot y, z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.4e+17) (not (<= y 3.2)))
   (+ 1.0 x)
   (-
    (+ x 1.0)
    (*
     (fma
      (* (fma 0.008333333333333333 (* y y) -0.16666666666666666) z)
      (* y y)
      z)
     y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.4e+17) || !(y <= 3.2)) {
		tmp = 1.0 + x;
	} else {
		tmp = (x + 1.0) - (fma((fma(0.008333333333333333, (y * y), -0.16666666666666666) * z), (y * y), z) * y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.4e+17) || !(y <= 3.2))
		tmp = Float64(1.0 + x);
	else
		tmp = Float64(Float64(x + 1.0) - Float64(fma(Float64(fma(0.008333333333333333, Float64(y * y), -0.16666666666666666) * z), Float64(y * y), z) * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.4e+17], N[Not[LessEqual[y, 3.2]], $MachinePrecision]], N[(1.0 + x), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] - N[(N[(N[(N[(0.008333333333333333 * N[(y * y), $MachinePrecision] + -0.16666666666666666), $MachinePrecision] * z), $MachinePrecision] * N[(y * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4e17 or 3.2000000000000002 < y

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. lower-+.f64 41.6

         \[\leadsto \color{blue}{1 + x} \]

   5. Applied rewrites 41.6%

      \[\leadsto \color{blue}{1 + x} \]

   if -5.4e17 < y < 3.2000000000000002

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \left(x + \color{blue}{1}\right) - z \cdot \sin y \]
   4. Step-by-step derivation

   5. Applied rewrites 100.0%

      \[\leadsto \left(x + \color{blue}{1}\right) - z \cdot \sin y \]

   6. Taylor expanded in y around 0

      \[\leadsto \left(x + 1\right) - \color{blue}{y \cdot \left(z + {y}^{2} \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x + 1\right) - \color{blue}{\left(z + {y}^{2} \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right)\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x + 1\right) - \color{blue}{\left(z + {y}^{2} \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right)\right) \cdot y} \]

      3. +-commutative N/A

         \[\leadsto \left(x + 1\right) - \color{blue}{\left({y}^{2} \cdot \left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right) + z\right)} \cdot y \]

      4. *-commutative N/A

         \[\leadsto \left(x + 1\right) - \left(\color{blue}{\left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right)\right) \cdot {y}^{2}} + z\right) \cdot y \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(x + 1\right) - \color{blue}{\mathsf{fma}\left(\frac{-1}{6} \cdot z + \frac{1}{120} \cdot \left({y}^{2} \cdot z\right), {y}^{2}, z\right)} \cdot y \]

      6. associate-*r* N/A

         \[\leadsto \left(x + 1\right) - \mathsf{fma}\left(\frac{-1}{6} \cdot z + \color{blue}{\left(\frac{1}{120} \cdot {y}^{2}\right) \cdot z}, {y}^{2}, z\right) \cdot y \]

      7. distribute-rgt-out N/A

         \[\leadsto \left(x + 1\right) - \mathsf{fma}\left(\color{blue}{z \cdot \left(\frac{-1}{6} + \frac{1}{120} \cdot {y}^{2}\right)}, {y}^{2}, z\right) \cdot y \]

      8. *-commutative N/A

         \[\leadsto \left(x + 1\right) - \mathsf{fma}\left(\color{blue}{\left(\frac{-1}{6} + \frac{1}{120} \cdot {y}^{2}\right) \cdot z}, {y}^{2}, z\right) \cdot y \]

      9. lower-*.f64 N/A

         \[\leadsto \left(x + 1\right) - \mathsf{fma}\left(\color{blue}{\left(\frac{-1}{6} + \frac{1}{120} \cdot {y}^{2}\right) \cdot z}, {y}^{2}, z\right) \cdot y \]

      10. +-commutative N/A

          \[\leadsto \left(x + 1\right) - \mathsf{fma}\left(\color{blue}{\left(\frac{1}{120} \cdot {y}^{2} + \frac{-1}{6}\right)} \cdot z, {y}^{2}, z\right) \cdot y \]

      11. lower-fma.f64 N/A

          \[\leadsto \left(x + 1\right) - \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{1}{120}, {y}^{2}, \frac{-1}{6}\right)} \cdot z, {y}^{2}, z\right) \cdot y \]

      12. unpow2 N/A

          \[\leadsto \left(x + 1\right) - \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{120}, \color{blue}{y \cdot y}, \frac{-1}{6}\right) \cdot z, {y}^{2}, z\right) \cdot y \]

      13. lower-*.f64 N/A

          \[\leadsto \left(x + 1\right) - \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{120}, \color{blue}{y \cdot y}, \frac{-1}{6}\right) \cdot z, {y}^{2}, z\right) \cdot y \]

      14. unpow2 N/A

          \[\leadsto \left(x + 1\right) - \mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{120}, y \cdot y, \frac{-1}{6}\right) \cdot z, \color{blue}{y \cdot y}, z\right) \cdot y \]

      15. lower-*.f64 99.1

          \[\leadsto \left(x + 1\right) - \mathsf{fma}\left(\mathsf{fma}\left(0.008333333333333333, y \cdot y, -0.16666666666666666\right) \cdot z, \color{blue}{y \cdot y}, z\right) \cdot y \]

   8. Applied rewrites 99.1%

      \[\leadsto \left(x + 1\right) - \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.008333333333333333, y \cdot y, -0.16666666666666666\right) \cdot z, y \cdot y, z\right) \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+17} \lor \neg \left(y \leq 3.2\right):\\ \;\;\;\;1 + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - \mathsf{fma}\left(\mathsf{fma}\left(0.008333333333333333, y \cdot y, -0.16666666666666666\right) \cdot z, y \cdot y, z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.0% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -17000 \lor \neg \left(y \leq 23.5\right):\\ \;\;\;\;1 + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(0.16666666666666666 \cdot \left(z \cdot y\right) - 0.5\right) \cdot y - z, y, 1 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -17000.0) (not (<= y 23.5)))
   (+ 1.0 x)
   (fma (- (* (- (* 0.16666666666666666 (* z y)) 0.5) y) z) y (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -17000.0) || !(y <= 23.5)) {
		tmp = 1.0 + x;
	} else {
		tmp = fma(((((0.16666666666666666 * (z * y)) - 0.5) * y) - z), y, (1.0 + x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -17000.0) || !(y <= 23.5))
		tmp = Float64(1.0 + x);
	else
		tmp = fma(Float64(Float64(Float64(Float64(0.16666666666666666 * Float64(z * y)) - 0.5) * y) - z), y, Float64(1.0 + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -17000.0], N[Not[LessEqual[y, 23.5]], $MachinePrecision]], N[(1.0 + x), $MachinePrecision], N[(N[(N[(N[(N[(0.16666666666666666 * N[(z * y), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision] * y + N[(1.0 + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -17000 or 23.5 < y

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. lower-+.f64 41.7

         \[\leadsto \color{blue}{1 + x} \]

   5. Applied rewrites 41.7%

      \[\leadsto \color{blue}{1 + x} \]

   if -17000 < y < 23.5

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(x + y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)\right) + 1} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right) + x\right)} + 1 \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right) + \left(x + 1\right)} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right) \cdot y} + \left(x + 1\right) \]

      5. +-commutative N/A

         \[\leadsto \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right) \cdot y + \color{blue}{\left(1 + x\right)} \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z, y, 1 + x\right)} \]

      7. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z}, y, 1 + x\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) \cdot y} - z, y, 1 + x\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) \cdot y} - z, y, 1 + x\right) \]

      10. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right)} \cdot y - z, y, 1 + x\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\color{blue}{\frac{1}{6} \cdot \left(y \cdot z\right)} - \frac{1}{2}\right) \cdot y - z, y, 1 + x\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(\frac{1}{6} \cdot \color{blue}{\left(z \cdot y\right)} - \frac{1}{2}\right) \cdot y - z, y, 1 + x\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\frac{1}{6} \cdot \color{blue}{\left(z \cdot y\right)} - \frac{1}{2}\right) \cdot y - z, y, 1 + x\right) \]

      14. lower-+.f64 99.0

          \[\leadsto \mathsf{fma}\left(\left(0.16666666666666666 \cdot \left(z \cdot y\right) - 0.5\right) \cdot y - z, y, \color{blue}{1 + x}\right) \]

   5. Applied rewrites 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.16666666666666666 \cdot \left(z \cdot y\right) - 0.5\right) \cdot y - z, y, 1 + x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -17000 \lor \neg \left(y \leq 23.5\right):\\ \;\;\;\;1 + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(0.16666666666666666 \cdot \left(z \cdot y\right) - 0.5\right) \cdot y - z, y, 1 + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.7% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+18} \lor \neg \left(y \leq 3.5 \cdot 10^{+61}\right):\\ \;\;\;\;1 + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, 1 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.95e+18) (not (<= y 3.5e+61)))
   (+ 1.0 x)
   (fma (- z) y (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.95e+18) || !(y <= 3.5e+61)) {
		tmp = 1.0 + x;
	} else {
		tmp = fma(-z, y, (1.0 + x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.95e+18) || !(y <= 3.5e+61))
		tmp = Float64(1.0 + x);
	else
		tmp = fma(Float64(-z), y, Float64(1.0 + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.95e+18], N[Not[LessEqual[y, 3.5e+61]], $MachinePrecision]], N[(1.0 + x), $MachinePrecision], N[((-z) * y + N[(1.0 + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.95e18 or 3.50000000000000018e61 < y

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. lower-+.f64 42.5

         \[\leadsto \color{blue}{1 + x} \]

   5. Applied rewrites 42.5%

      \[\leadsto \color{blue}{1 + x} \]

   if -2.95e18 < y < 3.50000000000000018e61

   1. Initial program 100.0%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + -1 \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(y \cdot z\right)\right) + 1} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot z\right) + x\right)} + 1 \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right) + \left(x + 1\right)} \]

      4. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(y \cdot z\right)\right)} + \left(x + 1\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{z \cdot y}\right)\right) + \left(x + 1\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot y} + \left(x + 1\right) \]

      7. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(z\right)\right) \cdot y + \color{blue}{\left(1 + x\right)} \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z\right), y, 1 + x\right)} \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-z}, y, 1 + x\right) \]

      10. lower-+.f64 93.4

          \[\leadsto \mathsf{fma}\left(-z, y, \color{blue}{1 + x}\right) \]

   5. Applied rewrites 93.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, y, 1 + x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+18} \lor \neg \left(y \leq 3.5 \cdot 10^{+61}\right):\\ \;\;\;\;1 + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, 1 + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.7% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+18} \lor \neg \left(y \leq 3.5 \cdot 10^{+61}\right):\\ \;\;\;\;1 + x\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(y, z, -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.95e+18) (not (<= y 3.5e+61)))
   (+ 1.0 x)
   (- x (fma y z -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.95e+18) || !(y <= 3.5e+61)) {
		tmp = 1.0 + x;
	} else {
		tmp = x - fma(y, z, -1.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.95e+18) || !(y <= 3.5e+61))
		tmp = Float64(1.0 + x);
	else
		tmp = Float64(x - fma(y, z, -1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.95e+18], N[Not[LessEqual[y, 3.5e+61]], $MachinePrecision]], N[(1.0 + x), $MachinePrecision], N[(x - N[(y * z + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.95e18 or 3.50000000000000018e61 < y

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. lower-+.f64 42.5

         \[\leadsto \color{blue}{1 + x} \]

   5. Applied rewrites 42.5%

      \[\leadsto \color{blue}{1 + x} \]

   if -2.95e18 < y < 3.50000000000000018e61

   1. Initial program 100.0%

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

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x + \cos y\right) - z \cdot \sin y} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x + \cos y\right)} - z \cdot \sin y \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{x + \left(\cos y - z \cdot \sin y\right)} \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\cos y - z \cdot \sin y\right) + x} \]

      5. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(\cos y - z \cdot \sin y\right) + x} \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\cos y - \color{blue}{z \cdot \sin y}\right) + x \]

      7. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(\cos y + \left(\mathsf{neg}\left(z\right)\right) \cdot \sin y\right)} + x \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \sin y + \cos y\right)} + x \]

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + -1 \cdot \left(y \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(y \cdot z\right)\right) + 1} \]

      2. associate-*r* N/A

         \[\leadsto \left(x + \color{blue}{\left(-1 \cdot y\right) \cdot z}\right) + 1 \]

      3. mul-1-neg N/A

         \[\leadsto \left(x + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot z\right) + 1 \]

      4. fp-cancel-sub-sign N/A

         \[\leadsto \color{blue}{\left(x - y \cdot z\right)} + 1 \]

      5. associate-+l- N/A

         \[\leadsto \color{blue}{x - \left(y \cdot z - 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto x - \left(y \cdot z - \color{blue}{1 \cdot 1}\right) \]

      7. fp-cancel-sub-sign N/A

         \[\leadsto x - \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(1\right)\right) \cdot 1\right)} \]

      8. metadata-eval N/A

         \[\leadsto x - \left(y \cdot z + \color{blue}{-1} \cdot 1\right) \]

      9. metadata-eval N/A

         \[\leadsto x - \left(y \cdot z + \color{blue}{-1}\right) \]

      10. lower--.f64 N/A

          \[\leadsto \color{blue}{x - \left(y \cdot z + -1\right)} \]

      11. lower-fma.f64 93.4

          \[\leadsto x - \color{blue}{\mathsf{fma}\left(y, z, -1\right)} \]

   7. Applied rewrites 93.4%

      \[\leadsto \color{blue}{x - \mathsf{fma}\left(y, z, -1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+18} \lor \neg \left(y \leq 3.5 \cdot 10^{+61}\right):\\ \;\;\;\;1 + x\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(y, z, -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.9% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-11} \lor \neg \left(x \leq 7.2 \cdot 10^{-54}\right):\\ \;\;\;\;1 + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.3e-11) (not (<= x 7.2e-54))) (+ 1.0 x) (fma (- z) y 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.3e-11) || !(x <= 7.2e-54)) {
		tmp = 1.0 + x;
	} else {
		tmp = fma(-z, y, 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.3e-11) || !(x <= 7.2e-54))
		tmp = Float64(1.0 + x);
	else
		tmp = fma(Float64(-z), y, 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.3e-11], N[Not[LessEqual[x, 7.2e-54]], $MachinePrecision]], N[(1.0 + x), $MachinePrecision], N[((-z) * y + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.30000000000000014e-11 or 7.19999999999999953e-54 < x

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. lower-+.f64 82.0

         \[\leadsto \color{blue}{1 + x} \]

   5. Applied rewrites 82.0%

      \[\leadsto \color{blue}{1 + x} \]

   if -2.30000000000000014e-11 < x < 7.19999999999999953e-54

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + -1 \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(x + -1 \cdot \left(y \cdot z\right)\right) + 1} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot z\right) + x\right)} + 1 \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right) + \left(x + 1\right)} \]

      4. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(y \cdot z\right)\right)} + \left(x + 1\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{z \cdot y}\right)\right) + \left(x + 1\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot y} + \left(x + 1\right) \]

      7. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(z\right)\right) \cdot y + \color{blue}{\left(1 + x\right)} \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(z\right), y, 1 + x\right)} \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-z}, y, 1 + x\right) \]

      10. lower-+.f64 55.9

          \[\leadsto \mathsf{fma}\left(-z, y, \color{blue}{1 + x}\right) \]

   5. Applied rewrites 55.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, y, 1 + x\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(-z, y, 1\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 55.9%

      \[\leadsto \mathsf{fma}\left(-z, y, 1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-11} \lor \neg \left(x \leq 7.2 \cdot 10^{-54}\right):\\ \;\;\;\;1 + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.4% accurate, 15.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{+227}:\\ \;\;\;\;1 + x\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 1.7e+227) (+ 1.0 x) (* (- y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.7e+227) {
		tmp = 1.0 + x;
	} else {
		tmp = -y * z;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 1.7d+227) then
        tmp = 1.0d0 + x
    else
        tmp = -y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.7e+227) {
		tmp = 1.0 + x;
	} else {
		tmp = -y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.7e+227:
		tmp = 1.0 + x
	else:
		tmp = -y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.7e+227)
		tmp = Float64(1.0 + x);
	else
		tmp = Float64(Float64(-y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.7e+227)
		tmp = 1.0 + x;
	else
		tmp = -y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.7e+227], N[(1.0 + x), $MachinePrecision], N[((-y) * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.69999999999999995e227

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. lower-+.f64 68.0

         \[\leadsto \color{blue}{1 + x} \]

   5. Applied rewrites 68.0%

      \[\leadsto \color{blue}{1 + x} \]

   if 1.69999999999999995e227 < z

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \sin y\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \sin y\right)} \]

      2. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot \sin y} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot \sin y} \]

      4. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(-z\right)} \cdot \sin y \]

      5. lower-sin.f64 87.5

         \[\leadsto \left(-z\right) \cdot \color{blue}{\sin y} \]

   5. Applied rewrites 87.5%

      \[\leadsto \color{blue}{\left(-z\right) \cdot \sin y} \]

   6. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \color{blue}{\left(y \cdot z\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.2%

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

Alternative 12: 61.6% accurate, 53.0× speedup

Math

\[\begin{array}{l} \\ 1 + x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 1.0 x))

C

double code(double x, double y, double z) {
	return 1.0 + 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + x
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + x;
}

Python

def code(x, y, z):
	return 1.0 + x

Julia

function code(x, y, z)
	return Float64(1.0 + x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + x;
end

Wolfram

code[x_, y_, z_] := N[(1.0 + x), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x + \cos y\right) - z \cdot \sin y \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{1 + x} \]
4. Step-by-step derivation

   1. lower-+.f64 65.3

      \[\leadsto \color{blue}{1 + x} \]

5. Applied rewrites 65.3%

   \[\leadsto \color{blue}{1 + x} \]
6. Add Preprocessing

Alternative 13: 21.2% accurate, 212.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

   \[\left(x + \cos y\right) - z \cdot \sin y \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{1 + x} \]
4. Step-by-step derivation

   1. lower-+.f64 65.3

      \[\leadsto \color{blue}{1 + x} \]

5. Applied rewrites 65.3%

   \[\leadsto \color{blue}{1 + x} \]

6. Taylor expanded in x around 0

   \[\leadsto 1 \]
7. Step-by-step derivation

8. Applied rewrites 23.6%

   \[\leadsto 1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2025008 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))