Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, B

Percentage Accurate: 68.1% → 99.5%

Time: 2.9s

Alternatives: 3

Speedup: 4.8×

Specification

Math

\[\begin{array}{l} \\ x \cdot \sqrt{y \cdot y - z \cdot z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (sqrt (- (* y y) (* z z)))))

C

double code(double x, double y, double z) {
	return x * sqrt(((y * y) - (z * z)));
}

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 * sqrt(((y * y) - (z * z)))
end function

Java

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

Python

def code(x, y, z):
	return x * math.sqrt(((y * y) - (z * z)))

Julia

function code(x, y, z)
	return Float64(x * sqrt(Float64(Float64(y * y) - Float64(z * z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * sqrt(((y * y) - (z * z)));
end

Wolfram

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

Initial Program: 68.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \sqrt{y \cdot y - z \cdot z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (sqrt (- (* y y) (* z z)))))

C

double code(double x, double y, double z) {
	return x * sqrt(((y * y) - (z * z)));
}

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 * sqrt(((y * y) - (z * z)))
end function

Java

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

Python

def code(x, y, z):
	return x * math.sqrt(((y * y) - (z * z)))

Julia

function code(x, y, z)
	return Float64(x * sqrt(Float64(Float64(y * y) - Float64(z * z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * sqrt(((y * y) - (z * z)));
end

Wolfram

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

Alternative 1: 99.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \left(\sqrt{z + y\_m} \cdot \sqrt{y\_m - z}\right) \cdot x \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z)
 :precision binary64
 (* (* (sqrt (+ z y_m)) (sqrt (- y_m z))) x))

C

y_m = fabs(y);
double code(double x, double y_m, double z) {
	return (sqrt((z + y_m)) * sqrt((y_m - z))) * x;
}

Fortran

y_m =     private
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_m, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    code = (sqrt((z + y_m)) * sqrt((y_m - z))) * x
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z) {
	return (Math.sqrt((z + y_m)) * Math.sqrt((y_m - z))) * x;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z):
	return (math.sqrt((z + y_m)) * math.sqrt((y_m - z))) * x

Julia

y_m = abs(y)
function code(x, y_m, z)
	return Float64(Float64(sqrt(Float64(z + y_m)) * sqrt(Float64(y_m - z))) * x)
end

MATLAB

y_m = abs(y);
function tmp = code(x, y_m, z)
	tmp = (sqrt((z + y_m)) * sqrt((y_m - z))) * x;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_] := N[(N[(N[Sqrt[N[(z + y$95$m), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(y$95$m - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]

Derivation

1. Initial program 69.7%

   \[x \cdot \sqrt{y \cdot y - z \cdot z} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift-sqrt.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 N/A

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

   8. lower-sqrt.f64 N/A

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

   9. difference-of-squares N/A

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

   10. lower-*.f64 N/A

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

   11. lower-+.f64 N/A

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

   12. lower--.f64 70.6

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

4. Applied rewrites 70.6%

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

   1. lift-sqrt.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. sqrt-prod N/A

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

   6. lower-*.f64 N/A

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

   7. lower-sqrt.f64 N/A

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

   8. +-commutative N/A

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

   9. lower-+.f64 N/A

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

   10. lower-sqrt.f64 N/A

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

   11. lift--.f64 53.6

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

6. Applied rewrites 53.6%

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

Alternative 2: 99.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \sqrt{z + y\_m} \cdot \left(\sqrt{y\_m - z} \cdot x\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z)
 :precision binary64
 (* (sqrt (+ z y_m)) (* (sqrt (- y_m z)) x)))

C

y_m = fabs(y);
double code(double x, double y_m, double z) {
	return sqrt((z + y_m)) * (sqrt((y_m - z)) * x);
}

Fortran

y_m =     private
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_m, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    code = sqrt((z + y_m)) * (sqrt((y_m - z)) * x)
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z) {
	return Math.sqrt((z + y_m)) * (Math.sqrt((y_m - z)) * x);
}

Python

y_m = math.fabs(y)
def code(x, y_m, z):
	return math.sqrt((z + y_m)) * (math.sqrt((y_m - z)) * x)

Julia

y_m = abs(y)
function code(x, y_m, z)
	return Float64(sqrt(Float64(z + y_m)) * Float64(sqrt(Float64(y_m - z)) * x))
end

MATLAB

y_m = abs(y);
function tmp = code(x, y_m, z)
	tmp = sqrt((z + y_m)) * (sqrt((y_m - z)) * x);
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_] := N[(N[Sqrt[N[(z + y$95$m), $MachinePrecision]], $MachinePrecision] * N[(N[Sqrt[N[(y$95$m - z), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.7%

   \[x \cdot \sqrt{y \cdot y - z \cdot z} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift-sqrt.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 N/A

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

   8. lower-sqrt.f64 N/A

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

   9. difference-of-squares N/A

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

   10. lower-*.f64 N/A

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

   11. lower-+.f64 N/A

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

   12. lower--.f64 70.6

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

4. Applied rewrites 70.6%

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

   1. lift-sqrt.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. sqrt-prod N/A

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

   6. lower-*.f64 N/A

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

   7. lower-sqrt.f64 N/A

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

   8. +-commutative N/A

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

   9. lower-+.f64 N/A

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

   10. lower-sqrt.f64 N/A

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

   11. lift--.f64 53.6

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

6. Applied rewrites 53.6%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-+.f64 N/A

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

   4. lift-sqrt.f64 N/A

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

   5. lift--.f64 N/A

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

   6. lift-sqrt.f64 N/A

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

   7. associate-*l* N/A

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

   8. lower-*.f64 N/A

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

   9. lift-sqrt.f64 N/A

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

   10. lift-+.f64 N/A

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

   11. lower-*.f64 N/A

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

   12. lift-sqrt.f64 N/A

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

   13. lift--.f64 53.6

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

8. Applied rewrites 53.6%

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

Alternative 3: 99.2% accurate, 4.8× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x \cdot y\_m \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z) :precision binary64 (* x y_m))

C

y_m = fabs(y);
double code(double x, double y_m, double z) {
	return x * y_m;
}

Fortran

y_m =     private
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_m, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    code = x * y_m
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z) {
	return x * y_m;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z):
	return x * y_m

Julia

y_m = abs(y)
function code(x, y_m, z)
	return Float64(x * y_m)
end

MATLAB

y_m = abs(y);
function tmp = code(x, y_m, z)
	tmp = x * y_m;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_] := N[(x * y$95$m), $MachinePrecision]

Derivation

1. Initial program 69.7%

   \[x \cdot \sqrt{y \cdot y - z \cdot z} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

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

5. Applied rewrites 55.1%

   \[\leadsto x \cdot \color{blue}{y} \]
6. Add Preprocessing

Developer Target 1: 99.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 2.5816096488251695 \cdot 10^{-278}:\\ \;\;\;\;-x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\sqrt{y + z} \cdot \sqrt{y - z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< y 2.5816096488251695e-278)
   (- (* x y))
   (* x (* (sqrt (+ y z)) (sqrt (- y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y < 2.5816096488251695e-278) {
		tmp = -(x * y);
	} else {
		tmp = x * (sqrt((y + z)) * sqrt((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 (y < 2.5816096488251695d-278) then
        tmp = -(x * y)
    else
        tmp = x * (sqrt((y + z)) * sqrt((y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y < 2.5816096488251695e-278) {
		tmp = -(x * y);
	} else {
		tmp = x * (Math.sqrt((y + z)) * Math.sqrt((y - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y < 2.5816096488251695e-278:
		tmp = -(x * y)
	else:
		tmp = x * (math.sqrt((y + z)) * math.sqrt((y - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y < 2.5816096488251695e-278)
		tmp = Float64(-Float64(x * y));
	else
		tmp = Float64(x * Float64(sqrt(Float64(y + z)) * sqrt(Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y < 2.5816096488251695e-278)
		tmp = -(x * y);
	else
		tmp = x * (sqrt((y + z)) * sqrt((y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[y, 2.5816096488251695e-278], (-N[(x * y), $MachinePrecision]), N[(x * N[(N[Sqrt[N[(y + z), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(y - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2025038 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y 5163219297650339/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x y)) (* x (* (sqrt (+ y z)) (sqrt (- y z))))))

  (* x (sqrt (- (* y y) (* z z)))))