bug366 (missed optimization)

Percentage Accurate: 44.5% → 99.4%

Time: 1.7min

Alternatives: 7

Speedup: 1.0×

Specification

Math

\[\sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \]

FPCore

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

C

double code(double x, double y, double z) {
	return sqrt(((x * x) + ((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 = sqrt(((x * x) + ((y * y) + (z * z))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 44.5% accurate, 1.0× speedup

Math

\[\sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \]

FPCore

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

C

double code(double x, double y, double z) {
	return sqrt(((x * x) + ((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 = sqrt(((x * x) + ((y * y) + (z * z))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|x\right|, \left|z\right|\right)\\ t_1 := \mathsf{max}\left(\left|x\right|, \left|z\right|\right)\\ t_2 := \mathsf{max}\left(\left|y\right|, t\_1\right)\\ t_3 := \mathsf{min}\left(\left|y\right|, t\_1\right)\\ t\_2 + \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\frac{1}{2}}{t\_2}\right), t\_3, t\_3, \left(-t\_0\right), t\_0\right) \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (fmin (fabs x) (fabs z)))
       (t_1 (fmax (fabs x) (fabs z)))
       (t_2 (fmax (fabs y) t_1))
       (t_3 (fmin (fabs y) t_1)))
  (+ t_2 (134-z0z1z2z3z4 (/ 1/2 t_2) t_3 t_3 (- t_0) t_0))))

Derivation

1. Initial program 44.5%

   \[\sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \]

2. Taylor expanded in z around inf

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

   1. lower-*.f64 N/A

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

   2. lower-+.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 N/A

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

   5. lower-+.f64 N/A

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

   6. lower-pow.f64 N/A

      \[\leadsto z \cdot \left(1 + \frac{1}{2} \cdot \frac{{x}^{2} + {y}^{2}}{{z}^{2}}\right) \]

   7. lower-pow.f64 N/A

      \[\leadsto z \cdot \left(1 + \frac{1}{2} \cdot \frac{{x}^{2} + {y}^{2}}{{z}^{2}}\right) \]

   8. lower-pow.f64 15.3%

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

4. Applied rewrites 15.3%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-+.f64 N/A

      \[\leadsto \left(1 + \frac{1}{2} \cdot \frac{{x}^{2} + {y}^{2}}{{z}^{2}}\right) \cdot z \]

   4. lift-*.f64 N/A

      \[\leadsto \left(1 + \frac{1}{2} \cdot \frac{{x}^{2} + {y}^{2}}{{z}^{2}}\right) \cdot z \]

   5. lift-/.f64 N/A

      \[\leadsto \left(1 + \frac{1}{2} \cdot \frac{{x}^{2} + {y}^{2}}{{z}^{2}}\right) \cdot z \]

   6. associate-*r/ N/A

      \[\leadsto \left(1 + \frac{\frac{1}{2} \cdot \left({x}^{2} + {y}^{2}\right)}{{z}^{2}}\right) \cdot z \]

   7. lift-pow.f64 N/A

      \[\leadsto \left(1 + \frac{\frac{1}{2} \cdot \left({x}^{2} + {y}^{2}\right)}{{z}^{2}}\right) \cdot z \]

   8. pow2 N/A

      \[\leadsto \left(1 + \frac{\frac{1}{2} \cdot \left({x}^{2} + {y}^{2}\right)}{z \cdot z}\right) \cdot z \]

   9. associate-/r* N/A

      \[\leadsto \left(1 + \frac{\frac{\frac{1}{2} \cdot \left({x}^{2} + {y}^{2}\right)}{z}}{z}\right) \cdot z \]

   10. sum-to-mult-rev N/A

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

   11. lower-+.f64 N/A

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

   12. lower-/.f64 N/A

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

6. Applied rewrites 16.0%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. lift-+.f64 N/A

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

   6. lift-*.f64 N/A

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

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

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

   8. lift-*.f64 N/A

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

   9. lift-neg.f64 N/A

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

   10. lower-134-z0z1z2z3z4 N/A

       \[\leadsto z + \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\frac{1}{2}}{z}\right), \color{blue}{y}, y, \left(-x\right), x\right) \]

   11. lower-/.f64 18.5%

       \[\leadsto z + \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\frac{1}{2}}{z}\right), y, y, \left(-x\right), x\right) \]

8. Applied rewrites 18.5%

   \[\leadsto z + \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{\frac{1}{2}}{z}\right), \color{blue}{y}, y, \left(-x\right), x\right) \]
9. Add Preprocessing

Alternative 2: 85.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\left|x\right|, \left|z\right|\right)\\ t_1 := \mathsf{max}\left(\left|x\right|, \left|z\right|\right)\\ t_2 := \mathsf{min}\left(\left|y\right|, t\_1\right)\\ t_3 := \mathsf{max}\left(\left|y\right|, t\_1\right)\\ t\_3 + \frac{\left(t\_2 \cdot t\_2 + t\_0 \cdot t\_0\right) \cdot \frac{1}{2}}{t\_3} \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (fmin (fabs x) (fabs z)))
       (t_1 (fmax (fabs x) (fabs z)))
       (t_2 (fmin (fabs y) t_1))
       (t_3 (fmax (fabs y) t_1)))
  (+ t_3 (/ (* (+ (* t_2 t_2) (* t_0 t_0)) 1/2) t_3))))

C

double code(double x, double y, double z) {
	double t_0 = fmin(fabs(x), fabs(z));
	double t_1 = fmax(fabs(x), fabs(z));
	double t_2 = fmin(fabs(y), t_1);
	double t_3 = fmax(fabs(y), t_1);
	return t_3 + ((((t_2 * t_2) + (t_0 * t_0)) * 0.5) / t_3);
}

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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    t_0 = fmin(abs(x), abs(z))
    t_1 = fmax(abs(x), abs(z))
    t_2 = fmin(abs(y), t_1)
    t_3 = fmax(abs(y), t_1)
    code = t_3 + ((((t_2 * t_2) + (t_0 * t_0)) * 0.5d0) / t_3)
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = fmin(Math.abs(x), Math.abs(z));
	double t_1 = fmax(Math.abs(x), Math.abs(z));
	double t_2 = fmin(Math.abs(y), t_1);
	double t_3 = fmax(Math.abs(y), t_1);
	return t_3 + ((((t_2 * t_2) + (t_0 * t_0)) * 0.5) / t_3);
}

Python

def code(x, y, z):
	t_0 = fmin(math.fabs(x), math.fabs(z))
	t_1 = fmax(math.fabs(x), math.fabs(z))
	t_2 = fmin(math.fabs(y), t_1)
	t_3 = fmax(math.fabs(y), t_1)
	return t_3 + ((((t_2 * t_2) + (t_0 * t_0)) * 0.5) / t_3)

Julia

function code(x, y, z)
	t_0 = fmin(abs(x), abs(z))
	t_1 = fmax(abs(x), abs(z))
	t_2 = fmin(abs(y), t_1)
	t_3 = fmax(abs(y), t_1)
	return Float64(t_3 + Float64(Float64(Float64(Float64(t_2 * t_2) + Float64(t_0 * t_0)) * 0.5) / t_3))
end

MATLAB

function tmp = code(x, y, z)
	t_0 = min(abs(x), abs(z));
	t_1 = max(abs(x), abs(z));
	t_2 = min(abs(y), t_1);
	t_3 = max(abs(y), t_1);
	tmp = t_3 + ((((t_2 * t_2) + (t_0 * t_0)) * 0.5) / t_3);
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Min[N[Abs[x], $MachinePrecision], N[Abs[z], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Abs[x], $MachinePrecision], N[Abs[z], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Min[N[Abs[y], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Max[N[Abs[y], $MachinePrecision], t$95$1], $MachinePrecision]}, N[(t$95$3 + N[(N[(N[(N[(t$95$2 * t$95$2), $MachinePrecision] + N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision] * 1/2), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Initial program 44.5%

   \[\sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \]

2. Taylor expanded in z around inf

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

   1. lower-*.f64 N/A

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

   2. lower-+.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 N/A

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

   5. lower-+.f64 N/A

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

   6. lower-pow.f64 N/A

      \[\leadsto z \cdot \left(1 + \frac{1}{2} \cdot \frac{{x}^{2} + {y}^{2}}{{z}^{2}}\right) \]

   7. lower-pow.f64 N/A

      \[\leadsto z \cdot \left(1 + \frac{1}{2} \cdot \frac{{x}^{2} + {y}^{2}}{{z}^{2}}\right) \]

   8. lower-pow.f64 15.3%

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

4. Applied rewrites 15.3%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-+.f64 N/A

      \[\leadsto \left(1 + \frac{1}{2} \cdot \frac{{x}^{2} + {y}^{2}}{{z}^{2}}\right) \cdot z \]

   4. lift-*.f64 N/A

      \[\leadsto \left(1 + \frac{1}{2} \cdot \frac{{x}^{2} + {y}^{2}}{{z}^{2}}\right) \cdot z \]

   5. lift-/.f64 N/A

      \[\leadsto \left(1 + \frac{1}{2} \cdot \frac{{x}^{2} + {y}^{2}}{{z}^{2}}\right) \cdot z \]

   6. associate-*r/ N/A

      \[\leadsto \left(1 + \frac{\frac{1}{2} \cdot \left({x}^{2} + {y}^{2}\right)}{{z}^{2}}\right) \cdot z \]

   7. lift-pow.f64 N/A

      \[\leadsto \left(1 + \frac{\frac{1}{2} \cdot \left({x}^{2} + {y}^{2}\right)}{{z}^{2}}\right) \cdot z \]

   8. pow2 N/A

      \[\leadsto \left(1 + \frac{\frac{1}{2} \cdot \left({x}^{2} + {y}^{2}\right)}{z \cdot z}\right) \cdot z \]

   9. associate-/r* N/A

      \[\leadsto \left(1 + \frac{\frac{\frac{1}{2} \cdot \left({x}^{2} + {y}^{2}\right)}{z}}{z}\right) \cdot z \]

   10. sum-to-mult-rev N/A

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

   11. lower-+.f64 N/A

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

   12. lower-/.f64 N/A

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

6. Applied rewrites 16.0%

   \[\leadsto z + \color{blue}{\frac{\left(y \cdot y + x \cdot x\right) \cdot \frac{1}{2}}{z}} \]
7. Add Preprocessing

Alternative 3: 44.5% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right)\\ t_1 := \mathsf{max}\left(\mathsf{max}\left(x, y\right), \mathsf{max}\left(\mathsf{min}\left(x, y\right), z\right)\right)\\ \sqrt{t\_0 \cdot t\_0 + t\_1 \cdot t\_1} \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (fmin (fmin x y) z))
       (t_1 (fmax (fmax x y) (fmax (fmin x y) z))))
  (sqrt (+ (* t_0 t_0) (* t_1 t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = fmin(fmin(x, y), z);
	double t_1 = fmax(fmax(x, y), fmax(fmin(x, y), z));
	return sqrt(((t_0 * t_0) + (t_1 * t_1)));
}

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) :: t_1
    t_0 = fmin(fmin(x, y), z)
    t_1 = fmax(fmax(x, y), fmax(fmin(x, y), z))
    code = sqrt(((t_0 * t_0) + (t_1 * t_1)))
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = fmin(fmin(x, y), z);
	double t_1 = fmax(fmax(x, y), fmax(fmin(x, y), z));
	return Math.sqrt(((t_0 * t_0) + (t_1 * t_1)));
}

Python

def code(x, y, z):
	t_0 = fmin(fmin(x, y), z)
	t_1 = fmax(fmax(x, y), fmax(fmin(x, y), z))
	return math.sqrt(((t_0 * t_0) + (t_1 * t_1)))

Julia

function code(x, y, z)
	t_0 = fmin(fmin(x, y), z)
	t_1 = fmax(fmax(x, y), fmax(fmin(x, y), z))
	return sqrt(Float64(Float64(t_0 * t_0) + Float64(t_1 * t_1)))
end

MATLAB

function tmp = code(x, y, z)
	t_0 = min(min(x, y), z);
	t_1 = max(max(x, y), max(min(x, y), z));
	tmp = sqrt(((t_0 * t_0) + (t_1 * t_1)));
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Min[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]}, Block[{t$95$1 = N[Max[N[Max[x, y], $MachinePrecision], N[Max[N[Min[x, y], $MachinePrecision], z], $MachinePrecision]], $MachinePrecision]}, N[Sqrt[N[(N[(t$95$0 * t$95$0), $MachinePrecision] + N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Initial program 44.5%

   \[\sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \]

2. Taylor expanded in y around 0

   \[\leadsto \sqrt{x \cdot x + \color{blue}{{z}^{2}}} \]
3. Step-by-step derivation

   1. lower-pow.f64 30.6%

      \[\leadsto \sqrt{x \cdot x + {z}^{\color{blue}{2}}} \]

4. Applied rewrites 30.6%

   \[\leadsto \sqrt{x \cdot x + \color{blue}{{z}^{2}}} \]
5. Step-by-step derivation

   1. lift-pow.f64 N/A

      \[\leadsto \sqrt{x \cdot x + {z}^{\color{blue}{2}}} \]

   2. pow2 N/A

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

   3. lower-*.f64 30.6%

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

6. Applied rewrites 30.6%

   \[\leadsto \sqrt{x \cdot x + z \cdot \color{blue}{z}} \]
7. Add Preprocessing

Alternative 4: 44.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{max}\left(\left|x\right|, \left|z\right|\right)\\ \frac{1}{2} \cdot \left(t\_0 \cdot \frac{t\_0}{\mathsf{min}\left(\left|x\right|, \left|z\right|\right)}\right) \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (fmax (fabs x) (fabs z))))
  (* 1/2 (* t_0 (/ t_0 (fmin (fabs x) (fabs z)))))))

C

double code(double x, double y, double z) {
	double t_0 = fmax(fabs(x), fabs(z));
	return 0.5 * (t_0 * (t_0 / fmin(fabs(x), fabs(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
    real(8) :: t_0
    t_0 = fmax(abs(x), abs(z))
    code = 0.5d0 * (t_0 * (t_0 / fmin(abs(x), abs(z))))
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = fmax(Math.abs(x), Math.abs(z));
	return 0.5 * (t_0 * (t_0 / fmin(Math.abs(x), Math.abs(z))));
}

Python

def code(x, y, z):
	t_0 = fmax(math.fabs(x), math.fabs(z))
	return 0.5 * (t_0 * (t_0 / fmin(math.fabs(x), math.fabs(z))))

Julia

function code(x, y, z)
	t_0 = fmax(abs(x), abs(z))
	return Float64(0.5 * Float64(t_0 * Float64(t_0 / fmin(abs(x), abs(z)))))
end

MATLAB

function tmp = code(x, y, z)
	t_0 = max(abs(x), abs(z));
	tmp = 0.5 * (t_0 * (t_0 / min(abs(x), abs(z))));
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[Abs[x], $MachinePrecision], N[Abs[z], $MachinePrecision]], $MachinePrecision]}, N[(1/2 * N[(t$95$0 * N[(t$95$0 / N[Min[N[Abs[x], $MachinePrecision], N[Abs[z], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 44.5%

   \[\sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \]

2. Taylor expanded in x around inf

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

   1. lower-*.f64 N/A

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

   2. lower-+.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 N/A

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

   5. lower-+.f64 N/A

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

   6. lower-pow.f64 N/A

      \[\leadsto x \cdot \left(1 + \frac{1}{2} \cdot \frac{{y}^{2} + {z}^{2}}{{x}^{2}}\right) \]

   7. lower-pow.f64 N/A

      \[\leadsto x \cdot \left(1 + \frac{1}{2} \cdot \frac{{y}^{2} + {z}^{2}}{{x}^{2}}\right) \]

   8. lower-pow.f64 16.1%

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

4. Applied rewrites 16.1%

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

5. Taylor expanded in z around inf

   \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{{z}^{2}}{x}} \]
6. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \frac{{z}^{2}}{\color{blue}{x}} \]

   2. lower-/.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \frac{{z}^{2}}{x} \]

   3. lower-pow.f64 3.0%

      \[\leadsto \frac{1}{2} \cdot \frac{{z}^{2}}{x} \]

7. Applied rewrites 3.0%

   \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{{z}^{2}}{x}} \]
8. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \frac{{z}^{2}}{x} \]

   2. lift-pow.f64 N/A

      \[\leadsto \frac{1}{2} \cdot \frac{{z}^{2}}{x} \]

   3. pow2 N/A

      \[\leadsto \frac{1}{2} \cdot \frac{z \cdot z}{x} \]

   4. associate-/l* N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 3.1%

      \[\leadsto \frac{1}{2} \cdot \left(z \cdot \frac{z}{x}\right) \]

9. Applied rewrites 3.1%

   \[\leadsto \frac{1}{2} \cdot \left(z \cdot \frac{z}{\color{blue}{x}}\right) \]
10. Add Preprocessing

Alternative 5: 36.7% accurate, 4.0× speedup

Math

\[\left|x\right| \cdot 1 \]

FPCore

(FPCore (x y z)
  :precision binary64
  (* (fabs x) 1))

C

double code(double x, double y, double z) {
	return fabs(x) * 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 = abs(x) * 1.0d0
end function

Java

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

Python

def code(x, y, z):
	return math.fabs(x) * 1.0

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[Abs[x], $MachinePrecision] * 1), $MachinePrecision]

Derivation

1. Initial program 44.5%

   \[\sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \]

2. Taylor expanded in x around inf

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

   1. lower-*.f64 N/A

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

   2. lower-+.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 N/A

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

   5. lower-+.f64 N/A

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

   6. lower-pow.f64 N/A

      \[\leadsto x \cdot \left(1 + \frac{1}{2} \cdot \frac{{y}^{2} + {z}^{2}}{{x}^{2}}\right) \]

   7. lower-pow.f64 N/A

      \[\leadsto x \cdot \left(1 + \frac{1}{2} \cdot \frac{{y}^{2} + {z}^{2}}{{x}^{2}}\right) \]

   8. lower-pow.f64 16.1%

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

4. Applied rewrites 16.1%

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

5. Taylor expanded in x around inf

   \[\leadsto x \cdot 1 \]
6. Step-by-step derivation

7. Applied rewrites 18.9%

   \[\leadsto x \cdot 1 \]
8. Add Preprocessing

Alternative 6: 6.6% accurate, 0.2× speedup

Math

\[-\mathsf{min}\left(\mathsf{min}\left(x, y\right), z\right) \]

FPCore

(FPCore (x y z)
  :precision binary64
  (- (fmin (fmin x y) z)))

C

double code(double x, double y, double z) {
	return -fmin(fmin(x, y), 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 = -fmin(fmin(x, y), z)
end function

Java

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

Python

def code(x, y, z):
	return -fmin(fmin(x, y), z)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 44.5%

   \[\sqrt{x \cdot x + \left(y \cdot y + z \cdot z\right)} \]

2. Taylor expanded in x around -inf

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

   1. lower-*.f64 19.0%

      \[\leadsto -1 \cdot \color{blue}{x} \]

4. Applied rewrites 19.0%

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

   1. lift-*.f64 N/A

      \[\leadsto -1 \cdot \color{blue}{x} \]

   2. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(x\right) \]

   3. lower-neg.f64 19.0%

      \[\leadsto -x \]

6. Applied rewrites 19.0%

   \[\leadsto -x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z)
  :name "bug366 (missed optimization)"
  :precision binary64
  (sqrt (+ (* x x) (+ (* y y) (* z z)))))