Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1

Percentage Accurate: 100.0% → 100.0%

Time: 13.7s

Alternatives: 7

Speedup: 1.4×

Specification

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))

C

double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + 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 / 2.0d0) + (y * x)) + z
end function

Java

public static double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + z;
}

Python

def code(x, y, z):
	return ((x / 2.0) + (y * x)) + z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x / 2.0) + Float64(y * x)) + z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x / 2.0) + (y * x)) + z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x / 2), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))

C

double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + 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 / 2.0d0) + (y * x)) + z
end function

Java

public static double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + z;
}

Python

def code(x, y, z):
	return ((x / 2.0) + (y * x)) + z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x / 2.0) + Float64(y * x)) + z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x / 2.0) + (y * x)) + z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x / 2), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.4× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  (- (+ z (* y x)) (* -1/2 x)))

C

double code(double x, double y, double z) {
	return (z + (y * x)) - (-0.5 * 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 = (z + (y * x)) - ((-0.5d0) * x)
end function

Java

public static double code(double x, double y, double z) {
	return (z + (y * x)) - (-0.5 * x);
}

Python

def code(x, y, z):
	return (z + (y * x)) - (-0.5 * x)

Julia

function code(x, y, z)
	return Float64(Float64(z + Float64(y * x)) - Float64(-0.5 * x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (z + (y * x)) - (-0.5 * x);
end

Wolfram

code[x_, y_, z_] := N[(N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision] - N[(-1/2 * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-+.f64 N/A

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

   4. +-commutative N/A

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

   5. associate-+r+ N/A

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

   6. +-commutative N/A

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

   7. lift-/.f64 N/A

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

   8. mult-flip N/A

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

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

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

   10. lower--.f64 N/A

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

   11. +-commutative N/A

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

   12. lower-+.f64 N/A

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

   13. mult-flip-rev N/A

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

   14. distribute-neg-frac N/A

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

   15. distribute-neg-frac2 N/A

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

   16. mult-flip N/A

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

   17. *-commutative N/A

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

   18. lower-*.f64 N/A

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

   19. metadata-eval N/A

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

   20. metadata-eval 100.0%

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

3. Applied rewrites 100.0%

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

Alternative 2: 100.0% accurate, 1.9× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  (- z (* (- -1/2 y) x)))

C

double code(double x, double y, double z) {
	return z - ((-0.5 - y) * 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 = z - (((-0.5d0) - y) * x)
end function

Java

public static double code(double x, double y, double z) {
	return z - ((-0.5 - y) * x);
}

Python

def code(x, y, z):
	return z - ((-0.5 - y) * x)

Julia

function code(x, y, z)
	return Float64(z - Float64(Float64(-0.5 - y) * x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = z - ((-0.5 - y) * x);
end

Wolfram

code[x_, y_, z_] := N[(z - N[(N[(-1/2 - y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. add-flip N/A

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

   4. lower--.f64 N/A

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

   5. lift-+.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

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

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

   9. lift-/.f64 N/A

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

   10. frac-2neg N/A

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

   11. mult-flip N/A

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

   12. distribute-lft-out-- N/A

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

   13. distribute-lft-neg-out N/A

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

   14. remove-double-neg N/A

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

   15. *-commutative N/A

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

   16. lower-*.f64 N/A

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

   17. lower--.f64 N/A

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

   18. metadata-eval N/A

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

   19. metadata-eval 100.0%

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

3. Applied rewrites 100.0%

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

Alternative 3: 84.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \frac{x}{2} + y \cdot x\\ t_1 := x \cdot \left(\frac{1}{2} + y\right)\\ \mathbf{if}\;t\_0 \leq -49999999999999997640261112569083403345625645676430849265210811744256:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 10000000000000000000000:\\ \;\;\;\;z + \frac{1}{2} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (+ (/ x 2) (* y x))) (t_1 (* x (+ 1/2 y))))
  (if (<=
       t_0
       -49999999999999997640261112569083403345625645676430849265210811744256)
    t_1
    (if (<= t_0 10000000000000000000000) (+ z (* 1/2 x)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (x / 2.0) + (y * x);
	double t_1 = x * (0.5 + y);
	double tmp;
	if (t_0 <= -5e+67) {
		tmp = t_1;
	} else if (t_0 <= 1e+22) {
		tmp = z + (0.5 * x);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (x / 2.0d0) + (y * x)
    t_1 = x * (0.5d0 + y)
    if (t_0 <= (-5d+67)) then
        tmp = t_1
    else if (t_0 <= 1d+22) then
        tmp = z + (0.5d0 * x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x / 2.0) + (y * x);
	double t_1 = x * (0.5 + y);
	double tmp;
	if (t_0 <= -5e+67) {
		tmp = t_1;
	} else if (t_0 <= 1e+22) {
		tmp = z + (0.5 * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / 2.0) + (y * x)
	t_1 = x * (0.5 + y)
	tmp = 0
	if t_0 <= -5e+67:
		tmp = t_1
	elif t_0 <= 1e+22:
		tmp = z + (0.5 * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / 2.0) + Float64(y * x))
	t_1 = Float64(x * Float64(0.5 + y))
	tmp = 0.0
	if (t_0 <= -5e+67)
		tmp = t_1;
	elseif (t_0 <= 1e+22)
		tmp = Float64(z + Float64(0.5 * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / 2.0) + (y * x);
	t_1 = x * (0.5 + y);
	tmp = 0.0;
	if (t_0 <= -5e+67)
		tmp = t_1;
	elseif (t_0 <= 1e+22)
		tmp = z + (0.5 * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / 2), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(1/2 + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -49999999999999997640261112569083403345625645676430849265210811744256], t$95$1, If[LessEqual[t$95$0, 10000000000000000000000], N[(z + N[(1/2 * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) < -4.9999999999999998e67 or 1e22 < (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. +-commutative N/A

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

      7. lift-/.f64 N/A

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

      8. mult-flip N/A

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

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

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

      13. mult-flip-rev N/A

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

      14. distribute-neg-frac N/A

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

      15. distribute-neg-frac2 N/A

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

      16. mult-flip N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. metadata-eval 100.0%

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

   3. Applied rewrites 100.0%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 61.2%

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

   6. Applied rewrites 61.2%

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

   if -4.9999999999999998e67 < (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) < 1e22

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 64.9%

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

   4. Applied rewrites 64.9%

      \[\leadsto \color{blue}{z + \frac{1}{2} \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 84.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -16000000000000001252664646473539901476885764798177869824:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 6800000000000000100663296:\\ \;\;\;\;z + \frac{1}{2} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<= y -16000000000000001252664646473539901476885764798177869824)
  (* x y)
  (if (<= y 6800000000000000100663296) (+ z (* 1/2 x)) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.6e+55) {
		tmp = x * y;
	} else if (y <= 6.8e+24) {
		tmp = z + (0.5 * x);
	} else {
		tmp = x * 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 (y <= (-1.6d+55)) then
        tmp = x * y
    else if (y <= 6.8d+24) then
        tmp = z + (0.5d0 * x)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.6e+55) {
		tmp = x * y;
	} else if (y <= 6.8e+24) {
		tmp = z + (0.5 * x);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.6e+55:
		tmp = x * y
	elif y <= 6.8e+24:
		tmp = z + (0.5 * x)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.6e+55)
		tmp = Float64(x * y);
	elseif (y <= 6.8e+24)
		tmp = Float64(z + Float64(0.5 * x));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.6e+55)
		tmp = x * y;
	elseif (y <= 6.8e+24)
		tmp = z + (0.5 * x);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -16000000000000001252664646473539901476885764798177869824], N[(x * y), $MachinePrecision], If[LessEqual[y, 6800000000000000100663296], N[(z + N[(1/2 * x), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6000000000000001e55 or 6.8000000000000001e24 < y

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. +-commutative N/A

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

      7. lift-/.f64 N/A

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

      8. mult-flip N/A

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

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

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

      13. mult-flip-rev N/A

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

      14. distribute-neg-frac N/A

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

      15. distribute-neg-frac2 N/A

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

      16. mult-flip N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. metadata-eval 100.0%

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

   3. Applied rewrites 100.0%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 61.2%

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

   6. Applied rewrites 61.2%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 26.8%

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

   10. Taylor expanded in y around inf

       \[\leadsto x \cdot y \]
   11. Step-by-step derivation

   12. Applied rewrites 36.6%

       \[\leadsto x \cdot y \]

   if -1.6000000000000001e55 < y < 6.8000000000000001e24

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 64.9%

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

   4. Applied rewrites 64.9%

      \[\leadsto \color{blue}{z + \frac{1}{2} \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 59.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \frac{x}{2} + y \cdot x\\ \mathbf{if}\;t\_0 \leq -49999999999999997640261112569083403345625645676430849265210811744256:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t\_0 \leq 199999999999999995497619646912068059136:\\ \;\;\;\;z\\ \mathbf{elif}\;t\_0 \leq 5000000000000000262523801276022101243522342905540795774579270577559012289944540978931856875402239320218522219164419390884712616176802152878223960923933534914241936004632879018689151168973940450296844766174853999725405595194838204400373263713900712472896293944100284214190578347360981934327297002700800:\\ \;\;\;\;x \cdot \frac{1}{2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (+ (/ x 2) (* y x))))
  (if (<=
       t_0
       -49999999999999997640261112569083403345625645676430849265210811744256)
    (* x y)
    (if (<= t_0 199999999999999995497619646912068059136)
      z
      (if (<=
           t_0
           5000000000000000262523801276022101243522342905540795774579270577559012289944540978931856875402239320218522219164419390884712616176802152878223960923933534914241936004632879018689151168973940450296844766174853999725405595194838204400373263713900712472896293944100284214190578347360981934327297002700800)
        (* x 1/2)
        (* x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x / 2.0) + (y * x);
	double tmp;
	if (t_0 <= -5e+67) {
		tmp = x * y;
	} else if (t_0 <= 2e+38) {
		tmp = z;
	} else if (t_0 <= 5e+300) {
		tmp = x * 0.5;
	} else {
		tmp = x * 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) :: t_0
    real(8) :: tmp
    t_0 = (x / 2.0d0) + (y * x)
    if (t_0 <= (-5d+67)) then
        tmp = x * y
    else if (t_0 <= 2d+38) then
        tmp = z
    else if (t_0 <= 5d+300) then
        tmp = x * 0.5d0
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x / 2.0) + (y * x);
	double tmp;
	if (t_0 <= -5e+67) {
		tmp = x * y;
	} else if (t_0 <= 2e+38) {
		tmp = z;
	} else if (t_0 <= 5e+300) {
		tmp = x * 0.5;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / 2.0) + (y * x)
	tmp = 0
	if t_0 <= -5e+67:
		tmp = x * y
	elif t_0 <= 2e+38:
		tmp = z
	elif t_0 <= 5e+300:
		tmp = x * 0.5
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / 2.0) + Float64(y * x))
	tmp = 0.0
	if (t_0 <= -5e+67)
		tmp = Float64(x * y);
	elseif (t_0 <= 2e+38)
		tmp = z;
	elseif (t_0 <= 5e+300)
		tmp = Float64(x * 0.5);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / 2.0) + (y * x);
	tmp = 0.0;
	if (t_0 <= -5e+67)
		tmp = x * y;
	elseif (t_0 <= 2e+38)
		tmp = z;
	elseif (t_0 <= 5e+300)
		tmp = x * 0.5;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / 2), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -49999999999999997640261112569083403345625645676430849265210811744256], N[(x * y), $MachinePrecision], If[LessEqual[t$95$0, 199999999999999995497619646912068059136], z, If[LessEqual[t$95$0, 5000000000000000262523801276022101243522342905540795774579270577559012289944540978931856875402239320218522219164419390884712616176802152878223960923933534914241936004632879018689151168973940450296844766174853999725405595194838204400373263713900712472896293944100284214190578347360981934327297002700800], N[(x * 1/2), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) < -4.9999999999999998e67 or 5.0000000000000003e300 < (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. +-commutative N/A

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

      7. lift-/.f64 N/A

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

      8. mult-flip N/A

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

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

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

      13. mult-flip-rev N/A

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

      14. distribute-neg-frac N/A

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

      15. distribute-neg-frac2 N/A

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

      16. mult-flip N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. metadata-eval 100.0%

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

   3. Applied rewrites 100.0%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 61.2%

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

   6. Applied rewrites 61.2%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 26.8%

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

   10. Taylor expanded in y around inf

       \[\leadsto x \cdot y \]
   11. Step-by-step derivation

   12. Applied rewrites 36.6%

       \[\leadsto x \cdot y \]

   if -4.9999999999999998e67 < (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) < 2e38

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 40.2%

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

   if 2e38 < (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) < 5.0000000000000003e300

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. +-commutative N/A

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

      7. lift-/.f64 N/A

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

      8. mult-flip N/A

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

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

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

      13. mult-flip-rev N/A

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

      14. distribute-neg-frac N/A

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

      15. distribute-neg-frac2 N/A

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

      16. mult-flip N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. metadata-eval 100.0%

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

   3. Applied rewrites 100.0%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 61.2%

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

   6. Applied rewrites 61.2%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 26.8%

      \[\leadsto x \cdot \frac{1}{2} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 50.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -339999999999999990744261413686282949153855044567478797263246375049027131228789615831797219808308176004137591354633276357074691968990303803880243200:\\ \;\;\;\;x \cdot \frac{1}{2}\\ \mathbf{elif}\;x \leq 16000000000000000718171402849214668568788992:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{2}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<=
     x
     -339999999999999990744261413686282949153855044567478797263246375049027131228789615831797219808308176004137591354633276357074691968990303803880243200)
  (* x 1/2)
  (if (<= x 16000000000000000718171402849214668568788992)
    z
    (* x 1/2))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e+146) {
		tmp = x * 0.5;
	} else if (x <= 1.6e+43) {
		tmp = z;
	} else {
		tmp = x * 0.5;
	}
	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 (x <= (-3.4d+146)) then
        tmp = x * 0.5d0
    else if (x <= 1.6d+43) then
        tmp = z
    else
        tmp = x * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e+146) {
		tmp = x * 0.5;
	} else if (x <= 1.6e+43) {
		tmp = z;
	} else {
		tmp = x * 0.5;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.4e+146:
		tmp = x * 0.5
	elif x <= 1.6e+43:
		tmp = z
	else:
		tmp = x * 0.5
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.4e+146)
		tmp = Float64(x * 0.5);
	elseif (x <= 1.6e+43)
		tmp = z;
	else
		tmp = Float64(x * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.4e+146)
		tmp = x * 0.5;
	elseif (x <= 1.6e+43)
		tmp = z;
	else
		tmp = x * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -339999999999999990744261413686282949153855044567478797263246375049027131228789615831797219808308176004137591354633276357074691968990303803880243200], N[(x * 1/2), $MachinePrecision], If[LessEqual[x, 16000000000000000718171402849214668568788992], z, N[(x * 1/2), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3999999999999999e146 or 1.6000000000000001e43 < x

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r+ N/A

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

      6. +-commutative N/A

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

      7. lift-/.f64 N/A

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

      8. mult-flip N/A

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

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

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

      13. mult-flip-rev N/A

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

      14. distribute-neg-frac N/A

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

      15. distribute-neg-frac2 N/A

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

      16. mult-flip N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval N/A

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

      20. metadata-eval 100.0%

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

   3. Applied rewrites 100.0%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 61.2%

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

   6. Applied rewrites 61.2%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 26.8%

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

   if -3.3999999999999999e146 < x < 1.6000000000000001e43

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 40.2%

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

Alternative 7: 40.2% accurate, 23.0× speedup

Math

\[z \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0

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

4. Applied rewrites 40.2%

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

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))