Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E

Percentage Accurate: 99.7% → 99.7%

Time: 3.8s

Alternatives: 11

Speedup: 1.1×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * 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 + (((y - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * 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 + (((y - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, z \cdot 6, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- y x) (* z 6.0) x))

C

double code(double x, double y, double z) {
	return fma((y - x), (z * 6.0), x);
}

Julia

function code(x, y, z)
	return fma(Float64(y - x), Float64(z * 6.0), x)
end

Wolfram

code[x_, y_, z_] := N[(N[(y - x), $MachinePrecision] * N[(z * 6.0), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. lower-fma.f64 N/A

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

   7. *-commutative N/A

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

   8. lower-*.f64 99.8

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

4. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, z \cdot 6, x\right)} \]
5. Add Preprocessing

Alternative 2: 61.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-44}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-36}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+145}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(-6 \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.4e-44)
   (* (* 6.0 y) z)
   (if (<= z 1.06e-36)
     (* 1.0 x)
     (if (<= z 3.7e+145) (* (* 6.0 z) y) (* (* -6.0 x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4e-44) {
		tmp = (6.0 * y) * z;
	} else if (z <= 1.06e-36) {
		tmp = 1.0 * x;
	} else if (z <= 3.7e+145) {
		tmp = (6.0 * z) * y;
	} else {
		tmp = (-6.0 * x) * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.4d-44)) then
        tmp = (6.0d0 * y) * z
    else if (z <= 1.06d-36) then
        tmp = 1.0d0 * x
    else if (z <= 3.7d+145) then
        tmp = (6.0d0 * z) * y
    else
        tmp = ((-6.0d0) * x) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4e-44) {
		tmp = (6.0 * y) * z;
	} else if (z <= 1.06e-36) {
		tmp = 1.0 * x;
	} else if (z <= 3.7e+145) {
		tmp = (6.0 * z) * y;
	} else {
		tmp = (-6.0 * x) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.4e-44:
		tmp = (6.0 * y) * z
	elif z <= 1.06e-36:
		tmp = 1.0 * x
	elif z <= 3.7e+145:
		tmp = (6.0 * z) * y
	else:
		tmp = (-6.0 * x) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.4e-44)
		tmp = Float64(Float64(6.0 * y) * z);
	elseif (z <= 1.06e-36)
		tmp = Float64(1.0 * x);
	elseif (z <= 3.7e+145)
		tmp = Float64(Float64(6.0 * z) * y);
	else
		tmp = Float64(Float64(-6.0 * x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.4e-44)
		tmp = (6.0 * y) * z;
	elseif (z <= 1.06e-36)
		tmp = 1.0 * x;
	elseif (z <= 3.7e+145)
		tmp = (6.0 * z) * y;
	else
		tmp = (-6.0 * x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.4e-44], N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 1.06e-36], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 3.7e+145], N[(N[(6.0 * z), $MachinePrecision] * y), $MachinePrecision], N[(N[(-6.0 * x), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.3999999999999998e-44

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

      4. lower-*.f64 53.9

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

   5. Applied rewrites 53.9%

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

   7. Applied rewrites 54.0%

      \[\leadsto \left(6 \cdot y\right) \cdot \color{blue}{z} \]

   if -5.3999999999999998e-44 < z < 1.05999999999999999e-36

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 71.7

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

   5. Applied rewrites 71.7%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 71.7%

      \[\leadsto 1 \cdot x \]

   if 1.05999999999999999e-36 < z < 3.69999999999999993e145

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

      4. lower-*.f64 60.4

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

   5. Applied rewrites 60.4%

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

   7. Applied rewrites 60.4%

      \[\leadsto \left(6 \cdot z\right) \cdot \color{blue}{y} \]

   if 3.69999999999999993e145 < z

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 66.5

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

   5. Applied rewrites 66.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 1.4%

      \[\leadsto 1 \cdot x \]

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 66.5%

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

   13. Applied rewrites 66.5%

       \[\leadsto \color{blue}{\left(-6 \cdot x\right) \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-44}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-36}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+145}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(-6 \cdot x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(6 \cdot y\right) \cdot z\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{-44}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-37}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+145}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(-6 \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* 6.0 y) z)))
   (if (<= z -5.4e-44)
     t_0
     (if (<= z 8.2e-37) (* 1.0 x) (if (<= z 3.7e+145) t_0 (* (* -6.0 x) z))))))

C

double code(double x, double y, double z) {
	double t_0 = (6.0 * y) * z;
	double tmp;
	if (z <= -5.4e-44) {
		tmp = t_0;
	} else if (z <= 8.2e-37) {
		tmp = 1.0 * x;
	} else if (z <= 3.7e+145) {
		tmp = t_0;
	} else {
		tmp = (-6.0 * x) * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (6.0d0 * y) * z
    if (z <= (-5.4d-44)) then
        tmp = t_0
    else if (z <= 8.2d-37) then
        tmp = 1.0d0 * x
    else if (z <= 3.7d+145) then
        tmp = t_0
    else
        tmp = ((-6.0d0) * x) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (6.0 * y) * z;
	double tmp;
	if (z <= -5.4e-44) {
		tmp = t_0;
	} else if (z <= 8.2e-37) {
		tmp = 1.0 * x;
	} else if (z <= 3.7e+145) {
		tmp = t_0;
	} else {
		tmp = (-6.0 * x) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (6.0 * y) * z
	tmp = 0
	if z <= -5.4e-44:
		tmp = t_0
	elif z <= 8.2e-37:
		tmp = 1.0 * x
	elif z <= 3.7e+145:
		tmp = t_0
	else:
		tmp = (-6.0 * x) * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(6.0 * y) * z)
	tmp = 0.0
	if (z <= -5.4e-44)
		tmp = t_0;
	elseif (z <= 8.2e-37)
		tmp = Float64(1.0 * x);
	elseif (z <= 3.7e+145)
		tmp = t_0;
	else
		tmp = Float64(Float64(-6.0 * x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (6.0 * y) * z;
	tmp = 0.0;
	if (z <= -5.4e-44)
		tmp = t_0;
	elseif (z <= 8.2e-37)
		tmp = 1.0 * x;
	elseif (z <= 3.7e+145)
		tmp = t_0;
	else
		tmp = (-6.0 * x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -5.4e-44], t$95$0, If[LessEqual[z, 8.2e-37], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 3.7e+145], t$95$0, N[(N[(-6.0 * x), $MachinePrecision] * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.3999999999999998e-44 or 8.1999999999999996e-37 < z < 3.69999999999999993e145

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

      4. lower-*.f64 56.0

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

   5. Applied rewrites 56.0%

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

   7. Applied rewrites 56.1%

      \[\leadsto \left(6 \cdot y\right) \cdot \color{blue}{z} \]

   if -5.3999999999999998e-44 < z < 8.1999999999999996e-37

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 71.7

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

   5. Applied rewrites 71.7%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 71.7%

      \[\leadsto 1 \cdot x \]

   if 3.69999999999999993e145 < z

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 66.5

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

   5. Applied rewrites 66.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 1.4%

      \[\leadsto 1 \cdot x \]

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 66.5%

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

   13. Applied rewrites 66.5%

       \[\leadsto \color{blue}{\left(-6 \cdot x\right) \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-44}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-37}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+145}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(-6 \cdot x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;\left(6 \cdot \left(y - x\right)\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot y, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 0.165)))
   (* (* 6.0 (- y x)) z)
   (fma (* 6.0 y) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 0.165)) {
		tmp = (6.0 * (y - x)) * z;
	} else {
		tmp = fma((6.0 * y), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 0.165))
		tmp = Float64(Float64(6.0 * Float64(y - x)) * z);
	else
		tmp = fma(Float64(6.0 * y), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 0.165]], $MachinePrecision]], N[(N[(6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[(6.0 * y), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 0.165000000000000008 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 99.8

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

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, z \cdot 6, x\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. lift--.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 99.7

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

   9. Applied rewrites 99.7%

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

   if -0.165000000000000008 < z < 0.165000000000000008

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, z \cdot 6, x\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. lift--.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 99.9

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{6 \cdot y}, z, x\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 98.1

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

   9. Applied rewrites 98.1%

      \[\leadsto \mathsf{fma}\left(\color{blue}{6 \cdot y}, z, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.165\right):\\ \;\;\;\;\left(6 \cdot \left(y - x\right)\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot y, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+126} \lor \neg \left(x \leq 195000000\right):\\ \;\;\;\;\mathsf{fma}\left(-6, z, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot y, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.05e+126) (not (<= x 195000000.0)))
   (* (fma -6.0 z 1.0) x)
   (fma (* 6.0 y) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e+126) || !(x <= 195000000.0)) {
		tmp = fma(-6.0, z, 1.0) * x;
	} else {
		tmp = fma((6.0 * y), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.05e+126) || !(x <= 195000000.0))
		tmp = Float64(fma(-6.0, z, 1.0) * x);
	else
		tmp = fma(Float64(6.0 * y), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.05e+126], N[Not[LessEqual[x, 195000000.0]], $MachinePrecision]], N[(N[(-6.0 * z + 1.0), $MachinePrecision] * x), $MachinePrecision], N[(N[(6.0 * y), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e126 or 1.95e8 < x

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 86.0

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

   5. Applied rewrites 86.0%

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

   if -1.05e126 < x < 1.95e8

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 99.8

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

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, z \cdot 6, x\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. lift--.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{6 \cdot y}, z, x\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 86.3

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

   9. Applied rewrites 86.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{6 \cdot y}, z, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+126} \lor \neg \left(x \leq 195000000\right):\\ \;\;\;\;\mathsf{fma}\left(-6, z, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot y, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{-61} \lor \neg \left(x \leq 9.2 \cdot 10^{-81}\right):\\ \;\;\;\;\mathsf{fma}\left(-6, z, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.9e-61) (not (<= x 9.2e-81)))
   (* (fma -6.0 z 1.0) x)
   (* (* 6.0 z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.9e-61) || !(x <= 9.2e-81)) {
		tmp = fma(-6.0, z, 1.0) * x;
	} else {
		tmp = (6.0 * z) * y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.9e-61) || !(x <= 9.2e-81))
		tmp = Float64(fma(-6.0, z, 1.0) * x);
	else
		tmp = Float64(Float64(6.0 * z) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.9e-61], N[Not[LessEqual[x, 9.2e-81]], $MachinePrecision]], N[(N[(-6.0 * z + 1.0), $MachinePrecision] * x), $MachinePrecision], N[(N[(6.0 * z), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.89999999999999972e-61 or 9.19999999999999965e-81 < x

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 78.1

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

   5. Applied rewrites 78.1%

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

   if -5.89999999999999972e-61 < x < 9.19999999999999965e-81

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

      4. lower-*.f64 74.0

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot 6 \]

   5. Applied rewrites 74.0%

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

   7. Applied rewrites 74.1%

      \[\leadsto \left(6 \cdot z\right) \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{-61} \lor \neg \left(x \leq 9.2 \cdot 10^{-81}\right):\\ \;\;\;\;\mathsf{fma}\left(-6, z, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 30\right):\\ \;\;\;\;\left(-6 \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 30.0))) (* (* -6.0 x) z) (* 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 30.0)) {
		tmp = (-6.0 * x) * z;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.165d0)) .or. (.not. (z <= 30.0d0))) then
        tmp = ((-6.0d0) * x) * z
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 30.0)) {
		tmp = (-6.0 * x) * z;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.165) or not (z <= 30.0):
		tmp = (-6.0 * x) * z
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 30.0))
		tmp = Float64(Float64(-6.0 * x) * z);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.165) || ~((z <= 30.0)))
		tmp = (-6.0 * x) * z;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 30.0]], $MachinePrecision]], N[(N[(-6.0 * x), $MachinePrecision] * z), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 30 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 53.8

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

   5. Applied rewrites 53.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 2.8%

      \[\leadsto 1 \cdot x \]

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 53.7%

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

   13. Applied rewrites 53.7%

       \[\leadsto \color{blue}{\left(-6 \cdot x\right) \cdot z} \]

   if -0.165000000000000008 < z < 30

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 65.9

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

   5. Applied rewrites 65.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 64.1%

      \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 30\right):\\ \;\;\;\;\left(-6 \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;\left(-6 \cdot z\right) \cdot x\\ \mathbf{elif}\;z \leq 30:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.165)
   (* (* -6.0 z) x)
   (if (<= z 30.0) (* 1.0 x) (* (* z x) -6.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = (-6.0 * z) * x;
	} else if (z <= 30.0) {
		tmp = 1.0 * x;
	} else {
		tmp = (z * x) * -6.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.165d0)) then
        tmp = ((-6.0d0) * z) * x
    else if (z <= 30.0d0) then
        tmp = 1.0d0 * x
    else
        tmp = (z * x) * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = (-6.0 * z) * x;
	} else if (z <= 30.0) {
		tmp = 1.0 * x;
	} else {
		tmp = (z * x) * -6.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.165:
		tmp = (-6.0 * z) * x
	elif z <= 30.0:
		tmp = 1.0 * x
	else:
		tmp = (z * x) * -6.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.165)
		tmp = Float64(Float64(-6.0 * z) * x);
	elseif (z <= 30.0)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(Float64(z * x) * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.165)
		tmp = (-6.0 * z) * x;
	elseif (z <= 30.0)
		tmp = 1.0 * x;
	else
		tmp = (z * x) * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.165], N[(N[(-6.0 * z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 30.0], N[(1.0 * x), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * -6.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.165000000000000008

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 50.3

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

   5. Applied rewrites 50.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 50.3%

      \[\leadsto \left(-6 \cdot z\right) \cdot x \]

   if -0.165000000000000008 < z < 30

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 65.9

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

   5. Applied rewrites 65.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 64.1%

      \[\leadsto 1 \cdot x \]

   if 30 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 57.6

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

   5. Applied rewrites 57.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 1.5%

      \[\leadsto 1 \cdot x \]

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 57.5%

       \[\leadsto \left(z \cdot x\right) \cdot \color{blue}{-6} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;\left(-6 \cdot z\right) \cdot x\\ \mathbf{elif}\;z \leq 30:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;\left(-6 \cdot x\right) \cdot z\\ \mathbf{elif}\;z \leq 30:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.165)
   (* (* -6.0 x) z)
   (if (<= z 30.0) (* 1.0 x) (* (* z x) -6.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = (-6.0 * x) * z;
	} else if (z <= 30.0) {
		tmp = 1.0 * x;
	} else {
		tmp = (z * x) * -6.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.165d0)) then
        tmp = ((-6.0d0) * x) * z
    else if (z <= 30.0d0) then
        tmp = 1.0d0 * x
    else
        tmp = (z * x) * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = (-6.0 * x) * z;
	} else if (z <= 30.0) {
		tmp = 1.0 * x;
	} else {
		tmp = (z * x) * -6.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.165:
		tmp = (-6.0 * x) * z
	elif z <= 30.0:
		tmp = 1.0 * x
	else:
		tmp = (z * x) * -6.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.165)
		tmp = Float64(Float64(-6.0 * x) * z);
	elseif (z <= 30.0)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(Float64(z * x) * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.165)
		tmp = (-6.0 * x) * z;
	elseif (z <= 30.0)
		tmp = 1.0 * x;
	else
		tmp = (z * x) * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.165], N[(N[(-6.0 * x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 30.0], N[(1.0 * x), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * -6.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.165000000000000008

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 50.3

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

   5. Applied rewrites 50.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 4.0%

      \[\leadsto 1 \cdot x \]

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 50.3%

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

   13. Applied rewrites 50.3%

       \[\leadsto \color{blue}{\left(-6 \cdot x\right) \cdot z} \]

   if -0.165000000000000008 < z < 30

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 65.9

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

   5. Applied rewrites 65.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 64.1%

      \[\leadsto 1 \cdot x \]

   if 30 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 57.6

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

   5. Applied rewrites 57.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 1.5%

      \[\leadsto 1 \cdot x \]

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 57.5%

       \[\leadsto \left(z \cdot x\right) \cdot \color{blue}{-6} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;\left(-6 \cdot x\right) \cdot z\\ \mathbf{elif}\;z \leq 30:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(6 \cdot \left(y - x\right), z, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (* 6.0 (- y x)) z x))

C

double code(double x, double y, double z) {
	return fma((6.0 * (y - x)), z, x);
}

Julia

function code(x, y, z)
	return fma(Float64(6.0 * Float64(y - x)), z, x)
end

Wolfram

code[x_, y_, z_] := N[(N[(6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. lower-fma.f64 N/A

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

   7. *-commutative N/A

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

   8. lower-*.f64 99.8

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

4. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, z \cdot 6, x\right)} \]
5. Step-by-step derivation

   1. lift-fma.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. associate-*l* N/A

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

   5. lift--.f64 N/A

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

   6. lower-fma.f64 N/A

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

   7. lift--.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 99.8

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

6. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(6 \cdot \left(y - x\right), z, x\right)} \]
7. Add Preprocessing

Alternative 11: 36.8% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. +-commutative N/A

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

   4. lower-fma.f64 59.9

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

5. Applied rewrites 59.9%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 33.9%

   \[\leadsto 1 \cdot x \]

9. Final simplification 33.9%

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

Developer Target 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \left(6 \cdot z\right) \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* 6.0 z) (- x y))))

C

double code(double x, double y, double z) {
	return x - ((6.0 * z) * (x - y));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x - ((6.0d0 * z) * (x - y))
end function

Java

public static double code(double x, double y, double z) {
	return x - ((6.0 * z) * (x - y));
}

Python

def code(x, y, z):
	return x - ((6.0 * z) * (x - y))

Julia

function code(x, y, z)
	return Float64(x - Float64(Float64(6.0 * z) * Float64(x - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - ((6.0 * z) * (x - y));
end

Wolfram

code[x_, y_, z_] := N[(x - N[(N[(6.0 * z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2025017 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (* 6 z) (- x y))))

  (+ x (* (* (- y x) 6.0) z)))