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

Percentage Accurate: 99.7% → 99.8%

Time: 2.6s

Alternatives: 12

Speedup: 1.1×

• 21.2% 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: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.7%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. 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. add-flip N/A

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

   4. *-lft-identity N/A

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

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

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

   6. lift-*.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. associate-*l* N/A

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

   9. *-commutative N/A

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

   10. associate-*r* N/A

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

   11. *-commutative N/A

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

   12. remove-double-neg N/A

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

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

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

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

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

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

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

   16. *-lft-identity N/A

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

   17. remove-double-neg N/A

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

   18. lower-fma.f64 N/A

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

   19. *-commutative N/A

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

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

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

   21. lift--.f64 N/A

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

   22. sub-negate-rev N/A

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

   23. lower-*.f64 N/A

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

   24. lower--.f64 N/A

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

   25. metadata-eval 99.8

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

3. Applied rewrites 99.8%

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

Alternative 2: 98.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, 6, x\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.165)
   (* (- y x) (* z 6.0))
   (if (<= z 3.15e-10) (fma (* y z) 6.0 x) (* -6.0 (* z (- x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.165) {
		tmp = (y - x) * (z * 6.0);
	} else if (z <= 3.15e-10) {
		tmp = fma((y * z), 6.0, x);
	} else {
		tmp = -6.0 * (z * (x - y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.165)
		tmp = Float64(Float64(y - x) * Float64(z * 6.0));
	elseif (z <= 3.15e-10)
		tmp = fma(Float64(y * z), 6.0, x);
	else
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.165], N[(N[(y - x), $MachinePrecision] * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.15e-10], N[(N[(y * z), $MachinePrecision] * 6.0 + x), $MachinePrecision], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.165000000000000008

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. 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. add-flip N/A

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

      4. *-lft-identity N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. remove-double-neg N/A

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

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

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

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

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

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

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

      16. *-lft-identity N/A

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

      17. remove-double-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. *-commutative N/A

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

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

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

      21. lift--.f64 N/A

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

      22. sub-negate-rev N/A

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

      23. lower-*.f64 N/A

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

      24. lower--.f64 N/A

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

      25. metadata-eval 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 66.0

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

   6. Applied rewrites 66.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

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

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

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

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

      9. distribute-rgt-neg-out N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 66.0

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

   8. Applied rewrites 66.0%

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

   if -0.165000000000000008 < z < 3.14999999999999998e-10

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 75.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 75.9

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

   6. Applied rewrites 75.9%

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

   if 3.14999999999999998e-10 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. 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. add-flip N/A

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

      4. *-lft-identity N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. remove-double-neg N/A

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

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

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

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

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

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

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

      16. *-lft-identity N/A

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

      17. remove-double-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. *-commutative N/A

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

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

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

      21. lift--.f64 N/A

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

      22. sub-negate-rev N/A

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

      23. lower-*.f64 N/A

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

      24. lower--.f64 N/A

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

      25. metadata-eval 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 66.0

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

   6. Applied rewrites 66.0%

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

Alternative 3: 98.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.2:\\ \;\;\;\;\left(6 \cdot \left(y - x\right)\right) \cdot z\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, 6, x\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.2)
   (* (* 6.0 (- y x)) z)
   (if (<= z 3.15e-10) (fma (* y z) 6.0 x) (* -6.0 (* z (- x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.2) {
		tmp = (6.0 * (y - x)) * z;
	} else if (z <= 3.15e-10) {
		tmp = fma((y * z), 6.0, x);
	} else {
		tmp = -6.0 * (z * (x - y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.2)
		tmp = Float64(Float64(6.0 * Float64(y - x)) * z);
	elseif (z <= 3.15e-10)
		tmp = fma(Float64(y * z), 6.0, x);
	else
		tmp = Float64(-6.0 * Float64(z * Float64(x - y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.2], N[(N[(6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 3.15e-10], N[(N[(y * z), $MachinePrecision] * 6.0 + x), $MachinePrecision], N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.20000000000000001

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. 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. add-flip N/A

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

      4. *-lft-identity N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. remove-double-neg N/A

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

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

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

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

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

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

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

      16. *-lft-identity N/A

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

      17. remove-double-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. *-commutative N/A

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

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

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

      21. lift--.f64 N/A

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

      22. sub-negate-rev N/A

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

      23. lower-*.f64 N/A

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

      24. lower--.f64 N/A

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

      25. metadata-eval 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 66.0

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

   6. Applied rewrites 66.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. sub-negate-rev N/A

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

      5. distribute-rgt-neg-out N/A

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

      6. distribute-rgt-neg-out N/A

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

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

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

      8. metadata-eval N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower--.f64 66.0

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

   8. Applied rewrites 66.0%

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

   if -0.20000000000000001 < z < 3.14999999999999998e-10

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 75.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 75.9

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

   6. Applied rewrites 75.9%

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

   if 3.14999999999999998e-10 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. 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. add-flip N/A

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

      4. *-lft-identity N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. remove-double-neg N/A

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

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

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

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

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

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

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

      16. *-lft-identity N/A

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

      17. remove-double-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. *-commutative N/A

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

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

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

      21. lift--.f64 N/A

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

      22. sub-negate-rev N/A

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

      23. lower-*.f64 N/A

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

      24. lower--.f64 N/A

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

      25. metadata-eval 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 66.0

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

   6. Applied rewrites 66.0%

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

Alternative 4: 98.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \mathbf{if}\;z \leq -0.16:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, 6, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z (- x y)))))
   (if (<= z -0.16) t_0 (if (<= z 3.15e-10) (fma (* y z) 6.0 x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (x - y));
	double tmp;
	if (z <= -0.16) {
		tmp = t_0;
	} else if (z <= 3.15e-10) {
		tmp = fma((y * z), 6.0, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * Float64(x - y)))
	tmp = 0.0
	if (z <= -0.16)
		tmp = t_0;
	elseif (z <= 3.15e-10)
		tmp = fma(Float64(y * z), 6.0, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.16], t$95$0, If[LessEqual[z, 3.15e-10], N[(N[(y * z), $MachinePrecision] * 6.0 + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.160000000000000003 or 3.14999999999999998e-10 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. 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. add-flip N/A

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

      4. *-lft-identity N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. remove-double-neg N/A

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

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

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

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

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

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

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

      16. *-lft-identity N/A

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

      17. remove-double-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. *-commutative N/A

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

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

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

      21. lift--.f64 N/A

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

      22. sub-negate-rev N/A

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

      23. lower-*.f64 N/A

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

      24. lower--.f64 N/A

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

      25. metadata-eval 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 66.0

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

   6. Applied rewrites 66.0%

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

   if -0.160000000000000003 < z < 3.14999999999999998e-10

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 75.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 75.9

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

   6. Applied rewrites 75.9%

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

Alternative 5: 86.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(-6 \cdot z, x, x\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+29}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot z, 6, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (* -6.0 z) x x)))
   (if (<= x -2.4e+29) t_0 (if (<= x 1.85e+46) (fma (* y z) 6.0 x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((-6.0 * z), x, x);
	double tmp;
	if (x <= -2.4e+29) {
		tmp = t_0;
	} else if (x <= 1.85e+46) {
		tmp = fma((y * z), 6.0, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(-6.0 * z), x, x)
	tmp = 0.0
	if (x <= -2.4e+29)
		tmp = t_0;
	elseif (x <= 1.85e+46)
		tmp = fma(Float64(y * z), 6.0, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-6.0 * z), $MachinePrecision] * x + x), $MachinePrecision]}, If[LessEqual[x, -2.4e+29], t$95$0, If[LessEqual[x, 1.85e+46], N[(N[(y * z), $MachinePrecision] * 6.0 + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4000000000000001e29 or 1.84999999999999995e46 < x

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. 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. add-flip N/A

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

      4. *-lft-identity N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. remove-double-neg N/A

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

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

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

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

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

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

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

      16. *-lft-identity N/A

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

      17. remove-double-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. *-commutative N/A

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

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

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

      21. lift--.f64 N/A

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

      22. sub-negate-rev N/A

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

      23. lower-*.f64 N/A

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

      24. lower--.f64 N/A

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

      25. metadata-eval 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 60.6

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

   6. Applied rewrites 60.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-+.f64 N/A

         \[\leadsto \left(1 + -6 \cdot z\right) \cdot x \]

      4. +-commutative N/A

         \[\leadsto \left(-6 \cdot z + 1\right) \cdot x \]

      5. distribute-lft1-in N/A

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

      6. lower-fma.f64 60.6

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

   8. Applied rewrites 60.6%

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

   if -2.4000000000000001e29 < x < 1.84999999999999995e46

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 75.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 75.9

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

   6. Applied rewrites 75.9%

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

Alternative 6: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(-6 \cdot z, x, x\right)\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{-140}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-82}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (* -6.0 z) x x)))
   (if (<= x -1.35e-140) t_0 (if (<= x 8.2e-82) (* (* 6.0 z) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((-6.0 * z), x, x);
	double tmp;
	if (x <= -1.35e-140) {
		tmp = t_0;
	} else if (x <= 8.2e-82) {
		tmp = (6.0 * z) * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(-6.0 * z), x, x)
	tmp = 0.0
	if (x <= -1.35e-140)
		tmp = t_0;
	elseif (x <= 8.2e-82)
		tmp = Float64(Float64(6.0 * z) * y);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-6.0 * z), $MachinePrecision] * x + x), $MachinePrecision]}, If[LessEqual[x, -1.35e-140], t$95$0, If[LessEqual[x, 8.2e-82], N[(N[(6.0 * z), $MachinePrecision] * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35e-140 or 8.19999999999999992e-82 < x

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. 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. add-flip N/A

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

      4. *-lft-identity N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. remove-double-neg N/A

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

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

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

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

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

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

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

      16. *-lft-identity N/A

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

      17. remove-double-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. *-commutative N/A

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

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

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

      21. lift--.f64 N/A

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

      22. sub-negate-rev N/A

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

      23. lower-*.f64 N/A

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

      24. lower--.f64 N/A

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

      25. metadata-eval 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 60.6

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

   6. Applied rewrites 60.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-+.f64 N/A

         \[\leadsto \left(1 + -6 \cdot z\right) \cdot x \]

      4. +-commutative N/A

         \[\leadsto \left(-6 \cdot z + 1\right) \cdot x \]

      5. distribute-lft1-in N/A

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

      6. lower-fma.f64 60.6

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

   8. Applied rewrites 60.6%

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

   if -1.35e-140 < x < 8.19999999999999992e-82

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.8

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

   4. Applied rewrites 42.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 42.8

         \[\leadsto \left(6 \cdot z\right) \cdot y \]

   6. Applied rewrites 42.8%

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

Alternative 7: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(-6 \cdot x, z, x\right)\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{-140}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-82}:\\ \;\;\;\;\left(6 \cdot z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (* -6.0 x) z x)))
   (if (<= x -1.35e-140) t_0 (if (<= x 8.2e-82) (* (* 6.0 z) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((-6.0 * x), z, x);
	double tmp;
	if (x <= -1.35e-140) {
		tmp = t_0;
	} else if (x <= 8.2e-82) {
		tmp = (6.0 * z) * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(-6.0 * x), z, x)
	tmp = 0.0
	if (x <= -1.35e-140)
		tmp = t_0;
	elseif (x <= 8.2e-82)
		tmp = Float64(Float64(6.0 * z) * y);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-6.0 * x), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[x, -1.35e-140], t$95$0, If[LessEqual[x, 8.2e-82], N[(N[(6.0 * z), $MachinePrecision] * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35e-140 or 8.19999999999999992e-82 < x

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. 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. add-flip N/A

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

      4. *-lft-identity N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. remove-double-neg N/A

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

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

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

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

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

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

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

      16. *-lft-identity N/A

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

      17. remove-double-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. *-commutative N/A

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

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

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

      21. lift--.f64 N/A

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

      22. sub-negate-rev N/A

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

      23. lower-*.f64 N/A

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

      24. lower--.f64 N/A

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

      25. metadata-eval 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 60.6

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

   6. Applied rewrites 60.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-+.f64 N/A

         \[\leadsto \left(1 + -6 \cdot z\right) \cdot x \]

      4. +-commutative N/A

         \[\leadsto \left(-6 \cdot z + 1\right) \cdot x \]

      5. distribute-lft1-in N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-rgt-identity N/A

         \[\leadsto \left(-6 \cdot z\right) \cdot \left(x \cdot 1\right) + x \]

      9. associate-*r* N/A

         \[\leadsto \left(\left(-6 \cdot z\right) \cdot x\right) \cdot 1 + x \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\left(-6 \cdot z\right) \cdot x\right) \cdot 1 + x \]

      11. metadata-eval N/A

          \[\leadsto \left(\left(-6 \cdot z\right) \cdot x\right) \cdot {y}^{0} + x \]

      12. metadata-eval N/A

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

      13. pow-plus N/A

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

      14. inv-pow N/A

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

      15. associate-*l* N/A

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

      16. mult-flip N/A

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

   8. Applied rewrites 60.5%

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

   if -1.35e-140 < x < 8.19999999999999992e-82

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.8

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

   4. Applied rewrites 42.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 42.8

         \[\leadsto \left(6 \cdot z\right) \cdot y \]

   6. Applied rewrites 42.8%

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

Alternative 8: 59.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+116}:\\ \;\;\;\;\left(-6 \cdot x\right) \cdot z\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-46}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-134}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq 65:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.1e+116)
   (* (* -6.0 x) z)
   (if (<= z -1.52e-46)
     (* (* 6.0 y) z)
     (if (<= z 1.15e-134)
       (* x 1.0)
       (if (<= z 65.0) (* 6.0 (* y z)) (* -6.0 (* x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.1e+116) {
		tmp = (-6.0 * x) * z;
	} else if (z <= -1.52e-46) {
		tmp = (6.0 * y) * z;
	} else if (z <= 1.15e-134) {
		tmp = x * 1.0;
	} else if (z <= 65.0) {
		tmp = 6.0 * (y * z);
	} 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 <= (-3.1d+116)) then
        tmp = ((-6.0d0) * x) * z
    else if (z <= (-1.52d-46)) then
        tmp = (6.0d0 * y) * z
    else if (z <= 1.15d-134) then
        tmp = x * 1.0d0
    else if (z <= 65.0d0) then
        tmp = 6.0d0 * (y * z)
    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 <= -3.1e+116) {
		tmp = (-6.0 * x) * z;
	} else if (z <= -1.52e-46) {
		tmp = (6.0 * y) * z;
	} else if (z <= 1.15e-134) {
		tmp = x * 1.0;
	} else if (z <= 65.0) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.1e+116:
		tmp = (-6.0 * x) * z
	elif z <= -1.52e-46:
		tmp = (6.0 * y) * z
	elif z <= 1.15e-134:
		tmp = x * 1.0
	elif z <= 65.0:
		tmp = 6.0 * (y * z)
	else:
		tmp = -6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.1e+116)
		tmp = Float64(Float64(-6.0 * x) * z);
	elseif (z <= -1.52e-46)
		tmp = Float64(Float64(6.0 * y) * z);
	elseif (z <= 1.15e-134)
		tmp = Float64(x * 1.0);
	elseif (z <= 65.0)
		tmp = Float64(6.0 * Float64(y * z));
	else
		tmp = Float64(-6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.1e+116)
		tmp = (-6.0 * x) * z;
	elseif (z <= -1.52e-46)
		tmp = (6.0 * y) * z;
	elseif (z <= 1.15e-134)
		tmp = x * 1.0;
	elseif (z <= 65.0)
		tmp = 6.0 * (y * z);
	else
		tmp = -6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.1e+116], N[(N[(-6.0 * x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, -1.52e-46], N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 1.15e-134], N[(x * 1.0), $MachinePrecision], If[LessEqual[z, 65.0], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.09999999999999996e116

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. 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. add-flip N/A

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

      4. *-lft-identity N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. remove-double-neg N/A

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

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

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

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

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

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

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

      16. *-lft-identity N/A

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

      17. remove-double-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. *-commutative N/A

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

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

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

      21. lift--.f64 N/A

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

      22. sub-negate-rev N/A

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

      23. lower-*.f64 N/A

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

      24. lower--.f64 N/A

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

      25. metadata-eval 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 66.0

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

   6. Applied rewrites 66.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. sub-negate-rev N/A

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

      5. distribute-rgt-neg-out N/A

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

      6. distribute-rgt-neg-out N/A

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

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

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

      8. metadata-eval N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower--.f64 66.0

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

   8. Applied rewrites 66.0%

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

   9. Taylor expanded in x around inf

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

       1. lower-*.f64 27.6

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

   11. Applied rewrites 27.6%

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

   if -3.09999999999999996e116 < z < -1.52000000000000006e-46

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.8

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

   4. Applied rewrites 42.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.8

         \[\leadsto \left(6 \cdot y\right) \cdot z \]

   6. Applied rewrites 42.8%

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

   if -1.52000000000000006e-46 < z < 1.15e-134

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. 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. add-flip N/A

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

      4. *-lft-identity N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. remove-double-neg N/A

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

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

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

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

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

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

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

      16. *-lft-identity N/A

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

      17. remove-double-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. *-commutative N/A

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

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

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

      21. lift--.f64 N/A

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

      22. sub-negate-rev N/A

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

      23. lower-*.f64 N/A

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

      24. lower--.f64 N/A

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

      25. metadata-eval 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 60.6

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

   6. Applied rewrites 60.6%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 35.4%

      \[\leadsto x \cdot 1 \]

   if 1.15e-134 < z < 65

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.8

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

   4. Applied rewrites 42.8%

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

   if 65 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. 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. add-flip N/A

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

      4. *-lft-identity N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. remove-double-neg N/A

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

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

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

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

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

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

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

      16. *-lft-identity N/A

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

      17. remove-double-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. *-commutative N/A

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

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

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

      21. lift--.f64 N/A

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

      22. sub-negate-rev N/A

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

      23. lower-*.f64 N/A

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

      24. lower--.f64 N/A

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

      25. metadata-eval 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 66.0

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

   6. Applied rewrites 66.0%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 27.6

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

   9. Applied rewrites 27.6%

      \[\leadsto -6 \cdot \left(x \cdot \color{blue}{z}\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 9: 59.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+116}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-46}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-134}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq 65:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))))
   (if (<= z -3.1e+116)
     t_0
     (if (<= z -1.52e-46)
       (* (* 6.0 y) z)
       (if (<= z 1.15e-134) (* x 1.0) (if (<= z 65.0) (* 6.0 (* y z)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double tmp;
	if (z <= -3.1e+116) {
		tmp = t_0;
	} else if (z <= -1.52e-46) {
		tmp = (6.0 * y) * z;
	} else if (z <= 1.15e-134) {
		tmp = x * 1.0;
	} else if (z <= 65.0) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (x * z)
    if (z <= (-3.1d+116)) then
        tmp = t_0
    else if (z <= (-1.52d-46)) then
        tmp = (6.0d0 * y) * z
    else if (z <= 1.15d-134) then
        tmp = x * 1.0d0
    else if (z <= 65.0d0) then
        tmp = 6.0d0 * (y * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double tmp;
	if (z <= -3.1e+116) {
		tmp = t_0;
	} else if (z <= -1.52e-46) {
		tmp = (6.0 * y) * z;
	} else if (z <= 1.15e-134) {
		tmp = x * 1.0;
	} else if (z <= 65.0) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (x * z)
	tmp = 0
	if z <= -3.1e+116:
		tmp = t_0
	elif z <= -1.52e-46:
		tmp = (6.0 * y) * z
	elif z <= 1.15e-134:
		tmp = x * 1.0
	elif z <= 65.0:
		tmp = 6.0 * (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -3.1e+116)
		tmp = t_0;
	elseif (z <= -1.52e-46)
		tmp = Float64(Float64(6.0 * y) * z);
	elseif (z <= 1.15e-134)
		tmp = Float64(x * 1.0);
	elseif (z <= 65.0)
		tmp = Float64(6.0 * Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -3.1e+116)
		tmp = t_0;
	elseif (z <= -1.52e-46)
		tmp = (6.0 * y) * z;
	elseif (z <= 1.15e-134)
		tmp = x * 1.0;
	elseif (z <= 65.0)
		tmp = 6.0 * (y * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+116], t$95$0, If[LessEqual[z, -1.52e-46], N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 1.15e-134], N[(x * 1.0), $MachinePrecision], If[LessEqual[z, 65.0], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.09999999999999996e116 or 65 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. 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. add-flip N/A

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

      4. *-lft-identity N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. remove-double-neg N/A

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

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

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

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

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

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

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

      16. *-lft-identity N/A

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

      17. remove-double-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. *-commutative N/A

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

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

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

      21. lift--.f64 N/A

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

      22. sub-negate-rev N/A

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

      23. lower-*.f64 N/A

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

      24. lower--.f64 N/A

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

      25. metadata-eval 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 66.0

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

   6. Applied rewrites 66.0%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 27.6

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

   9. Applied rewrites 27.6%

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

   if -3.09999999999999996e116 < z < -1.52000000000000006e-46

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.8

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

   4. Applied rewrites 42.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.8

         \[\leadsto \left(6 \cdot y\right) \cdot z \]

   6. Applied rewrites 42.8%

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

   if -1.52000000000000006e-46 < z < 1.15e-134

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. 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. add-flip N/A

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

      4. *-lft-identity N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. remove-double-neg N/A

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

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

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

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

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

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

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

      16. *-lft-identity N/A

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

      17. remove-double-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. *-commutative N/A

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

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

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

      21. lift--.f64 N/A

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

      22. sub-negate-rev N/A

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

      23. lower-*.f64 N/A

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

      24. lower--.f64 N/A

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

      25. metadata-eval 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 60.6

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

   6. Applied rewrites 60.6%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 35.4%

      \[\leadsto x \cdot 1 \]

   if 1.15e-134 < z < 65

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.8

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

   4. Applied rewrites 42.8%

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

Alternative 10: 59.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{-46}:\\ \;\;\;\;\left(6 \cdot y\right) \cdot z\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-134}:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.52e-46)
   (* (* 6.0 y) z)
   (if (<= z 1.15e-134) (* x 1.0) (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.52e-46) {
		tmp = (6.0 * y) * z;
	} else if (z <= 1.15e-134) {
		tmp = x * 1.0;
	} else {
		tmp = 6.0 * (y * z);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.52d-46)) then
        tmp = (6.0d0 * y) * z
    else if (z <= 1.15d-134) then
        tmp = x * 1.0d0
    else
        tmp = 6.0d0 * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.52e-46) {
		tmp = (6.0 * y) * z;
	} else if (z <= 1.15e-134) {
		tmp = x * 1.0;
	} else {
		tmp = 6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.52e-46:
		tmp = (6.0 * y) * z
	elif z <= 1.15e-134:
		tmp = x * 1.0
	else:
		tmp = 6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.52e-46)
		tmp = Float64(Float64(6.0 * y) * z);
	elseif (z <= 1.15e-134)
		tmp = Float64(x * 1.0);
	else
		tmp = Float64(6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.52e-46)
		tmp = (6.0 * y) * z;
	elseif (z <= 1.15e-134)
		tmp = x * 1.0;
	else
		tmp = 6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.52e-46], N[(N[(6.0 * y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 1.15e-134], N[(x * 1.0), $MachinePrecision], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.52000000000000006e-46

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.8

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

   4. Applied rewrites 42.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.8

         \[\leadsto \left(6 \cdot y\right) \cdot z \]

   6. Applied rewrites 42.8%

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

   if -1.52000000000000006e-46 < z < 1.15e-134

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. 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. add-flip N/A

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

      4. *-lft-identity N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. remove-double-neg N/A

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

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

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

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

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

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

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

      16. *-lft-identity N/A

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

      17. remove-double-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. *-commutative N/A

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

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

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

      21. lift--.f64 N/A

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

      22. sub-negate-rev N/A

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

      23. lower-*.f64 N/A

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

      24. lower--.f64 N/A

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

      25. metadata-eval 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 60.6

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

   6. Applied rewrites 60.6%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 35.4%

      \[\leadsto x \cdot 1 \]

   if 1.15e-134 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.8

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

   4. Applied rewrites 42.8%

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

Alternative 11: 59.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.52 \cdot 10^{-46}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-134}:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))))
   (if (<= z -1.52e-46) t_0 (if (<= z 1.15e-134) (* x 1.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (z <= -1.52e-46) {
		tmp = t_0;
	} else if (z <= 1.15e-134) {
		tmp = x * 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    if (z <= (-1.52d-46)) then
        tmp = t_0
    else if (z <= 1.15d-134) then
        tmp = x * 1.0d0
    else
        tmp = t_0
    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 <= -1.52e-46) {
		tmp = t_0;
	} else if (z <= 1.15e-134) {
		tmp = x * 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	tmp = 0
	if z <= -1.52e-46:
		tmp = t_0
	elif z <= 1.15e-134:
		tmp = x * 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.52e-46)
		tmp = t_0;
	elseif (z <= 1.15e-134)
		tmp = Float64(x * 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.52e-46)
		tmp = t_0;
	elseif (z <= 1.15e-134)
		tmp = x * 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.52e-46], t$95$0, If[LessEqual[z, 1.15e-134], N[(x * 1.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.52000000000000006e-46 or 1.15e-134 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 42.8

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

   4. Applied rewrites 42.8%

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

   if -1.52000000000000006e-46 < z < 1.15e-134

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. 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. add-flip N/A

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

      4. *-lft-identity N/A

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

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

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. *-commutative N/A

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

      12. remove-double-neg N/A

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

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

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

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

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

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

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

      16. *-lft-identity N/A

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

      17. remove-double-neg N/A

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

      18. lower-fma.f64 N/A

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

      19. *-commutative N/A

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

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

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

      21. lift--.f64 N/A

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

      22. sub-negate-rev N/A

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

      23. lower-*.f64 N/A

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

      24. lower--.f64 N/A

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

      25. metadata-eval 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 60.6

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

   6. Applied rewrites 60.6%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 35.4%

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

Alternative 12: 35.4% accurate, 3.1× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. 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. add-flip N/A

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

   4. *-lft-identity N/A

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

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

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

   6. lift-*.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. associate-*l* N/A

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

   9. *-commutative N/A

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

   10. associate-*r* N/A

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

   11. *-commutative N/A

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

   12. remove-double-neg N/A

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

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

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

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

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

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

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

   16. *-lft-identity N/A

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

   17. remove-double-neg N/A

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

   18. lower-fma.f64 N/A

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

   19. *-commutative N/A

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

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

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

   21. lift--.f64 N/A

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

   22. sub-negate-rev N/A

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

   23. lower-*.f64 N/A

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

   24. lower--.f64 N/A

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

   25. metadata-eval 99.8

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

3. Applied rewrites 99.8%

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

4. Taylor expanded in x around inf

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

   1. lower-*.f64 N/A

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

   2. lower-+.f64 N/A

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

   3. lower-*.f64 60.6

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

6. Applied rewrites 60.6%

   \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]

7. Taylor expanded in z around 0

   \[\leadsto x \cdot 1 \]
8. Step-by-step derivation

9. Applied rewrites 35.4%

   \[\leadsto x \cdot 1 \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2025156 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64
  (+ x (* (* (- y x) 6.0) z)))