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

Percentage Accurate: 99.5% → 99.8%

Time: 3.2s

Alternatives: 15

Speedup: 1.3×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - 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) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - 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) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.9× speedup

Math

\[\mathsf{fma}\left(y - x, -6 \cdot z, \mathsf{fma}\left(-3, x, 4 \cdot y\right)\right) \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fma (- y x) (* -6.0 z) (fma -3.0 x (* 4.0 y))))

C

double code(double x, double y, double z) {
	return fma((y - x), (-6.0 * z), fma(-3.0, x, (4.0 * y)));
}

Julia

function code(x, y, z)
	return fma(Float64(y - x), Float64(-6.0 * z), fma(-3.0, x, Float64(4.0 * y)))
end

Wolfram

code[x_, y_, z_] := N[(N[(y - x), $MachinePrecision] * N[(-6.0 * z), $MachinePrecision] + N[(-3.0 * x + N[(4.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

   2. lift-*.f64 N/A

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

   3. lift--.f64 N/A

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} - z\right)} \]

   4. sub-flip N/A

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right)} \]

   5. distribute-lft-in N/A

      \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} \]

   6. associate-+r+ N/A

      \[\leadsto \color{blue}{\left(x + \left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

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

      \[\leadsto \color{blue}{\left(x - \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right) \cdot \frac{2}{3}\right)} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

   8. *-commutative N/A

      \[\leadsto \left(x - \color{blue}{\frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

   9. +-commutative N/A

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

   10. lift-*.f64 N/A

       \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right)} \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

   11. associate-*l* N/A

       \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

   12. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\mathsf{neg}\left(z\right)\right), x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

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

       \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{neg}\left(6 \cdot z\right)}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

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

       \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

   15. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

   16. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{-6} \cdot z, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

3. Applied rewrites 99.7%

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

4. Taylor expanded in x around 0

   \[\leadsto \mathsf{fma}\left(y - x, -6 \cdot z, \color{blue}{-3 \cdot x + 4 \cdot y}\right) \]
5. Step-by-step derivation

   1. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(y - x, -6 \cdot z, \mathsf{fma}\left(-3, \color{blue}{x}, 4 \cdot y\right)\right) \]

   2. lower-*.f64 99.8

      \[\leadsto \mathsf{fma}\left(y - x, -6 \cdot z, \mathsf{fma}\left(-3, x, 4 \cdot y\right)\right) \]

6. Applied rewrites 99.8%

   \[\leadsto \mathsf{fma}\left(y - x, -6 \cdot z, \color{blue}{\mathsf{fma}\left(-3, x, 4 \cdot y\right)}\right) \]
7. Add Preprocessing

Alternative 2: 99.8% accurate, 1.0× speedup

Math

\[\mathsf{fma}\left(y - x, -6 \cdot z, \mathsf{fma}\left(-4, x - y, x\right)\right) \]

FPCore

(FPCore (x y z)
 :precision binary64
 (fma (- y x) (* -6.0 z) (fma -4.0 (- x y) x)))

C

double code(double x, double y, double z) {
	return fma((y - x), (-6.0 * z), fma(-4.0, (x - y), x));
}

Julia

function code(x, y, z)
	return fma(Float64(y - x), Float64(-6.0 * z), fma(-4.0, Float64(x - y), x))
end

Wolfram

code[x_, y_, z_] := N[(N[(y - x), $MachinePrecision] * N[(-6.0 * z), $MachinePrecision] + N[(-4.0 * N[(x - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

   2. lift-*.f64 N/A

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

   3. lift--.f64 N/A

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} - z\right)} \]

   4. sub-flip N/A

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right)} \]

   5. distribute-lft-in N/A

      \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} \]

   6. associate-+r+ N/A

      \[\leadsto \color{blue}{\left(x + \left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

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

      \[\leadsto \color{blue}{\left(x - \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right) \cdot \frac{2}{3}\right)} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

   8. *-commutative N/A

      \[\leadsto \left(x - \color{blue}{\frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

   9. +-commutative N/A

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

   10. lift-*.f64 N/A

       \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right)} \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

   11. associate-*l* N/A

       \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

   12. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\mathsf{neg}\left(z\right)\right), x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

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

       \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{neg}\left(6 \cdot z\right)}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

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

       \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

   15. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

   16. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{-6} \cdot z, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

3. Applied rewrites 99.7%

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

Alternative 3: 99.7% accurate, 1.3× speedup

Math

\[\mathsf{fma}\left(\mathsf{fma}\left(z, 6, -4\right), x - y, x\right) \]

FPCore

(FPCore (x y z) :precision binary64 (fma (fma z 6.0 -4.0) (- x y) x))

C

double code(double x, double y, double z) {
	return fma(fma(z, 6.0, -4.0), (x - y), x);
}

Julia

function code(x, y, z)
	return fma(fma(z, 6.0, -4.0), Float64(x - y), x)
end

Wolfram

code[x_, y_, z_] := N[(N[(z * 6.0 + -4.0), $MachinePrecision] * N[(x - y), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} + x \]

   4. *-commutative N/A

      \[\leadsto \color{blue}{\left(\frac{2}{3} - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

   5. lift-*.f64 N/A

      \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

   6. *-commutative N/A

      \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} + x \]

   7. associate-*r* N/A

      \[\leadsto \color{blue}{\left(\left(\frac{2}{3} - z\right) \cdot 6\right) \cdot \left(y - x\right)} + x \]

   8. *-commutative N/A

      \[\leadsto \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)} \cdot \left(y - x\right) + x \]

   9. lift--.f64 N/A

      \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(y - x\right)} + x \]

   10. sub-negate-rev N/A

       \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right)} + x \]

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

       \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \left(x - y\right)\right)\right)} + x \]

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

       \[\leadsto \color{blue}{\left(\mathsf{neg}\left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right) \cdot \left(x - y\right)} + x \]

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

       \[\leadsto \color{blue}{\left(6 \cdot \left(\mathsf{neg}\left(\left(\frac{2}{3} - z\right)\right)\right)\right)} \cdot \left(x - y\right) + x \]

   14. lift--.f64 N/A

       \[\leadsto \left(6 \cdot \left(\mathsf{neg}\left(\color{blue}{\left(\frac{2}{3} - z\right)}\right)\right)\right) \cdot \left(x - y\right) + x \]

   15. sub-negate-rev N/A

       \[\leadsto \left(6 \cdot \color{blue}{\left(z - \frac{2}{3}\right)}\right) \cdot \left(x - y\right) + x \]

   16. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(6 \cdot \left(z - \frac{2}{3}\right), x - y, x\right)} \]

3. Applied rewrites 99.8%

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

Alternative 4: 97.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -1.2:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot z, x - y, x\right)\\ \mathbf{elif}\;z \leq 95000:\\ \;\;\;\;\left(x + -4 \cdot x\right) + \left(-y\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - x\right) \cdot -6\right) \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.2)
   (fma (* 6.0 z) (- x y) x)
   (if (<= z 95000.0)
     (+ (+ x (* -4.0 x)) (* (- y) -4.0))
     (* (* (- y x) -6.0) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.2) {
		tmp = fma((6.0 * z), (x - y), x);
	} else if (z <= 95000.0) {
		tmp = (x + (-4.0 * x)) + (-y * -4.0);
	} else {
		tmp = ((y - x) * -6.0) * z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.2)
		tmp = fma(Float64(6.0 * z), Float64(x - y), x);
	elseif (z <= 95000.0)
		tmp = Float64(Float64(x + Float64(-4.0 * x)) + Float64(Float64(-y) * -4.0));
	else
		tmp = Float64(Float64(Float64(y - x) * -6.0) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.2], N[(N[(6.0 * z), $MachinePrecision] * N[(x - y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 95000.0], N[(N[(x + N[(-4.0 * x), $MachinePrecision]), $MachinePrecision] + N[((-y) * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999996

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{2}{3} - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. *-commutative N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} + x \]

      7. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\frac{2}{3} - z\right) \cdot 6\right) \cdot \left(y - x\right)} + x \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)} \cdot \left(y - x\right) + x \]

      9. lift--.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(y - x\right)} + x \]

      10. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right) \cdot \left(x - y\right)} + x \]

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

          \[\leadsto \color{blue}{\left(6 \cdot \left(\mathsf{neg}\left(\left(\frac{2}{3} - z\right)\right)\right)\right)} \cdot \left(x - y\right) + x \]

      14. lift--.f64 N/A

          \[\leadsto \left(6 \cdot \left(\mathsf{neg}\left(\color{blue}{\left(\frac{2}{3} - z\right)}\right)\right)\right) \cdot \left(x - y\right) + x \]

      15. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \color{blue}{\left(z - \frac{2}{3}\right)}\right) \cdot \left(x - y\right) + x \]

      16. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(6 \cdot \left(z - \frac{2}{3}\right), x - y, x\right)} \]

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 50.8

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

   6. Applied rewrites 50.8%

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

   if -1.19999999999999996 < z < 95000

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{2}{3} - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. *-commutative N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} + x \]

      7. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\frac{2}{3} - z\right) \cdot 6\right) \cdot \left(y - x\right)} + x \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)} \cdot \left(y - x\right) + x \]

      9. lift--.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(y - x\right)} + x \]

      10. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right) \cdot \left(x - y\right)} + x \]

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

          \[\leadsto \color{blue}{\left(6 \cdot \left(\mathsf{neg}\left(\left(\frac{2}{3} - z\right)\right)\right)\right)} \cdot \left(x - y\right) + x \]

      14. lift--.f64 N/A

          \[\leadsto \left(6 \cdot \left(\mathsf{neg}\left(\color{blue}{\left(\frac{2}{3} - z\right)}\right)\right)\right) \cdot \left(x - y\right) + x \]

      15. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \color{blue}{\left(z - \frac{2}{3}\right)}\right) \cdot \left(x - y\right) + x \]

      16. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(6 \cdot \left(z - \frac{2}{3}\right), x - y, x\right)} \]

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4}, x - y, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 50.1%

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4}, x - y, x\right) \]
   7. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \left(x - y\right) + x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{x + -4 \cdot \left(x - y\right)} \]

      3. lift--.f64 N/A

         \[\leadsto x + -4 \cdot \color{blue}{\left(x - y\right)} \]

      4. sub-flip N/A

         \[\leadsto x + -4 \cdot \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)} \]

      5. distribute-rgt-in N/A

         \[\leadsto x + \color{blue}{\left(x \cdot -4 + \left(\mathsf{neg}\left(y\right)\right) \cdot -4\right)} \]

      6. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(x + x \cdot -4\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot -4} \]

      7. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(x + x \cdot -4\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot -4} \]

      8. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(x + x \cdot -4\right)} + \left(\mathsf{neg}\left(y\right)\right) \cdot -4 \]

      9. *-commutative N/A

         \[\leadsto \left(x + \color{blue}{-4 \cdot x}\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot -4 \]

      10. lower-*.f64 N/A

          \[\leadsto \left(x + \color{blue}{-4 \cdot x}\right) + \left(\mathsf{neg}\left(y\right)\right) \cdot -4 \]

      11. lower-*.f64 N/A

          \[\leadsto \left(x + -4 \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right) \cdot -4} \]

      12. lower-neg.f64 50.1

          \[\leadsto \left(x + -4 \cdot x\right) + \color{blue}{\left(-y\right)} \cdot -4 \]

   8. Applied rewrites 50.1%

      \[\leadsto \color{blue}{\left(x + -4 \cdot x\right) + \left(-y\right) \cdot -4} \]

   if 95000 < z

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      3. lift--.f64 N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} - z\right)} \]

      4. sub-flip N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      5. distribute-lft-in N/A

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      6. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(x + \left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

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

         \[\leadsto \color{blue}{\left(x - \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right) \cdot \frac{2}{3}\right)} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(x - \color{blue}{\frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right)} \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\mathsf{neg}\left(z\right)\right), x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

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

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{neg}\left(6 \cdot z\right)}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{-6} \cdot z, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.3

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

   6. Applied rewrites 51.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

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

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

      11. metadata-eval N/A

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

      12. associate-*r* N/A

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

      13. lift--.f64 N/A

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

      14. sub-flip N/A

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

      15. distribute-rgt-in N/A

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

      16. metadata-eval N/A

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

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

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

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

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. distribute-neg-in N/A

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

      22. lift-fma.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 N/A

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

   8. Applied rewrites 51.4%

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

Alternative 5: 97.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -1.2:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot z, x - y, x\right)\\ \mathbf{elif}\;z \leq 95000:\\ \;\;\;\;\mathsf{fma}\left(-4, x, \mathsf{fma}\left(-y, -4, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - x\right) \cdot -6\right) \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.2)
   (fma (* 6.0 z) (- x y) x)
   (if (<= z 95000.0) (fma -4.0 x (fma (- y) -4.0 x)) (* (* (- y x) -6.0) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.2) {
		tmp = fma((6.0 * z), (x - y), x);
	} else if (z <= 95000.0) {
		tmp = fma(-4.0, x, fma(-y, -4.0, x));
	} else {
		tmp = ((y - x) * -6.0) * z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.2)
		tmp = fma(Float64(6.0 * z), Float64(x - y), x);
	elseif (z <= 95000.0)
		tmp = fma(-4.0, x, fma(Float64(-y), -4.0, x));
	else
		tmp = Float64(Float64(Float64(y - x) * -6.0) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.2], N[(N[(6.0 * z), $MachinePrecision] * N[(x - y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 95000.0], N[(-4.0 * x + N[((-y) * -4.0 + x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999996

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{2}{3} - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. *-commutative N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} + x \]

      7. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\frac{2}{3} - z\right) \cdot 6\right) \cdot \left(y - x\right)} + x \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)} \cdot \left(y - x\right) + x \]

      9. lift--.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(y - x\right)} + x \]

      10. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right) \cdot \left(x - y\right)} + x \]

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

          \[\leadsto \color{blue}{\left(6 \cdot \left(\mathsf{neg}\left(\left(\frac{2}{3} - z\right)\right)\right)\right)} \cdot \left(x - y\right) + x \]

      14. lift--.f64 N/A

          \[\leadsto \left(6 \cdot \left(\mathsf{neg}\left(\color{blue}{\left(\frac{2}{3} - z\right)}\right)\right)\right) \cdot \left(x - y\right) + x \]

      15. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \color{blue}{\left(z - \frac{2}{3}\right)}\right) \cdot \left(x - y\right) + x \]

      16. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(6 \cdot \left(z - \frac{2}{3}\right), x - y, x\right)} \]

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 50.8

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

   6. Applied rewrites 50.8%

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

   if -1.19999999999999996 < z < 95000

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{2}{3} - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. *-commutative N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} + x \]

      7. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\frac{2}{3} - z\right) \cdot 6\right) \cdot \left(y - x\right)} + x \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)} \cdot \left(y - x\right) + x \]

      9. lift--.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(y - x\right)} + x \]

      10. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right) \cdot \left(x - y\right)} + x \]

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

          \[\leadsto \color{blue}{\left(6 \cdot \left(\mathsf{neg}\left(\left(\frac{2}{3} - z\right)\right)\right)\right)} \cdot \left(x - y\right) + x \]

      14. lift--.f64 N/A

          \[\leadsto \left(6 \cdot \left(\mathsf{neg}\left(\color{blue}{\left(\frac{2}{3} - z\right)}\right)\right)\right) \cdot \left(x - y\right) + x \]

      15. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \color{blue}{\left(z - \frac{2}{3}\right)}\right) \cdot \left(x - y\right) + x \]

      16. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(6 \cdot \left(z - \frac{2}{3}\right), x - y, x\right)} \]

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4}, x - y, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 50.1%

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4}, x - y, x\right) \]
   7. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \color{blue}{-4 \cdot \left(x - y\right) + x} \]

      2. lift--.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\left(x - y\right)} + x \]

      3. sub-flip N/A

         \[\leadsto -4 \cdot \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)} + x \]

      4. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(x \cdot -4 + \left(\mathsf{neg}\left(y\right)\right) \cdot -4\right)} + x \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{x \cdot -4 + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot -4 + x\right)} \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{-4 \cdot x} + \left(\left(\mathsf{neg}\left(y\right)\right) \cdot -4 + x\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4, x, \left(\mathsf{neg}\left(y\right)\right) \cdot -4 + x\right)} \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4, x, \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(y\right), -4, x\right)}\right) \]

      9. lower-neg.f64 50.1

         \[\leadsto \mathsf{fma}\left(-4, x, \mathsf{fma}\left(\color{blue}{-y}, -4, x\right)\right) \]

   8. Applied rewrites 50.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4, x, \mathsf{fma}\left(-y, -4, x\right)\right)} \]

   if 95000 < z

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      3. lift--.f64 N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} - z\right)} \]

      4. sub-flip N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      5. distribute-lft-in N/A

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      6. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(x + \left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

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

         \[\leadsto \color{blue}{\left(x - \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right) \cdot \frac{2}{3}\right)} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(x - \color{blue}{\frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right)} \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\mathsf{neg}\left(z\right)\right), x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

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

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{neg}\left(6 \cdot z\right)}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{-6} \cdot z, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.3

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

   6. Applied rewrites 51.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

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

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

      11. metadata-eval N/A

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

      12. associate-*r* N/A

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

      13. lift--.f64 N/A

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

      14. sub-flip N/A

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

      15. distribute-rgt-in N/A

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

      16. metadata-eval N/A

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

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

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

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

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. distribute-neg-in N/A

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

      22. lift-fma.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 N/A

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

   8. Applied rewrites 51.4%

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

Alternative 6: 97.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -1.2:\\ \;\;\;\;\mathsf{fma}\left(6 \cdot z, x - y, x\right)\\ \mathbf{elif}\;z \leq 95000:\\ \;\;\;\;\mathsf{fma}\left(-4, x - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - x\right) \cdot -6\right) \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.2)
   (fma (* 6.0 z) (- x y) x)
   (if (<= z 95000.0) (fma -4.0 (- x y) x) (* (* (- y x) -6.0) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.2) {
		tmp = fma((6.0 * z), (x - y), x);
	} else if (z <= 95000.0) {
		tmp = fma(-4.0, (x - y), x);
	} else {
		tmp = ((y - x) * -6.0) * z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.2)
		tmp = fma(Float64(6.0 * z), Float64(x - y), x);
	elseif (z <= 95000.0)
		tmp = fma(-4.0, Float64(x - y), x);
	else
		tmp = Float64(Float64(Float64(y - x) * -6.0) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.2], N[(N[(6.0 * z), $MachinePrecision] * N[(x - y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 95000.0], N[(-4.0 * N[(x - y), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999996

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{2}{3} - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. *-commutative N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} + x \]

      7. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\frac{2}{3} - z\right) \cdot 6\right) \cdot \left(y - x\right)} + x \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)} \cdot \left(y - x\right) + x \]

      9. lift--.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(y - x\right)} + x \]

      10. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right) \cdot \left(x - y\right)} + x \]

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

          \[\leadsto \color{blue}{\left(6 \cdot \left(\mathsf{neg}\left(\left(\frac{2}{3} - z\right)\right)\right)\right)} \cdot \left(x - y\right) + x \]

      14. lift--.f64 N/A

          \[\leadsto \left(6 \cdot \left(\mathsf{neg}\left(\color{blue}{\left(\frac{2}{3} - z\right)}\right)\right)\right) \cdot \left(x - y\right) + x \]

      15. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \color{blue}{\left(z - \frac{2}{3}\right)}\right) \cdot \left(x - y\right) + x \]

      16. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(6 \cdot \left(z - \frac{2}{3}\right), x - y, x\right)} \]

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 50.8

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

   6. Applied rewrites 50.8%

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

   if -1.19999999999999996 < z < 95000

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{2}{3} - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. *-commutative N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} + x \]

      7. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\frac{2}{3} - z\right) \cdot 6\right) \cdot \left(y - x\right)} + x \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)} \cdot \left(y - x\right) + x \]

      9. lift--.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(y - x\right)} + x \]

      10. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right) \cdot \left(x - y\right)} + x \]

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

          \[\leadsto \color{blue}{\left(6 \cdot \left(\mathsf{neg}\left(\left(\frac{2}{3} - z\right)\right)\right)\right)} \cdot \left(x - y\right) + x \]

      14. lift--.f64 N/A

          \[\leadsto \left(6 \cdot \left(\mathsf{neg}\left(\color{blue}{\left(\frac{2}{3} - z\right)}\right)\right)\right) \cdot \left(x - y\right) + x \]

      15. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \color{blue}{\left(z - \frac{2}{3}\right)}\right) \cdot \left(x - y\right) + x \]

      16. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(6 \cdot \left(z - \frac{2}{3}\right), x - y, x\right)} \]

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4}, x - y, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 50.1%

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4}, x - y, x\right) \]

   if 95000 < z

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      3. lift--.f64 N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} - z\right)} \]

      4. sub-flip N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      5. distribute-lft-in N/A

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      6. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(x + \left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

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

         \[\leadsto \color{blue}{\left(x - \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right) \cdot \frac{2}{3}\right)} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(x - \color{blue}{\frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right)} \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\mathsf{neg}\left(z\right)\right), x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

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

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{neg}\left(6 \cdot z\right)}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{-6} \cdot z, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.3

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

   6. Applied rewrites 51.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

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

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

      11. metadata-eval N/A

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

      12. associate-*r* N/A

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

      13. lift--.f64 N/A

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

      14. sub-flip N/A

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

      15. distribute-rgt-in N/A

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

      16. metadata-eval N/A

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

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

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

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

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. distribute-neg-in N/A

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

      22. lift-fma.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 N/A

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

   8. Applied rewrites 51.4%

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

Alternative 7: 97.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -1.2:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 95000:\\ \;\;\;\;\mathsf{fma}\left(-4, x - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - x\right) \cdot -6\right) \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.2)
   (* -6.0 (* z (- y x)))
   (if (<= z 95000.0) (fma -4.0 (- x y) x) (* (* (- y x) -6.0) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.2) {
		tmp = -6.0 * (z * (y - x));
	} else if (z <= 95000.0) {
		tmp = fma(-4.0, (x - y), x);
	} else {
		tmp = ((y - x) * -6.0) * z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.2)
		tmp = Float64(-6.0 * Float64(z * Float64(y - x)));
	elseif (z <= 95000.0)
		tmp = fma(-4.0, Float64(x - y), x);
	else
		tmp = Float64(Float64(Float64(y - x) * -6.0) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.2], N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 95000.0], N[(-4.0 * N[(x - y), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999996

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.3

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

   4. Applied rewrites 51.3%

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

   if -1.19999999999999996 < z < 95000

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{2}{3} - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. *-commutative N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} + x \]

      7. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\frac{2}{3} - z\right) \cdot 6\right) \cdot \left(y - x\right)} + x \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)} \cdot \left(y - x\right) + x \]

      9. lift--.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(y - x\right)} + x \]

      10. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right) \cdot \left(x - y\right)} + x \]

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

          \[\leadsto \color{blue}{\left(6 \cdot \left(\mathsf{neg}\left(\left(\frac{2}{3} - z\right)\right)\right)\right)} \cdot \left(x - y\right) + x \]

      14. lift--.f64 N/A

          \[\leadsto \left(6 \cdot \left(\mathsf{neg}\left(\color{blue}{\left(\frac{2}{3} - z\right)}\right)\right)\right) \cdot \left(x - y\right) + x \]

      15. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \color{blue}{\left(z - \frac{2}{3}\right)}\right) \cdot \left(x - y\right) + x \]

      16. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(6 \cdot \left(z - \frac{2}{3}\right), x - y, x\right)} \]

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4}, x - y, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 50.1%

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4}, x - y, x\right) \]

   if 95000 < z

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      3. lift--.f64 N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} - z\right)} \]

      4. sub-flip N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      5. distribute-lft-in N/A

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      6. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(x + \left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

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

         \[\leadsto \color{blue}{\left(x - \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right) \cdot \frac{2}{3}\right)} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(x - \color{blue}{\frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right)} \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\mathsf{neg}\left(z\right)\right), x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

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

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{neg}\left(6 \cdot z\right)}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{-6} \cdot z, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.3

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

   6. Applied rewrites 51.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

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

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

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

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

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

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

      11. metadata-eval N/A

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

      12. associate-*r* N/A

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

      13. lift--.f64 N/A

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

      14. sub-flip N/A

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

      15. distribute-rgt-in N/A

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

      16. metadata-eval N/A

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

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

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

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

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. distribute-neg-in N/A

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

      22. lift-fma.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 N/A

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

   8. Applied rewrites 51.4%

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

Alternative 8: 97.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -1.2:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 95000:\\ \;\;\;\;\mathsf{fma}\left(-4, x - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z (- y x)))))
   (if (<= z -1.2) t_0 (if (<= z 95000.0) (fma -4.0 (- x y) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -1.2) {
		tmp = t_0;
	} else if (z <= 95000.0) {
		tmp = fma(-4.0, (x - y), x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -1.2)
		tmp = t_0;
	elseif (z <= 95000.0)
		tmp = fma(-4.0, Float64(x - y), x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2], t$95$0, If[LessEqual[z, 95000.0], N[(-4.0 * N[(x - y), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.19999999999999996 or 95000 < z

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.3

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

   4. Applied rewrites 51.3%

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

   if -1.19999999999999996 < z < 95000

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{2}{3} - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. *-commutative N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} + x \]

      7. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\frac{2}{3} - z\right) \cdot 6\right) \cdot \left(y - x\right)} + x \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)} \cdot \left(y - x\right) + x \]

      9. lift--.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(y - x\right)} + x \]

      10. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right) \cdot \left(x - y\right)} + x \]

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

          \[\leadsto \color{blue}{\left(6 \cdot \left(\mathsf{neg}\left(\left(\frac{2}{3} - z\right)\right)\right)\right)} \cdot \left(x - y\right) + x \]

      14. lift--.f64 N/A

          \[\leadsto \left(6 \cdot \left(\mathsf{neg}\left(\color{blue}{\left(\frac{2}{3} - z\right)}\right)\right)\right) \cdot \left(x - y\right) + x \]

      15. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \color{blue}{\left(z - \frac{2}{3}\right)}\right) \cdot \left(x - y\right) + x \]

      16. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(6 \cdot \left(z - \frac{2}{3}\right), x - y, x\right)} \]

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4}, x - y, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 50.1%

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

Alternative 9: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \frac{2}{3} - z\\ t_1 := \mathsf{fma}\left(z, -6, 4\right) \cdot y\\ \mathbf{if}\;t\_0 \leq 0.666666666666:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.667:\\ \;\;\;\;\mathsf{fma}\left(-4, x - y, x\right)\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+228}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (/ 2.0 3.0) z)) (t_1 (* (fma z -6.0 4.0) y)))
   (if (<= t_0 0.666666666666)
     t_1
     (if (<= t_0 0.667)
       (fma -4.0 (- x y) x)
       (if (<= t_0 5e+228) t_1 (* 6.0 (* x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (2.0 / 3.0) - z;
	double t_1 = fma(z, -6.0, 4.0) * y;
	double tmp;
	if (t_0 <= 0.666666666666) {
		tmp = t_1;
	} else if (t_0 <= 0.667) {
		tmp = fma(-4.0, (x - y), x);
	} else if (t_0 <= 5e+228) {
		tmp = t_1;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(2.0 / 3.0) - z)
	t_1 = Float64(fma(z, -6.0, 4.0) * y)
	tmp = 0.0
	if (t_0 <= 0.666666666666)
		tmp = t_1;
	elseif (t_0 <= 0.667)
		tmp = fma(-4.0, Float64(x - y), x);
	elseif (t_0 <= 5e+228)
		tmp = t_1;
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(z * -6.0 + 4.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$0, 0.666666666666], t$95$1, If[LessEqual[t$95$0, 0.667], N[(-4.0 * N[(x - y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$0, 5e+228], t$95$1, N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 0.666666666666000052 or 0.66700000000000004 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 5e228

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto 6 \cdot \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \color{blue}{\left(\frac{2}{3} - z\right)}\right) \]

      4. lower--.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - \color{blue}{z}\right)\right) \]

      5. metadata-eval 51.5

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) \]

   4. Applied rewrites 51.5%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto 6 \cdot \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \color{blue}{\left(\frac{2}{3} - z\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto 6 \cdot \left(\left(\frac{2}{3} - z\right) \cdot \color{blue}{y}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{y} \]

      7. lift--.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot y \]

      8. sub-flip N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right)\right) \cdot y \]

      9. distribute-lft-in N/A

         \[\leadsto \left(6 \cdot \frac{2}{3} + 6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot y \]

      10. metadata-eval N/A

          \[\leadsto \left(6 \cdot \frac{2}{3} + 6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot y \]

      11. metadata-eval N/A

          \[\leadsto \left(4 + 6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot y \]

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

          \[\leadsto \left(4 + \left(\mathsf{neg}\left(6 \cdot z\right)\right)\right) \cdot y \]

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

          \[\leadsto \left(4 + \left(\mathsf{neg}\left(6\right)\right) \cdot z\right) \cdot y \]

      14. metadata-eval N/A

          \[\leadsto \left(4 + -6 \cdot z\right) \cdot y \]

      15. lift-*.f64 N/A

          \[\leadsto \left(4 + -6 \cdot z\right) \cdot y \]

      16. +-commutative N/A

          \[\leadsto \left(-6 \cdot z + 4\right) \cdot y \]

      17. lift-*.f64 N/A

          \[\leadsto \left(-6 \cdot z + 4\right) \cdot y \]

      18. *-commutative N/A

          \[\leadsto \left(z \cdot -6 + 4\right) \cdot y \]

      19. lower-fma.f64 51.6

          \[\leadsto \mathsf{fma}\left(z, -6, 4\right) \cdot y \]

   6. Applied rewrites 51.6%

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

   if 0.666666666666000052 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 0.66700000000000004

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{2}{3} - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. *-commutative N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} + x \]

      7. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\frac{2}{3} - z\right) \cdot 6\right) \cdot \left(y - x\right)} + x \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)} \cdot \left(y - x\right) + x \]

      9. lift--.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(y - x\right)} + x \]

      10. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right) \cdot \left(x - y\right)} + x \]

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

          \[\leadsto \color{blue}{\left(6 \cdot \left(\mathsf{neg}\left(\left(\frac{2}{3} - z\right)\right)\right)\right)} \cdot \left(x - y\right) + x \]

      14. lift--.f64 N/A

          \[\leadsto \left(6 \cdot \left(\mathsf{neg}\left(\color{blue}{\left(\frac{2}{3} - z\right)}\right)\right)\right) \cdot \left(x - y\right) + x \]

      15. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \color{blue}{\left(z - \frac{2}{3}\right)}\right) \cdot \left(x - y\right) + x \]

      16. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(6 \cdot \left(z - \frac{2}{3}\right), x - y, x\right)} \]

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4}, x - y, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 50.1%

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4}, x - y, x\right) \]

   if 5e228 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z)

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      3. lift--.f64 N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} - z\right)} \]

      4. sub-flip N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      5. distribute-lft-in N/A

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      6. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(x + \left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

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

         \[\leadsto \color{blue}{\left(x - \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right) \cdot \frac{2}{3}\right)} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(x - \color{blue}{\frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right)} \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\mathsf{neg}\left(z\right)\right), x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

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

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{neg}\left(6 \cdot z\right)}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{-6} \cdot z, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.3

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

   6. Applied rewrites 51.3%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 27.1

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

   9. Applied rewrites 27.1%

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

Alternative 10: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \frac{2}{3} - z\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;t\_0 \leq -50000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 20000:\\ \;\;\;\;\mathsf{fma}\left(-4, x - y, x\right)\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+228}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (/ 2.0 3.0) z)) (t_1 (* -6.0 (* y z))))
   (if (<= t_0 -50000.0)
     t_1
     (if (<= t_0 20000.0)
       (fma -4.0 (- x y) x)
       (if (<= t_0 5e+228) t_1 (* 6.0 (* x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (2.0 / 3.0) - z;
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (t_0 <= -50000.0) {
		tmp = t_1;
	} else if (t_0 <= 20000.0) {
		tmp = fma(-4.0, (x - y), x);
	} else if (t_0 <= 5e+228) {
		tmp = t_1;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(2.0 / 3.0) - z)
	t_1 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (t_0 <= -50000.0)
		tmp = t_1;
	elseif (t_0 <= 20000.0)
		tmp = fma(-4.0, Float64(x - y), x);
	elseif (t_0 <= 5e+228)
		tmp = t_1;
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -50000.0], t$95$1, If[LessEqual[t$95$0, 20000.0], N[(-4.0 * N[(x - y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$0, 5e+228], t$95$1, N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < -5e4 or 2e4 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 5e228

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto 6 \cdot \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \color{blue}{\left(\frac{2}{3} - z\right)}\right) \]

      4. lower--.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - \color{blue}{z}\right)\right) \]

      5. metadata-eval 51.5

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) \]

   4. Applied rewrites 51.5%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 28.4

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

   7. Applied rewrites 28.4%

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

   if -5e4 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z) < 2e4

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} + x \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{2}{3} - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)} + x \]

      6. *-commutative N/A

         \[\leadsto \left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(6 \cdot \left(y - x\right)\right)} + x \]

      7. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\frac{2}{3} - z\right) \cdot 6\right) \cdot \left(y - x\right)} + x \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)} \cdot \left(y - x\right) + x \]

      9. lift--.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(y - x\right)} + x \]

      10. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \left(x - y\right)\right)\right)} + x \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(6 \cdot \left(\frac{2}{3} - z\right)\right)\right) \cdot \left(x - y\right)} + x \]

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

          \[\leadsto \color{blue}{\left(6 \cdot \left(\mathsf{neg}\left(\left(\frac{2}{3} - z\right)\right)\right)\right)} \cdot \left(x - y\right) + x \]

      14. lift--.f64 N/A

          \[\leadsto \left(6 \cdot \left(\mathsf{neg}\left(\color{blue}{\left(\frac{2}{3} - z\right)}\right)\right)\right) \cdot \left(x - y\right) + x \]

      15. sub-negate-rev N/A

          \[\leadsto \left(6 \cdot \color{blue}{\left(z - \frac{2}{3}\right)}\right) \cdot \left(x - y\right) + x \]

      16. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(6 \cdot \left(z - \frac{2}{3}\right), x - y, x\right)} \]

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4}, x - y, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 50.1%

      \[\leadsto \mathsf{fma}\left(\color{blue}{-4}, x - y, x\right) \]

   if 5e228 < (-.f64 (/.f64 #s(literal 2 binary64) #s(literal 3 binary64)) z)

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      3. lift--.f64 N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} - z\right)} \]

      4. sub-flip N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      5. distribute-lft-in N/A

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      6. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(x + \left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

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

         \[\leadsto \color{blue}{\left(x - \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right) \cdot \frac{2}{3}\right)} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(x - \color{blue}{\frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right)} \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\mathsf{neg}\left(z\right)\right), x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

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

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{neg}\left(6 \cdot z\right)}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{-6} \cdot z, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.3

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

   6. Applied rewrites 51.3%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 27.1

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

   9. Applied rewrites 27.1%

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

Alternative 11: 50.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+233}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-221}:\\ \;\;\;\;x + -4 \cdot x\\ \mathbf{elif}\;z \leq 95000:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -1.5e+233)
     (* 6.0 (* x z))
     (if (<= z -3.7e-18)
       t_0
       (if (<= z -1.45e-221)
         (+ x (* -4.0 x))
         (if (<= z 95000.0) (* 4.0 y) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.5e+233) {
		tmp = 6.0 * (x * z);
	} else if (z <= -3.7e-18) {
		tmp = t_0;
	} else if (z <= -1.45e-221) {
		tmp = x + (-4.0 * x);
	} else if (z <= 95000.0) {
		tmp = 4.0 * y;
	} 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 <= (-1.5d+233)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-3.7d-18)) then
        tmp = t_0
    else if (z <= (-1.45d-221)) then
        tmp = x + ((-4.0d0) * x)
    else if (z <= 95000.0d0) then
        tmp = 4.0d0 * y
    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 <= -1.5e+233) {
		tmp = 6.0 * (x * z);
	} else if (z <= -3.7e-18) {
		tmp = t_0;
	} else if (z <= -1.45e-221) {
		tmp = x + (-4.0 * x);
	} else if (z <= 95000.0) {
		tmp = 4.0 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -1.5e+233:
		tmp = 6.0 * (x * z)
	elif z <= -3.7e-18:
		tmp = t_0
	elif z <= -1.45e-221:
		tmp = x + (-4.0 * x)
	elif z <= 95000.0:
		tmp = 4.0 * y
	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 <= -1.5e+233)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -3.7e-18)
		tmp = t_0;
	elseif (z <= -1.45e-221)
		tmp = Float64(x + Float64(-4.0 * x));
	elseif (z <= 95000.0)
		tmp = Float64(4.0 * y);
	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 <= -1.5e+233)
		tmp = 6.0 * (x * z);
	elseif (z <= -3.7e-18)
		tmp = t_0;
	elseif (z <= -1.45e-221)
		tmp = x + (-4.0 * x);
	elseif (z <= 95000.0)
		tmp = 4.0 * y;
	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, -1.5e+233], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.7e-18], t$95$0, If[LessEqual[z, -1.45e-221], N[(x + N[(-4.0 * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 95000.0], N[(4.0 * y), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.50000000000000007e233

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)} \]

      3. lift--.f64 N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} - z\right)} \]

      4. sub-flip N/A

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      5. distribute-lft-in N/A

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} \]

      6. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(x + \left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

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

         \[\leadsto \color{blue}{\left(x - \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right) \cdot \frac{2}{3}\right)} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \left(x - \color{blue}{\frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right)} \cdot \left(\mathsf{neg}\left(z\right)\right) + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)} + \left(x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\mathsf{neg}\left(z\right)\right), x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right)} \]

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

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{neg}\left(6 \cdot z\right)}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

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

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(\mathsf{neg}\left(6\right)\right) \cdot z}, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{-6} \cdot z, x - \frac{2}{3} \cdot \left(\mathsf{neg}\left(\left(y - x\right) \cdot 6\right)\right)\right) \]

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.3

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

   6. Applied rewrites 51.3%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 27.1

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

   9. Applied rewrites 27.1%

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

   if -1.50000000000000007e233 < z < -3.7000000000000003e-18 or 95000 < z

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto 6 \cdot \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \color{blue}{\left(\frac{2}{3} - z\right)}\right) \]

      4. lower--.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - \color{blue}{z}\right)\right) \]

      5. metadata-eval 51.5

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) \]

   4. Applied rewrites 51.5%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 28.4

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

   7. Applied rewrites 28.4%

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

   if -3.7000000000000003e-18 < z < -1.44999999999999997e-221

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

         \[\leadsto x + 4 \cdot \color{blue}{\left(y - x\right)} \]

      2. lower--.f64 50.1

         \[\leadsto x + 4 \cdot \left(y - \color{blue}{x}\right) \]

   4. Applied rewrites 50.1%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 26.5

         \[\leadsto x + -4 \cdot x \]

   7. Applied rewrites 26.5%

      \[\leadsto x + -4 \cdot \color{blue}{x} \]

   if -1.44999999999999997e-221 < z < 95000

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto 6 \cdot \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \color{blue}{\left(\frac{2}{3} - z\right)}\right) \]

      4. lower--.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - \color{blue}{z}\right)\right) \]

      5. metadata-eval 51.5

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) \]

   4. Applied rewrites 51.5%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto 6 \cdot \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \color{blue}{\left(\frac{2}{3} - z\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto 6 \cdot \left(\left(\frac{2}{3} - z\right) \cdot \color{blue}{y}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{y} \]

      7. lift--.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot y \]

      8. sub-flip N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right)\right) \cdot y \]

      9. distribute-lft-in N/A

         \[\leadsto \left(6 \cdot \frac{2}{3} + 6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot y \]

      10. metadata-eval N/A

          \[\leadsto \left(6 \cdot \frac{2}{3} + 6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot y \]

      11. metadata-eval N/A

          \[\leadsto \left(4 + 6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot y \]

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

          \[\leadsto \left(4 + \left(\mathsf{neg}\left(6 \cdot z\right)\right)\right) \cdot y \]

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

          \[\leadsto \left(4 + \left(\mathsf{neg}\left(6\right)\right) \cdot z\right) \cdot y \]

      14. metadata-eval N/A

          \[\leadsto \left(4 + -6 \cdot z\right) \cdot y \]

      15. lift-*.f64 N/A

          \[\leadsto \left(4 + -6 \cdot z\right) \cdot y \]

      16. +-commutative N/A

          \[\leadsto \left(-6 \cdot z + 4\right) \cdot y \]

      17. lift-*.f64 N/A

          \[\leadsto \left(-6 \cdot z + 4\right) \cdot y \]

      18. *-commutative N/A

          \[\leadsto \left(z \cdot -6 + 4\right) \cdot y \]

      19. lower-fma.f64 51.6

          \[\leadsto \mathsf{fma}\left(z, -6, 4\right) \cdot y \]

   6. Applied rewrites 51.6%

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

   7. Taylor expanded in z around 0

      \[\leadsto 4 \cdot y \]
   8. Step-by-step derivation

   9. Applied rewrites 25.4%

      \[\leadsto 4 \cdot y \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 12: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-221}:\\ \;\;\;\;x + -4 \cdot x\\ \mathbf{elif}\;z \leq 95000:\\ \;\;\;\;4 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -3.7e-18)
     t_0
     (if (<= z -1.45e-221)
       (+ x (* -4.0 x))
       (if (<= z 95000.0) (* 4.0 y) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -3.7e-18) {
		tmp = t_0;
	} else if (z <= -1.45e-221) {
		tmp = x + (-4.0 * x);
	} else if (z <= 95000.0) {
		tmp = 4.0 * y;
	} 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 <= (-3.7d-18)) then
        tmp = t_0
    else if (z <= (-1.45d-221)) then
        tmp = x + ((-4.0d0) * x)
    else if (z <= 95000.0d0) then
        tmp = 4.0d0 * y
    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 <= -3.7e-18) {
		tmp = t_0;
	} else if (z <= -1.45e-221) {
		tmp = x + (-4.0 * x);
	} else if (z <= 95000.0) {
		tmp = 4.0 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -3.7e-18:
		tmp = t_0
	elif z <= -1.45e-221:
		tmp = x + (-4.0 * x)
	elif z <= 95000.0:
		tmp = 4.0 * y
	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 <= -3.7e-18)
		tmp = t_0;
	elseif (z <= -1.45e-221)
		tmp = Float64(x + Float64(-4.0 * x));
	elseif (z <= 95000.0)
		tmp = Float64(4.0 * y);
	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 <= -3.7e-18)
		tmp = t_0;
	elseif (z <= -1.45e-221)
		tmp = x + (-4.0 * x);
	elseif (z <= 95000.0)
		tmp = 4.0 * y;
	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, -3.7e-18], t$95$0, If[LessEqual[z, -1.45e-221], N[(x + N[(-4.0 * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 95000.0], N[(4.0 * y), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7000000000000003e-18 or 95000 < z

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto 6 \cdot \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \color{blue}{\left(\frac{2}{3} - z\right)}\right) \]

      4. lower--.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - \color{blue}{z}\right)\right) \]

      5. metadata-eval 51.5

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) \]

   4. Applied rewrites 51.5%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 28.4

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

   7. Applied rewrites 28.4%

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

   if -3.7000000000000003e-18 < z < -1.44999999999999997e-221

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

         \[\leadsto x + 4 \cdot \color{blue}{\left(y - x\right)} \]

      2. lower--.f64 50.1

         \[\leadsto x + 4 \cdot \left(y - \color{blue}{x}\right) \]

   4. Applied rewrites 50.1%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 26.5

         \[\leadsto x + -4 \cdot x \]

   7. Applied rewrites 26.5%

      \[\leadsto x + -4 \cdot \color{blue}{x} \]

   if -1.44999999999999997e-221 < z < 95000

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto 6 \cdot \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \color{blue}{\left(\frac{2}{3} - z\right)}\right) \]

      4. lower--.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - \color{blue}{z}\right)\right) \]

      5. metadata-eval 51.5

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) \]

   4. Applied rewrites 51.5%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto 6 \cdot \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \color{blue}{\left(\frac{2}{3} - z\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto 6 \cdot \left(\left(\frac{2}{3} - z\right) \cdot \color{blue}{y}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{y} \]

      7. lift--.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot y \]

      8. sub-flip N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right)\right) \cdot y \]

      9. distribute-lft-in N/A

         \[\leadsto \left(6 \cdot \frac{2}{3} + 6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot y \]

      10. metadata-eval N/A

          \[\leadsto \left(6 \cdot \frac{2}{3} + 6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot y \]

      11. metadata-eval N/A

          \[\leadsto \left(4 + 6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot y \]

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

          \[\leadsto \left(4 + \left(\mathsf{neg}\left(6 \cdot z\right)\right)\right) \cdot y \]

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

          \[\leadsto \left(4 + \left(\mathsf{neg}\left(6\right)\right) \cdot z\right) \cdot y \]

      14. metadata-eval N/A

          \[\leadsto \left(4 + -6 \cdot z\right) \cdot y \]

      15. lift-*.f64 N/A

          \[\leadsto \left(4 + -6 \cdot z\right) \cdot y \]

      16. +-commutative N/A

          \[\leadsto \left(-6 \cdot z + 4\right) \cdot y \]

      17. lift-*.f64 N/A

          \[\leadsto \left(-6 \cdot z + 4\right) \cdot y \]

      18. *-commutative N/A

          \[\leadsto \left(z \cdot -6 + 4\right) \cdot y \]

      19. lower-fma.f64 51.6

          \[\leadsto \mathsf{fma}\left(z, -6, 4\right) \cdot y \]

   6. Applied rewrites 51.6%

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

   7. Taylor expanded in z around 0

      \[\leadsto 4 \cdot y \]
   8. Step-by-step derivation

   9. Applied rewrites 25.4%

      \[\leadsto 4 \cdot y \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 34.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_0 := x + 4 \cdot y\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{-166}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+117}:\\ \;\;\;\;x + -4 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* 4.0 y))))
   (if (<= y -5.5e-166) t_0 (if (<= y 9.8e+117) (+ x (* -4.0 x)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (4.0 * y);
	double tmp;
	if (y <= -5.5e-166) {
		tmp = t_0;
	} else if (y <= 9.8e+117) {
		tmp = x + (-4.0 * x);
	} 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 = x + (4.0d0 * y)
    if (y <= (-5.5d-166)) then
        tmp = t_0
    else if (y <= 9.8d+117) then
        tmp = x + ((-4.0d0) * x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (4.0 * y);
	double tmp;
	if (y <= -5.5e-166) {
		tmp = t_0;
	} else if (y <= 9.8e+117) {
		tmp = x + (-4.0 * x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (4.0 * y)
	tmp = 0
	if y <= -5.5e-166:
		tmp = t_0
	elif y <= 9.8e+117:
		tmp = x + (-4.0 * x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(4.0 * y))
	tmp = 0.0
	if (y <= -5.5e-166)
		tmp = t_0;
	elseif (y <= 9.8e+117)
		tmp = Float64(x + Float64(-4.0 * x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (4.0 * y);
	tmp = 0.0;
	if (y <= -5.5e-166)
		tmp = t_0;
	elseif (y <= 9.8e+117)
		tmp = x + (-4.0 * x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(4.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e-166], t$95$0, If[LessEqual[y, 9.8e+117], N[(x + N[(-4.0 * x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4999999999999997e-166 or 9.8000000000000002e117 < y

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

         \[\leadsto x + 4 \cdot \color{blue}{\left(y - x\right)} \]

      2. lower--.f64 50.1

         \[\leadsto x + 4 \cdot \left(y - \color{blue}{x}\right) \]

   4. Applied rewrites 50.1%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + 4 \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 25.1%

      \[\leadsto x + 4 \cdot y \]

   if -5.4999999999999997e-166 < y < 9.8000000000000002e117

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

         \[\leadsto x + 4 \cdot \color{blue}{\left(y - x\right)} \]

      2. lower--.f64 50.1

         \[\leadsto x + 4 \cdot \left(y - \color{blue}{x}\right) \]

   4. Applied rewrites 50.1%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 26.5

         \[\leadsto x + -4 \cdot x \]

   7. Applied rewrites 26.5%

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

Alternative 14: 34.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-166}:\\ \;\;\;\;4 \cdot y\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+117}:\\ \;\;\;\;x + -4 \cdot x\\ \mathbf{else}:\\ \;\;\;\;4 \cdot y\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.5e-166)
   (* 4.0 y)
   (if (<= y 9.8e+117) (+ x (* -4.0 x)) (* 4.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e-166) {
		tmp = 4.0 * y;
	} else if (y <= 9.8e+117) {
		tmp = x + (-4.0 * x);
	} else {
		tmp = 4.0 * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.5d-166)) then
        tmp = 4.0d0 * y
    else if (y <= 9.8d+117) then
        tmp = x + ((-4.0d0) * x)
    else
        tmp = 4.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e-166) {
		tmp = 4.0 * y;
	} else if (y <= 9.8e+117) {
		tmp = x + (-4.0 * x);
	} else {
		tmp = 4.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.5e-166:
		tmp = 4.0 * y
	elif y <= 9.8e+117:
		tmp = x + (-4.0 * x)
	else:
		tmp = 4.0 * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.5e-166)
		tmp = Float64(4.0 * y);
	elseif (y <= 9.8e+117)
		tmp = Float64(x + Float64(-4.0 * x));
	else
		tmp = Float64(4.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.5e-166)
		tmp = 4.0 * y;
	elseif (y <= 9.8e+117)
		tmp = x + (-4.0 * x);
	else
		tmp = 4.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.5e-166], N[(4.0 * y), $MachinePrecision], If[LessEqual[y, 9.8e+117], N[(x + N[(-4.0 * x), $MachinePrecision]), $MachinePrecision], N[(4.0 * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4999999999999997e-166 or 9.8000000000000002e117 < y

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto 6 \cdot \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \color{blue}{\left(\frac{2}{3} - z\right)}\right) \]

      4. lower--.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - \color{blue}{z}\right)\right) \]

      5. metadata-eval 51.5

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) \]

   4. Applied rewrites 51.5%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto 6 \cdot \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto 6 \cdot \left(y \cdot \color{blue}{\left(\frac{2}{3} - z\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto 6 \cdot \left(\left(\frac{2}{3} - z\right) \cdot \color{blue}{y}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{y} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{y} \]

      7. lift--.f64 N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot y \]

      8. sub-flip N/A

         \[\leadsto \left(6 \cdot \left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right)\right) \cdot y \]

      9. distribute-lft-in N/A

         \[\leadsto \left(6 \cdot \frac{2}{3} + 6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot y \]

      10. metadata-eval N/A

          \[\leadsto \left(6 \cdot \frac{2}{3} + 6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot y \]

      11. metadata-eval N/A

          \[\leadsto \left(4 + 6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot y \]

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

          \[\leadsto \left(4 + \left(\mathsf{neg}\left(6 \cdot z\right)\right)\right) \cdot y \]

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

          \[\leadsto \left(4 + \left(\mathsf{neg}\left(6\right)\right) \cdot z\right) \cdot y \]

      14. metadata-eval N/A

          \[\leadsto \left(4 + -6 \cdot z\right) \cdot y \]

      15. lift-*.f64 N/A

          \[\leadsto \left(4 + -6 \cdot z\right) \cdot y \]

      16. +-commutative N/A

          \[\leadsto \left(-6 \cdot z + 4\right) \cdot y \]

      17. lift-*.f64 N/A

          \[\leadsto \left(-6 \cdot z + 4\right) \cdot y \]

      18. *-commutative N/A

          \[\leadsto \left(z \cdot -6 + 4\right) \cdot y \]

      19. lower-fma.f64 51.6

          \[\leadsto \mathsf{fma}\left(z, -6, 4\right) \cdot y \]

   6. Applied rewrites 51.6%

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

   7. Taylor expanded in z around 0

      \[\leadsto 4 \cdot y \]
   8. Step-by-step derivation

   9. Applied rewrites 25.4%

      \[\leadsto 4 \cdot y \]

   if -5.4999999999999997e-166 < y < 9.8000000000000002e117

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

         \[\leadsto x + 4 \cdot \color{blue}{\left(y - x\right)} \]

      2. lower--.f64 50.1

         \[\leadsto x + 4 \cdot \left(y - \color{blue}{x}\right) \]

   4. Applied rewrites 50.1%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 26.5

         \[\leadsto x + -4 \cdot x \]

   7. Applied rewrites 26.5%

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

Alternative 15: 25.4% accurate, 4.6× speedup

Math

\[4 \cdot y \]

FPCore

(FPCore (x y z) :precision binary64 (* 4.0 y))

C

double code(double x, double y, double z) {
	return 4.0 * y;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 4.0d0 * y
end function

Java

public static double code(double x, double y, double z) {
	return 4.0 * y;
}

Python

def code(x, y, z):
	return 4.0 * y

Julia

function code(x, y, z)
	return Float64(4.0 * y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 4.0 * y;
end

Wolfram

code[x_, y_, z_] := N[(4.0 * y), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

2. Taylor expanded in x around 0

   \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
3. Step-by-step derivation

   1. metadata-eval N/A

      \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right) \]

   2. lower-*.f64 N/A

      \[\leadsto 6 \cdot \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]

   3. lower-*.f64 N/A

      \[\leadsto 6 \cdot \left(y \cdot \color{blue}{\left(\frac{2}{3} - z\right)}\right) \]

   4. lower--.f64 N/A

      \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - \color{blue}{z}\right)\right) \]

   5. metadata-eval 51.5

      \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) \]

4. Applied rewrites 51.5%

   \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
5. Step-by-step derivation

   1. metadata-eval N/A

      \[\leadsto 6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right) \]

   2. lift-*.f64 N/A

      \[\leadsto 6 \cdot \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto 6 \cdot \left(y \cdot \color{blue}{\left(\frac{2}{3} - z\right)}\right) \]

   4. *-commutative N/A

      \[\leadsto 6 \cdot \left(\left(\frac{2}{3} - z\right) \cdot \color{blue}{y}\right) \]

   5. associate-*r* N/A

      \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{y} \]

   6. lower-*.f64 N/A

      \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \color{blue}{y} \]

   7. lift--.f64 N/A

      \[\leadsto \left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot y \]

   8. sub-flip N/A

      \[\leadsto \left(6 \cdot \left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right)\right) \cdot y \]

   9. distribute-lft-in N/A

      \[\leadsto \left(6 \cdot \frac{2}{3} + 6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot y \]

   10. metadata-eval N/A

       \[\leadsto \left(6 \cdot \frac{2}{3} + 6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot y \]

   11. metadata-eval N/A

       \[\leadsto \left(4 + 6 \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot y \]

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

       \[\leadsto \left(4 + \left(\mathsf{neg}\left(6 \cdot z\right)\right)\right) \cdot y \]

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

       \[\leadsto \left(4 + \left(\mathsf{neg}\left(6\right)\right) \cdot z\right) \cdot y \]

   14. metadata-eval N/A

       \[\leadsto \left(4 + -6 \cdot z\right) \cdot y \]

   15. lift-*.f64 N/A

       \[\leadsto \left(4 + -6 \cdot z\right) \cdot y \]

   16. +-commutative N/A

       \[\leadsto \left(-6 \cdot z + 4\right) \cdot y \]

   17. lift-*.f64 N/A

       \[\leadsto \left(-6 \cdot z + 4\right) \cdot y \]

   18. *-commutative N/A

       \[\leadsto \left(z \cdot -6 + 4\right) \cdot y \]

   19. lower-fma.f64 51.6

       \[\leadsto \mathsf{fma}\left(z, -6, 4\right) \cdot y \]

6. Applied rewrites 51.6%

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

7. Taylor expanded in z around 0

   \[\leadsto 4 \cdot y \]
8. Step-by-step derivation

9. Applied rewrites 25.4%

   \[\leadsto 4 \cdot y \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2025172 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))