Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J

Percentage Accurate: 96.2% → 99.9%

Time: 2.4s

Alternatives: 8

Speedup: 0.5×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.2% accurate, 1.0× speedup

Math

\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.5× speedup

Math

\[\mathsf{copysign}\left(1, x\right) \cdot \begin{array}{l} \mathbf{if}\;\left|x\right| \leq 5 \cdot 10^{-44}:\\ \;\;\;\;\mathsf{fma}\left(\left(y - 1\right) \cdot \left|x\right|, z, \left|x\right|\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 1, z \cdot \left|x\right|, \left|x\right|\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (*
  (copysign 1.0 x)
  (if (<= (fabs x) 5e-44)
    (fma (* (- y 1.0) (fabs x)) z (fabs x))
    (fma (- y 1.0) (* z (fabs x)) (fabs x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (fabs(x) <= 5e-44) {
		tmp = fma(((y - 1.0) * fabs(x)), z, fabs(x));
	} else {
		tmp = fma((y - 1.0), (z * fabs(x)), fabs(x));
	}
	return copysign(1.0, x) * tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (abs(x) <= 5e-44)
		tmp = fma(Float64(Float64(y - 1.0) * abs(x)), z, abs(x));
	else
		tmp = fma(Float64(y - 1.0), Float64(z * abs(x)), abs(x));
	end
	return Float64(copysign(1.0, x) * tmp)
end

Wolfram

code[x_, y_, z_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[x], $MachinePrecision], 5e-44], N[(N[(N[(y - 1.0), $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision] * z + N[Abs[x], $MachinePrecision]), $MachinePrecision], N[(N[(y - 1.0), $MachinePrecision] * N[(z * N[Abs[x], $MachinePrecision]), $MachinePrecision] + N[Abs[x], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 5.00000000000000039e-44

   1. Initial program 96.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-in N/A

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

      6. *-rgt-identity N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. associate-*r* N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower--.f64 95.9

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

   3. Applied rewrites 95.9%

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

   if 5.00000000000000039e-44 < x

   1. Initial program 96.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-in N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

      15. lower--.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 98.0

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

   3. Applied rewrites 98.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - 1, z \cdot x, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 97.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ t_1 := \mathsf{fma}\left(x \cdot y, z, x\right)\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq -100000:\\ \;\;\;\;x \cdot \left(z \cdot y - z\right)\\ \mathbf{elif}\;t\_0 \leq 10000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;t\_0 \leq 10^{+307}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)) (t_1 (fma (* x y) z x)))
   (if (<= t_0 -2e+290)
     t_1
     (if (<= t_0 -100000.0)
       (* x (- (* z y) z))
       (if (<= t_0 10000000000.0)
         (* x (- 1.0 z))
         (if (<= t_0 1e+307) (* x (* z (- y 1.0))) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double t_1 = fma((x * y), z, x);
	double tmp;
	if (t_0 <= -2e+290) {
		tmp = t_1;
	} else if (t_0 <= -100000.0) {
		tmp = x * ((z * y) - z);
	} else if (t_0 <= 10000000000.0) {
		tmp = x * (1.0 - z);
	} else if (t_0 <= 1e+307) {
		tmp = x * (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	t_1 = fma(Float64(x * y), z, x)
	tmp = 0.0
	if (t_0 <= -2e+290)
		tmp = t_1;
	elseif (t_0 <= -100000.0)
		tmp = Float64(x * Float64(Float64(z * y) - z));
	elseif (t_0 <= 10000000000.0)
		tmp = Float64(x * Float64(1.0 - z));
	elseif (t_0 <= 1e+307)
		tmp = Float64(x * Float64(z * Float64(y - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+290], t$95$1, If[LessEqual[t$95$0, -100000.0], N[(x * N[(N[(z * y), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 10000000000.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+307], N[(x * N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -2.00000000000000012e290 or 9.99999999999999986e306 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 96.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-in N/A

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

      6. *-rgt-identity N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. associate-*r* N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower--.f64 95.9

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

   3. Applied rewrites 95.9%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 72.7

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

   6. Applied rewrites 72.7%

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

   if -2.00000000000000012e290 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -1e5

   1. Initial program 96.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 58.3

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

   4. Applied rewrites 58.3%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. distribute-rgt-in N/A

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

      5. lift-*.f64 N/A

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

      6. add-flip N/A

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

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

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

      8. remove-double-neg N/A

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

      9. *-lft-identity N/A

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

      10. lower--.f64 58.3

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 58.3

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

   6. Applied rewrites 58.3%

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

   if -1e5 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 1e10

   1. Initial program 96.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 66.6%

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

   if 1e10 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 9.99999999999999986e306

   1. Initial program 96.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 58.3

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

   4. Applied rewrites 58.3%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(y - 1\right)\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 96.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := x \cdot \left(z \cdot \left(y - 1\right)\right)\\ t_1 := 1 - \left(1 - y\right) \cdot z\\ t_2 := \mathsf{fma}\left(x \cdot y, z, x\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+31}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+280}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z (- y 1.0))))
        (t_1 (- 1.0 (* (- 1.0 y) z)))
        (t_2 (fma (* x y) z x)))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -2e+31)
       t_0
       (if (<= t_1 5.0) (* x (- 1.0 z)) (if (<= t_1 5e+280) t_0 t_2))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * (y - 1.0));
	double t_1 = 1.0 - ((1.0 - y) * z);
	double t_2 = fma((x * y), z, x);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -2e+31) {
		tmp = t_0;
	} else if (t_1 <= 5.0) {
		tmp = x * (1.0 - z);
	} else if (t_1 <= 5e+280) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * Float64(y - 1.0)))
	t_1 = Float64(1.0 - Float64(Float64(1.0 - y) * z))
	t_2 = fma(Float64(x * y), z, x)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -2e+31)
		tmp = t_0;
	elseif (t_1 <= 5.0)
		tmp = Float64(x * Float64(1.0 - z));
	elseif (t_1 <= 5e+280)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -2e+31], t$95$0, If[LessEqual[t$95$1, 5.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+280], t$95$0, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z)) < -inf.0 or 5.0000000000000002e280 < (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z))

   1. Initial program 96.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-in N/A

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

      6. *-rgt-identity N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. associate-*r* N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower--.f64 95.9

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

   3. Applied rewrites 95.9%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 72.7

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

   6. Applied rewrites 72.7%

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

   if -inf.0 < (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z)) < -1.9999999999999999e31 or 5 < (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z)) < 5.0000000000000002e280

   1. Initial program 96.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 58.3

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

   4. Applied rewrites 58.3%

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

   if -1.9999999999999999e31 < (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z)) < 5

   1. Initial program 96.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 66.6%

      \[\leadsto x \cdot \left(1 - \color{blue}{z}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 95.9% accurate, 1.1× speedup

Math

\[\mathsf{fma}\left(\left(y - 1\right) \cdot x, z, x\right) \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.2%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift--.f64 N/A

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

   3. sub-flip N/A

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

   4. +-commutative N/A

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

   5. distribute-lft-in N/A

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

   6. *-rgt-identity N/A

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

   7. lift-*.f64 N/A

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

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

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

   9. lift--.f64 N/A

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

   10. sub-negate-rev N/A

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

   11. associate-*r* N/A

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

   12. lower-fma.f64 N/A

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

   13. *-commutative N/A

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

   14. lower-*.f64 N/A

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

   15. lower--.f64 95.9

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

3. Applied rewrites 95.9%

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

Alternative 5: 95.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{fma}\left(x \cdot y, z, x\right)\\ \mathbf{if}\;1 - y \leq -500:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - y \leq 1.1:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (* x y) z x)))
   (if (<= (- 1.0 y) -500.0) t_0 (if (<= (- 1.0 y) 1.1) (* x (- 1.0 z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((x * y), z, x);
	double tmp;
	if ((1.0 - y) <= -500.0) {
		tmp = t_0;
	} else if ((1.0 - y) <= 1.1) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(x * y), z, x)
	tmp = 0.0
	if (Float64(1.0 - y) <= -500.0)
		tmp = t_0;
	elseif (Float64(1.0 - y) <= 1.1)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * y), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[N[(1.0 - y), $MachinePrecision], -500.0], t$95$0, If[LessEqual[N[(1.0 - y), $MachinePrecision], 1.1], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -500 or 1.1000000000000001 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 96.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-in N/A

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

      6. *-rgt-identity N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. associate-*r* N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower--.f64 95.9

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

   3. Applied rewrites 95.9%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 72.7

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

   6. Applied rewrites 72.7%

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

   if -500 < (-.f64 #s(literal 1 binary64) y) < 1.1000000000000001

   1. Initial program 96.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 66.6%

      \[\leadsto x \cdot \left(1 - \color{blue}{z}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;1 - y \leq -5 \cdot 10^{+31}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;1 - y \leq 2 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* y z))))
   (if (<= (- 1.0 y) -5e+31)
     t_0
     (if (<= (- 1.0 y) 2e+53) (* x (- 1.0 z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y * z);
	double tmp;
	if ((1.0 - y) <= -5e+31) {
		tmp = t_0;
	} else if ((1.0 - y) <= 2e+53) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y * z)
    if ((1.0d0 - y) <= (-5d+31)) then
        tmp = t_0
    else if ((1.0d0 - y) <= 2d+53) then
        tmp = x * (1.0d0 - z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y * z);
	double tmp;
	if ((1.0 - y) <= -5e+31) {
		tmp = t_0;
	} else if ((1.0 - y) <= 2e+53) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y * z)
	tmp = 0
	if (1.0 - y) <= -5e+31:
		tmp = t_0
	elif (1.0 - y) <= 2e+53:
		tmp = x * (1.0 - z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (Float64(1.0 - y) <= -5e+31)
		tmp = t_0;
	elseif (Float64(1.0 - y) <= 2e+53)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y * z);
	tmp = 0.0;
	if ((1.0 - y) <= -5e+31)
		tmp = t_0;
	elseif ((1.0 - y) <= 2e+53)
		tmp = x * (1.0 - z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(1.0 - y), $MachinePrecision], -5e+31], t$95$0, If[LessEqual[N[(1.0 - y), $MachinePrecision], 2e+53], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -5.00000000000000027e31 or 2e53 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 96.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 35.9

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

   4. Applied rewrites 35.9%

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

   if -5.00000000000000027e31 < (-.f64 #s(literal 1 binary64) y) < 2e53

   1. Initial program 96.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 66.6%

      \[\leadsto x \cdot \left(1 - \color{blue}{z}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 66.6% accurate, 1.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x * (1.0 - 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 * (1.0d0 - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

2. Taylor expanded in y around 0

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

4. Applied rewrites 66.6%

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

Alternative 8: 39.9% accurate, 3.1× speedup

Math

\[x \cdot 1 \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

2. Taylor expanded in y around 0

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

4. Applied rewrites 66.6%

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

5. Taylor expanded in z around 0

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

7. Applied rewrites 39.9%

   \[\leadsto x \cdot \color{blue}{1} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025167 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64
  (* x (- 1.0 (* (- 1.0 y) z))))