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

Percentage Accurate: 96.0% → 99.7%

Time: 2.8s

Alternatives: 10

Speedup: 0.8×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \end{array} \]

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: 96.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \end{array} \]

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: 99.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left(y - 1\right) \cdot x, z, x\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{-17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-92}:\\ \;\;\;\;x \cdot \left(1 - \left(-y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (* (- y 1.0) x) z x)))
   (if (<= z -2e-17) t_0 (if (<= z 1.05e-92) (* x (- 1.0 (* (- y) z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(((y - 1.0) * x), z, x);
	double tmp;
	if (z <= -2e-17) {
		tmp = t_0;
	} else if (z <= 1.05e-92) {
		tmp = x * (1.0 - (-y * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(Float64(y - 1.0) * x), z, x)
	tmp = 0.0
	if (z <= -2e-17)
		tmp = t_0;
	elseif (z <= 1.05e-92)
		tmp = Float64(x * Float64(1.0 - Float64(Float64(-y) * z)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y - 1.0), $MachinePrecision] * x), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[z, -2e-17], t$95$0, If[LessEqual[z, 1.05e-92], N[(x * N[(1.0 - N[((-y) * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000014e-17 or 1.05e-92 < z

   1. Initial program 96.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

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

      10. sub-negate-rev N/A

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

      11. +-commutative N/A

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

      12. distribute-lft1-in N/A

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

      13. *-commutative N/A

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

      14. sub-negate-rev N/A

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

      15. mul-1-neg N/A

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

      16. *-commutative N/A

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

      17. associate-*l* N/A

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

      18. mul-1-neg N/A

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

      19. sub-negate-rev N/A

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

      20. lower-fma.f64 N/A

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

   3. Applied rewrites 95.9%

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

   if -2.00000000000000014e-17 < z < 1.05e-92

   1. Initial program 96.0%

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

   2. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 71.7

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

   4. Applied rewrites 71.7%

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

Alternative 2: 97.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(\left(y - 1\right) \cdot x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 1, z \cdot x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1e-16) (fma (* (- y 1.0) x) z x) (fma (- y 1.0) (* z x) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1e-16) {
		tmp = fma(((y - 1.0) * x), z, x);
	} else {
		tmp = fma((y - 1.0), (z * x), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1e-16)
		tmp = fma(Float64(Float64(y - 1.0) * x), z, x);
	else
		tmp = fma(Float64(y - 1.0), Float64(z * x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1e-16], N[(N[(N[(y - 1.0), $MachinePrecision] * x), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(y - 1.0), $MachinePrecision] * N[(z * x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9.9999999999999998e-17

   1. Initial program 96.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

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

      10. sub-negate-rev N/A

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

      11. +-commutative N/A

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

      12. distribute-lft1-in N/A

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

      13. *-commutative N/A

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

      14. sub-negate-rev N/A

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

      15. mul-1-neg N/A

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

      16. *-commutative N/A

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

      17. associate-*l* N/A

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

      18. mul-1-neg N/A

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

      19. sub-negate-rev N/A

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

      20. lower-fma.f64 N/A

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

   3. Applied rewrites 95.9%

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

   if 9.9999999999999998e-17 < x

   1. Initial program 96.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

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

      10. sub-negate-rev N/A

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

      11. +-commutative N/A

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

      12. distribute-lft1-in N/A

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

      13. *-commutative N/A

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

      14. sub-negate-rev N/A

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

      15. mul-1-neg N/A

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

      16. associate-*r* N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. mul-1-neg N/A

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

      20. sub-negate-rev N/A

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

      21. lower--.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 97.8

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

   3. Applied rewrites 97.8%

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

Alternative 3: 96.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ t_1 := x \cdot \left(z \cdot y - z\right)\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 20:\\ \;\;\;\;x \cdot \left(1 - \left(-y\right) \cdot z\right)\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+299}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot y, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)) (t_1 (* x (- (* z y) z))))
   (if (<= t_0 -2e+24)
     t_1
     (if (<= t_0 20.0)
       (* x (- 1.0 (* (- y) z)))
       (if (<= t_0 2e+299) t_1 (fma (* x y) z x))))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double t_1 = x * ((z * y) - z);
	double tmp;
	if (t_0 <= -2e+24) {
		tmp = t_1;
	} else if (t_0 <= 20.0) {
		tmp = x * (1.0 - (-y * z));
	} else if (t_0 <= 2e+299) {
		tmp = t_1;
	} else {
		tmp = fma((x * y), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	t_1 = Float64(x * Float64(Float64(z * y) - z))
	tmp = 0.0
	if (t_0 <= -2e+24)
		tmp = t_1;
	elseif (t_0 <= 20.0)
		tmp = Float64(x * Float64(1.0 - Float64(Float64(-y) * z)));
	elseif (t_0 <= 2e+299)
		tmp = t_1;
	else
		tmp = fma(Float64(x * y), z, x);
	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[(x * N[(N[(z * y), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+24], t$95$1, If[LessEqual[t$95$0, 20.0], N[(x * N[(1.0 - N[((-y) * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+299], t$95$1, N[(N[(x * y), $MachinePrecision] * z + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -2e24 or 20 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 2.0000000000000001e299

   1. Initial program 96.0%

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

   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. sub-flip N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. mul-1-neg N/A

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

      5. sub-flip N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 59.4

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

   4. Applied rewrites 59.4%

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

   if -2e24 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 20

   1. Initial program 96.0%

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

   2. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 71.7

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

   4. Applied rewrites 71.7%

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

   if 2.0000000000000001e299 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 96.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

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

      10. sub-negate-rev N/A

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

      11. +-commutative N/A

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

      12. distribute-lft1-in N/A

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

      13. *-commutative N/A

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

      14. sub-negate-rev N/A

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

      15. mul-1-neg N/A

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

      16. *-commutative N/A

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

      17. associate-*l* N/A

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

      18. mul-1-neg N/A

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

      19. sub-negate-rev N/A

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

      20. lower-fma.f64 N/A

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

   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 71.6

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

   6. Applied rewrites 71.6%

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

Alternative 4: 95.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot y - z\right)\\ t_1 := 1 - \left(1 - y\right) \cdot z\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(x \cdot y, z, x\right)\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\mathsf{fma}\left(-x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- (* z y) z))) (t_1 (- 1.0 (* (- 1.0 y) z))))
   (if (<= t_1 (- INFINITY))
     (fma (* x y) z x)
     (if (<= t_1 -1e+15) t_0 (if (<= t_1 2.0) (fma (- x) z x) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * ((z * y) - z);
	double t_1 = 1.0 - ((1.0 - y) * z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma((x * y), z, x);
	} else if (t_1 <= -1e+15) {
		tmp = t_0;
	} else if (t_1 <= 2.0) {
		tmp = fma(-x, z, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(z * y) - z))
	t_1 = Float64(1.0 - Float64(Float64(1.0 - y) * z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = fma(Float64(x * y), z, x);
	elseif (t_1 <= -1e+15)
		tmp = t_0;
	elseif (t_1 <= 2.0)
		tmp = fma(Float64(-x), z, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(z * y), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x * y), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[t$95$1, -1e+15], t$95$0, If[LessEqual[t$95$1, 2.0], N[((-x) * z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 96.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

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

      10. sub-negate-rev N/A

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

      11. +-commutative N/A

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

      12. distribute-lft1-in N/A

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

      13. *-commutative N/A

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

      14. sub-negate-rev N/A

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

      15. mul-1-neg N/A

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

      16. *-commutative N/A

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

      17. associate-*l* N/A

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

      18. mul-1-neg N/A

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

      19. sub-negate-rev N/A

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

      20. lower-fma.f64 N/A

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

   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 71.6

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

   6. Applied rewrites 71.6%

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

   if -inf.0 < (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z)) < -1e15 or 2 < (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z))

   1. Initial program 96.0%

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

   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. sub-flip N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. mul-1-neg N/A

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

      5. sub-flip N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 59.4

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

   4. Applied rewrites 59.4%

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

   if -1e15 < (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) y) z)) < 2

   1. Initial program 96.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

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

      10. sub-negate-rev N/A

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

      11. +-commutative N/A

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

      12. distribute-lft1-in N/A

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

      13. *-commutative N/A

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

      14. sub-negate-rev N/A

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

      15. mul-1-neg N/A

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

      16. *-commutative N/A

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

      17. associate-*l* N/A

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

      18. mul-1-neg N/A

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

      19. sub-negate-rev N/A

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

      20. lower-fma.f64 N/A

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

   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 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 66.1

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

   6. Applied rewrites 66.1%

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

Alternative 5: 94.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(x \cdot y, z, x\right)\\ \mathbf{if}\;y \leq -600000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-13}:\\ \;\;\;\;\mathsf{fma}\left(-x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (* x y) z x)))
   (if (<= y -600000000000.0) t_0 (if (<= y 1.2e-13) (fma (- x) z x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((x * y), z, x);
	double tmp;
	if (y <= -600000000000.0) {
		tmp = t_0;
	} else if (y <= 1.2e-13) {
		tmp = fma(-x, z, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(x * y), z, x)
	tmp = 0.0
	if (y <= -600000000000.0)
		tmp = t_0;
	elseif (y <= 1.2e-13)
		tmp = fma(Float64(-x), z, x);
	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[y, -600000000000.0], t$95$0, If[LessEqual[y, 1.2e-13], N[((-x) * z + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -6e11 or 1.1999999999999999e-13 < y

   1. Initial program 96.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

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

      10. sub-negate-rev N/A

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

      11. +-commutative N/A

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

      12. distribute-lft1-in N/A

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

      13. *-commutative N/A

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

      14. sub-negate-rev N/A

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

      15. mul-1-neg N/A

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

      16. *-commutative N/A

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

      17. associate-*l* N/A

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

      18. mul-1-neg N/A

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

      19. sub-negate-rev N/A

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

      20. lower-fma.f64 N/A

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

   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 71.6

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

   6. Applied rewrites 71.6%

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

   if -6e11 < y < 1.1999999999999999e-13

   1. Initial program 96.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

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

      10. sub-negate-rev N/A

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

      11. +-commutative N/A

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

      12. distribute-lft1-in N/A

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

      13. *-commutative N/A

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

      14. sub-negate-rev N/A

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

      15. mul-1-neg N/A

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

      16. *-commutative N/A

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

      17. associate-*l* N/A

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

      18. mul-1-neg N/A

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

      19. sub-negate-rev N/A

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

      20. lower-fma.f64 N/A

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

   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 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 66.1

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

   6. Applied rewrites 66.1%

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

Alternative 6: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot y\right)\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+130}:\\ \;\;\;\;\mathsf{fma}\left(-x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z y))))
   (if (<= y -5.6e+15) t_0 (if (<= y 4.6e+130) (fma (- x) z x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * y);
	double tmp;
	if (y <= -5.6e+15) {
		tmp = t_0;
	} else if (y <= 4.6e+130) {
		tmp = fma(-x, z, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * y))
	tmp = 0.0
	if (y <= -5.6e+15)
		tmp = t_0;
	elseif (y <= 4.6e+130)
		tmp = fma(Float64(-x), z, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e+15], t$95$0, If[LessEqual[y, 4.6e+130], N[((-x) * z + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6e15 or 4.60000000000000042e130 < y

   1. Initial program 96.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 35.8

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

   4. Applied rewrites 35.8%

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

   if -5.6e15 < y < 4.60000000000000042e130

   1. Initial program 96.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. mul-1-neg N/A

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

      10. sub-negate-rev N/A

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

      11. +-commutative N/A

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

      12. distribute-lft1-in N/A

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

      13. *-commutative N/A

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

      14. sub-negate-rev N/A

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

      15. mul-1-neg N/A

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

      16. *-commutative N/A

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

      17. associate-*l* N/A

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

      18. mul-1-neg N/A

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

      19. sub-negate-rev N/A

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

      20. lower-fma.f64 N/A

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

   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 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 66.1

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

   6. Applied rewrites 66.1%

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

Alternative 7: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot y\right)\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z y))))
   (if (<= y -5.6e+15) t_0 (if (<= y 4.6e+130) (* x (- 1.0 z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * y);
	double tmp;
	if (y <= -5.6e+15) {
		tmp = t_0;
	} else if (y <= 4.6e+130) {
		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 * (z * y)
    if (y <= (-5.6d+15)) then
        tmp = t_0
    else if (y <= 4.6d+130) 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 * (z * y);
	double tmp;
	if (y <= -5.6e+15) {
		tmp = t_0;
	} else if (y <= 4.6e+130) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * y)
	tmp = 0
	if y <= -5.6e+15:
		tmp = t_0
	elif y <= 4.6e+130:
		tmp = x * (1.0 - z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * y))
	tmp = 0.0
	if (y <= -5.6e+15)
		tmp = t_0;
	elseif (y <= 4.6e+130)
		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 * (z * y);
	tmp = 0.0;
	if (y <= -5.6e+15)
		tmp = t_0;
	elseif (y <= 4.6e+130)
		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[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e+15], t$95$0, If[LessEqual[y, 4.6e+130], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6e15 or 4.60000000000000042e130 < y

   1. Initial program 96.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 35.8

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

   4. Applied rewrites 35.8%

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

   if -5.6e15 < y < 4.60000000000000042e130

   1. Initial program 96.0%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 66.1%

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

Alternative 8: 66.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - z\right) \end{array} \]

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 96.0%

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

2. Taylor expanded in y around 0

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

4. Applied rewrites 66.1%

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

Alternative 9: 64.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-7}:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -2.7e+19) t_0 (if (<= z 4e-7) (* x 1.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -2.7e+19) {
		tmp = t_0;
	} else if (z <= 4e-7) {
		tmp = x * 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * -z
    if (z <= (-2.7d+19)) then
        tmp = t_0
    else if (z <= 4d-7) then
        tmp = x * 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -2.7e+19) {
		tmp = t_0;
	} else if (z <= 4e-7) {
		tmp = x * 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -2.7e+19:
		tmp = t_0
	elif z <= 4e-7:
		tmp = x * 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -2.7e+19)
		tmp = t_0;
	elseif (z <= 4e-7)
		tmp = Float64(x * 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (z <= -2.7e+19)
		tmp = t_0;
	elseif (z <= 4e-7)
		tmp = x * 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -2.7e+19], t$95$0, If[LessEqual[z, 4e-7], N[(x * 1.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e19 or 3.9999999999999998e-7 < z

   1. Initial program 96.0%

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

   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. sub-flip N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. mul-1-neg N/A

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

      5. sub-flip N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 59.4

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

   4. Applied rewrites 59.4%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 30.3

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

   7. Applied rewrites 30.3%

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

   if -2.7e19 < z < 3.9999999999999998e-7

   1. Initial program 96.0%

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

   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. sub-flip N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. mul-1-neg N/A

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

      5. sub-flip N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 59.4

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

   4. Applied rewrites 59.4%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 30.3

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

   7. Applied rewrites 30.3%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 38.6%

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

Alternative 10: 38.6% accurate, 3.1× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.0%

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

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. sub-flip N/A

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

   2. metadata-eval N/A

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

   3. distribute-rgt-in N/A

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

   4. mul-1-neg N/A

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

   5. sub-flip N/A

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

   6. lower--.f64 N/A

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

   7. *-commutative N/A

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

   8. lower-*.f64 59.4

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

4. Applied rewrites 59.4%

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

5. Taylor expanded in y around 0

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 30.3

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

7. Applied rewrites 30.3%

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

8. Taylor expanded in z around 0

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

10. Applied rewrites 38.6%

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

Reproduce

herbie shell --seed 2025134 
(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))))