Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C

Percentage Accurate: 99.9% → 100.0%

Time: 5.1s

Alternatives: 11

Speedup: 1.1×

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(y + z\right) + z \cdot 5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x (+ y z)) (* z 5.0)))

C

double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

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 * (y + z)) + (z * 5.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Python

def code(x, y, z):
	return (x * (y + z)) + (z * 5.0)

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y + z)) + Float64(z * 5.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y + z)) + (z * 5.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(y + z\right) + z \cdot 5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x (+ y z)) (* z 5.0)))

C

double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

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 * (y + z)) + (z * 5.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Python

def code(x, y, z):
	return (x * (y + z)) + (z * 5.0)

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y + z)) + Float64(z * 5.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y + z)) + (z * 5.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z, 5, \left(z + y\right) \cdot x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma z 5.0 (* (+ z y) x)))

C

double code(double x, double y, double z) {
	return fma(z, 5.0, ((z + y) * x));
}

Julia

function code(x, y, z)
	return fma(z, 5.0, Float64(Float64(z + y) * x))
end

Wolfram

code[x_, y_, z_] := N[(z * 5.0 + N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(y + z\right) + z \cdot 5 \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x \cdot \left(y + z\right) + z \cdot 5} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{z \cdot 5 + x \cdot \left(y + z\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{z \cdot 5} + x \cdot \left(y + z\right) \]

   4. lower-fma.f64 100.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, 5, x \cdot \left(y + z\right)\right)} \]

   5. lift-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{x \cdot \left(y + z\right)}\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(y + z\right) \cdot x}\right) \]

   7. lower-*.f64 100.0

      \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(y + z\right) \cdot x}\right) \]

   8. lift-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(y + z\right)} \cdot x\right) \]

   9. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(z + y\right)} \cdot x\right) \]

   10. lower-+.f64 100.0

       \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(z + y\right)} \cdot x\right) \]

4. Applied rewrites 100.0%

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

Alternative 2: 84.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -650000000 \lor \neg \left(x \leq 2.5 \cdot 10^{-81}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, 5, x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -650000000.0) (not (<= x 2.5e-81)))
   (* (+ y z) x)
   (fma z 5.0 (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -650000000.0) || !(x <= 2.5e-81)) {
		tmp = (y + z) * x;
	} else {
		tmp = fma(z, 5.0, (x * z));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -650000000.0) || !(x <= 2.5e-81))
		tmp = Float64(Float64(y + z) * x);
	else
		tmp = fma(z, 5.0, Float64(x * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -650000000.0], N[Not[LessEqual[x, 2.5e-81]], $MachinePrecision]], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], N[(z * 5.0 + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5e8 or 2.4999999999999999e-81 < x

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right) + z \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right)} + z \cdot 5 \]

      3. lift-+.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y + z\right)} + z \cdot 5 \]

      4. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(y \cdot x + z \cdot x\right)} + z \cdot 5 \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{y \cdot x + \left(z \cdot x + z \cdot 5\right)} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot x + z \cdot 5\right) + y \cdot x} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(z \cdot x + \color{blue}{z \cdot 5}\right) + y \cdot x \]

      8. distribute-lft-out N/A

         \[\leadsto \color{blue}{z \cdot \left(x + 5\right)} + y \cdot x \]

      9. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x + 5, y \cdot x\right)} \]

      10. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{x + 5}, y \cdot x\right) \]

      11. lower-*.f64 99.2

          \[\leadsto \mathsf{fma}\left(z, x + 5, \color{blue}{y \cdot x}\right) \]

   4. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, x + 5, y \cdot x\right)} \]

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 94.8

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

   7. Applied rewrites 94.8%

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

   if -6.5e8 < x < 2.4999999999999999e-81

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{5 \cdot z + x \cdot z} \]
   4. Step-by-step derivation

      1. distribute-rgt-in N/A

         \[\leadsto \color{blue}{z \cdot \left(5 + x\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

      4. lower-+.f64 72.9

         \[\leadsto \color{blue}{\left(5 + x\right)} \cdot z \]

   5. Applied rewrites 72.9%

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

   7. Applied rewrites 73.0%

      \[\leadsto \mathsf{fma}\left(z, \color{blue}{5}, x \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -650000000 \lor \neg \left(x \leq 2.5 \cdot 10^{-81}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, 5, x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+49}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -5:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-56}:\\ \;\;\;\;5 \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.85e+49)
   (* y x)
   (if (<= x -5.0) (* x z) (if (<= x 3e-56) (* 5.0 z) (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.85e+49) {
		tmp = y * x;
	} else if (x <= -5.0) {
		tmp = x * z;
	} else if (x <= 3e-56) {
		tmp = 5.0 * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.85d+49)) then
        tmp = y * x
    else if (x <= (-5.0d0)) then
        tmp = x * z
    else if (x <= 3d-56) then
        tmp = 5.0d0 * z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.85e+49) {
		tmp = y * x;
	} else if (x <= -5.0) {
		tmp = x * z;
	} else if (x <= 3e-56) {
		tmp = 5.0 * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.85e+49:
		tmp = y * x
	elif x <= -5.0:
		tmp = x * z
	elif x <= 3e-56:
		tmp = 5.0 * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.85e+49)
		tmp = Float64(y * x);
	elseif (x <= -5.0)
		tmp = Float64(x * z);
	elseif (x <= 3e-56)
		tmp = Float64(5.0 * z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.85e+49)
		tmp = y * x;
	elseif (x <= -5.0)
		tmp = x * z;
	elseif (x <= 3e-56)
		tmp = 5.0 * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.85e+49], N[(y * x), $MachinePrecision], If[LessEqual[x, -5.0], N[(x * z), $MachinePrecision], If[LessEqual[x, 3e-56], N[(5.0 * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.85000000000000009e49 or 2.99999999999999989e-56 < x

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot x} \]

      2. lower-*.f64 59.2

         \[\leadsto \color{blue}{y \cdot x} \]

   5. Applied rewrites 59.2%

      \[\leadsto \color{blue}{y \cdot x} \]

   if -1.85000000000000009e49 < x < -5

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{5 \cdot z + x \cdot z} \]
   4. Step-by-step derivation

      1. distribute-rgt-in N/A

         \[\leadsto \color{blue}{z \cdot \left(5 + x\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

      4. lower-+.f64 81.1

         \[\leadsto \color{blue}{\left(5 + x\right)} \cdot z \]

   5. Applied rewrites 81.1%

      \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 70.1%

      \[\leadsto x \cdot \color{blue}{z} \]

   if -5 < x < 2.99999999999999989e-56

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{5 \cdot z} \]
   4. Step-by-step derivation

      1. lower-*.f64 70.9

         \[\leadsto \color{blue}{5 \cdot z} \]

   5. Applied rewrites 70.9%

      \[\leadsto \color{blue}{5 \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+49}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq -5:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-56}:\\ \;\;\;\;5 \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5:\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{elif}\;x \leq 0.000235:\\ \;\;\;\;\mathsf{fma}\left(5, z, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.0)
   (* (+ y z) x)
   (if (<= x 0.000235) (fma 5.0 z (* y x)) (fma z x (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.0) {
		tmp = (y + z) * x;
	} else if (x <= 0.000235) {
		tmp = fma(5.0, z, (y * x));
	} else {
		tmp = fma(z, x, (x * y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.0)
		tmp = Float64(Float64(y + z) * x);
	elseif (x <= 0.000235)
		tmp = fma(5.0, z, Float64(y * x));
	else
		tmp = fma(z, x, Float64(x * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.0], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 0.000235], N[(5.0 * z + N[(y * x), $MachinePrecision]), $MachinePrecision], N[(z * x + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right) + z \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right)} + z \cdot 5 \]

      3. lift-+.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y + z\right)} + z \cdot 5 \]

      4. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(y \cdot x + z \cdot x\right)} + z \cdot 5 \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{y \cdot x + \left(z \cdot x + z \cdot 5\right)} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot x + z \cdot 5\right) + y \cdot x} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(z \cdot x + \color{blue}{z \cdot 5}\right) + y \cdot x \]

      8. distribute-lft-out N/A

         \[\leadsto \color{blue}{z \cdot \left(x + 5\right)} + y \cdot x \]

      9. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x + 5, y \cdot x\right)} \]

      10. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{x + 5}, y \cdot x\right) \]

      11. lower-*.f64 98.1

          \[\leadsto \mathsf{fma}\left(z, x + 5, \color{blue}{y \cdot x}\right) \]

   4. Applied rewrites 98.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, x + 5, y \cdot x\right)} \]

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 97.9

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

   7. Applied rewrites 97.9%

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

   if -5 < x < 2.34999999999999993e-4

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right) + z \cdot 5} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot 5 + x \cdot \left(y + z\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot 5} + x \cdot \left(y + z\right) \]

      4. lower-fma.f64 100.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, 5, x \cdot \left(y + z\right)\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{x \cdot \left(y + z\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(y + z\right) \cdot x}\right) \]

      7. lower-*.f64 100.0

         \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(y + z\right) \cdot x}\right) \]

      8. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(y + z\right)} \cdot x\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(z + y\right)} \cdot x\right) \]

      10. lower-+.f64 100.0

          \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(z + y\right)} \cdot x\right) \]

   4. Applied rewrites 100.0%

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

      1. lift-fma.f64 N/A

         \[\leadsto \color{blue}{z \cdot 5 + \left(z + y\right) \cdot x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + y\right) \cdot x + z \cdot 5} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(z + y\right) \cdot x} + z \cdot 5 \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot \left(z + y\right)} + z \cdot 5 \]

      5. lift-+.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(z + y\right)} + z \cdot 5 \]

      6. +-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(y + z\right)} + z \cdot 5 \]

      7. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(y \cdot x + z \cdot x\right)} + z \cdot 5 \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{y \cdot x} + z \cdot x\right) + z \cdot 5 \]

      9. associate-+r+ N/A

         \[\leadsto \color{blue}{y \cdot x + \left(z \cdot x + z \cdot 5\right)} \]

      10. distribute-lft-in N/A

          \[\leadsto y \cdot x + \color{blue}{z \cdot \left(x + 5\right)} \]

      11. lift-+.f64 N/A

          \[\leadsto y \cdot x + z \cdot \color{blue}{\left(x + 5\right)} \]

      12. lift-*.f64 N/A

          \[\leadsto \color{blue}{y \cdot x} + z \cdot \left(x + 5\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, z \cdot \left(x + 5\right)\right)} \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{\left(x + 5\right) \cdot z}\right) \]

      15. lower-*.f64 99.9

          \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{\left(x + 5\right) \cdot z}\right) \]

   6. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \left(x + 5\right) \cdot z\right)} \]

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 99.1%

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

       1. lift-fma.f64 N/A

          \[\leadsto \color{blue}{y \cdot x + 5 \cdot z} \]

       2. +-commutative N/A

          \[\leadsto \color{blue}{5 \cdot z + y \cdot x} \]

       3. lift-*.f64 N/A

          \[\leadsto \color{blue}{5 \cdot z} + y \cdot x \]

       4. lower-fma.f64 N/A

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

       5. lower-*.f64 99.1

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

   11. Applied rewrites 99.1%

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

   if 2.34999999999999993e-4 < x

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right) + z \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right)} + z \cdot 5 \]

      3. lift-+.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y + z\right)} + z \cdot 5 \]

      4. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(y \cdot x + z \cdot x\right)} + z \cdot 5 \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{y \cdot x + \left(z \cdot x + z \cdot 5\right)} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot x + z \cdot 5\right) + y \cdot x} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(z \cdot x + \color{blue}{z \cdot 5}\right) + y \cdot x \]

      8. distribute-lft-out N/A

         \[\leadsto \color{blue}{z \cdot \left(x + 5\right)} + y \cdot x \]

      9. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x + 5, y \cdot x\right)} \]

      10. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{x + 5}, y \cdot x\right) \]

      11. lower-*.f64 100.0

          \[\leadsto \mathsf{fma}\left(z, x + 5, \color{blue}{y \cdot x}\right) \]

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, x + 5, y \cdot x\right)} \]

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 99.9

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

   7. Applied rewrites 99.9%

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

   9. Applied rewrites 100.0%

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

Alternative 5: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5:\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{elif}\;x \leq 0.000235:\\ \;\;\;\;\mathsf{fma}\left(y, x, 5 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.0)
   (* (+ y z) x)
   (if (<= x 0.000235) (fma y x (* 5.0 z)) (fma z x (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.0) {
		tmp = (y + z) * x;
	} else if (x <= 0.000235) {
		tmp = fma(y, x, (5.0 * z));
	} else {
		tmp = fma(z, x, (x * y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.0)
		tmp = Float64(Float64(y + z) * x);
	elseif (x <= 0.000235)
		tmp = fma(y, x, Float64(5.0 * z));
	else
		tmp = fma(z, x, Float64(x * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.0], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 0.000235], N[(y * x + N[(5.0 * z), $MachinePrecision]), $MachinePrecision], N[(z * x + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right) + z \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right)} + z \cdot 5 \]

      3. lift-+.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y + z\right)} + z \cdot 5 \]

      4. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(y \cdot x + z \cdot x\right)} + z \cdot 5 \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{y \cdot x + \left(z \cdot x + z \cdot 5\right)} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot x + z \cdot 5\right) + y \cdot x} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(z \cdot x + \color{blue}{z \cdot 5}\right) + y \cdot x \]

      8. distribute-lft-out N/A

         \[\leadsto \color{blue}{z \cdot \left(x + 5\right)} + y \cdot x \]

      9. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x + 5, y \cdot x\right)} \]

      10. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{x + 5}, y \cdot x\right) \]

      11. lower-*.f64 98.1

          \[\leadsto \mathsf{fma}\left(z, x + 5, \color{blue}{y \cdot x}\right) \]

   4. Applied rewrites 98.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, x + 5, y \cdot x\right)} \]

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 97.9

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

   7. Applied rewrites 97.9%

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

   if -5 < x < 2.34999999999999993e-4

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right) + z \cdot 5} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot 5 + x \cdot \left(y + z\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot 5} + x \cdot \left(y + z\right) \]

      4. lower-fma.f64 100.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, 5, x \cdot \left(y + z\right)\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{x \cdot \left(y + z\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(y + z\right) \cdot x}\right) \]

      7. lower-*.f64 100.0

         \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(y + z\right) \cdot x}\right) \]

      8. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(y + z\right)} \cdot x\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(z + y\right)} \cdot x\right) \]

      10. lower-+.f64 100.0

          \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(z + y\right)} \cdot x\right) \]

   4. Applied rewrites 100.0%

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

      1. lift-fma.f64 N/A

         \[\leadsto \color{blue}{z \cdot 5 + \left(z + y\right) \cdot x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(z + y\right) \cdot x + z \cdot 5} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(z + y\right) \cdot x} + z \cdot 5 \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot \left(z + y\right)} + z \cdot 5 \]

      5. lift-+.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(z + y\right)} + z \cdot 5 \]

      6. +-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(y + z\right)} + z \cdot 5 \]

      7. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(y \cdot x + z \cdot x\right)} + z \cdot 5 \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{y \cdot x} + z \cdot x\right) + z \cdot 5 \]

      9. associate-+r+ N/A

         \[\leadsto \color{blue}{y \cdot x + \left(z \cdot x + z \cdot 5\right)} \]

      10. distribute-lft-in N/A

          \[\leadsto y \cdot x + \color{blue}{z \cdot \left(x + 5\right)} \]

      11. lift-+.f64 N/A

          \[\leadsto y \cdot x + z \cdot \color{blue}{\left(x + 5\right)} \]

      12. lift-*.f64 N/A

          \[\leadsto \color{blue}{y \cdot x} + z \cdot \left(x + 5\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, z \cdot \left(x + 5\right)\right)} \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{\left(x + 5\right) \cdot z}\right) \]

      15. lower-*.f64 99.9

          \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{\left(x + 5\right) \cdot z}\right) \]

   6. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \left(x + 5\right) \cdot z\right)} \]

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 99.1%

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

   if 2.34999999999999993e-4 < x

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right) + z \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right)} + z \cdot 5 \]

      3. lift-+.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y + z\right)} + z \cdot 5 \]

      4. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(y \cdot x + z \cdot x\right)} + z \cdot 5 \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{y \cdot x + \left(z \cdot x + z \cdot 5\right)} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot x + z \cdot 5\right) + y \cdot x} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(z \cdot x + \color{blue}{z \cdot 5}\right) + y \cdot x \]

      8. distribute-lft-out N/A

         \[\leadsto \color{blue}{z \cdot \left(x + 5\right)} + y \cdot x \]

      9. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x + 5, y \cdot x\right)} \]

      10. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{x + 5}, y \cdot x\right) \]

      11. lower-*.f64 100.0

          \[\leadsto \mathsf{fma}\left(z, x + 5, \color{blue}{y \cdot x}\right) \]

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, x + 5, y \cdot x\right)} \]

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 99.9

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

   7. Applied rewrites 99.9%

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

   9. Applied rewrites 100.0%

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

Alternative 6: 83.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -650000000:\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-81}:\\ \;\;\;\;\mathsf{fma}\left(z, 5, x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -650000000.0)
   (* (+ y z) x)
   (if (<= x 2.5e-81) (fma z 5.0 (* x z)) (fma z x (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -650000000.0) {
		tmp = (y + z) * x;
	} else if (x <= 2.5e-81) {
		tmp = fma(z, 5.0, (x * z));
	} else {
		tmp = fma(z, x, (x * y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -650000000.0)
		tmp = Float64(Float64(y + z) * x);
	elseif (x <= 2.5e-81)
		tmp = fma(z, 5.0, Float64(x * z));
	else
		tmp = fma(z, x, Float64(x * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -650000000.0], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 2.5e-81], N[(z * 5.0 + N[(x * z), $MachinePrecision]), $MachinePrecision], N[(z * x + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.5e8

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right) + z \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right)} + z \cdot 5 \]

      3. lift-+.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y + z\right)} + z \cdot 5 \]

      4. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(y \cdot x + z \cdot x\right)} + z \cdot 5 \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{y \cdot x + \left(z \cdot x + z \cdot 5\right)} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot x + z \cdot 5\right) + y \cdot x} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(z \cdot x + \color{blue}{z \cdot 5}\right) + y \cdot x \]

      8. distribute-lft-out N/A

         \[\leadsto \color{blue}{z \cdot \left(x + 5\right)} + y \cdot x \]

      9. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x + 5, y \cdot x\right)} \]

      10. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{x + 5}, y \cdot x\right) \]

      11. lower-*.f64 98.0

          \[\leadsto \mathsf{fma}\left(z, x + 5, \color{blue}{y \cdot x}\right) \]

   4. Applied rewrites 98.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, x + 5, y \cdot x\right)} \]

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 99.9

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

   7. Applied rewrites 99.9%

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

   if -6.5e8 < x < 2.4999999999999999e-81

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{5 \cdot z + x \cdot z} \]
   4. Step-by-step derivation

      1. distribute-rgt-in N/A

         \[\leadsto \color{blue}{z \cdot \left(5 + x\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

      4. lower-+.f64 72.9

         \[\leadsto \color{blue}{\left(5 + x\right)} \cdot z \]

   5. Applied rewrites 72.9%

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

   7. Applied rewrites 73.0%

      \[\leadsto \mathsf{fma}\left(z, \color{blue}{5}, x \cdot z\right) \]

   if 2.4999999999999999e-81 < x

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right) + z \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right)} + z \cdot 5 \]

      3. lift-+.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y + z\right)} + z \cdot 5 \]

      4. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(y \cdot x + z \cdot x\right)} + z \cdot 5 \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{y \cdot x + \left(z \cdot x + z \cdot 5\right)} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot x + z \cdot 5\right) + y \cdot x} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(z \cdot x + \color{blue}{z \cdot 5}\right) + y \cdot x \]

      8. distribute-lft-out N/A

         \[\leadsto \color{blue}{z \cdot \left(x + 5\right)} + y \cdot x \]

      9. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x + 5, y \cdot x\right)} \]

      10. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{x + 5}, y \cdot x\right) \]

      11. lower-*.f64 99.9

          \[\leadsto \mathsf{fma}\left(z, x + 5, \color{blue}{y \cdot x}\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, x + 5, y \cdot x\right)} \]

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 91.6

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

   7. Applied rewrites 91.6%

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

   9. Applied rewrites 91.6%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -650000000:\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-81}:\\ \;\;\;\;\mathsf{fma}\left(z, 5, x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -650000000 \lor \neg \left(x \leq 2.5 \cdot 10^{-81}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(5 + x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -650000000.0) (not (<= x 2.5e-81)))
   (* (+ y z) x)
   (* (+ 5.0 x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -650000000.0) || !(x <= 2.5e-81)) {
		tmp = (y + z) * x;
	} else {
		tmp = (5.0 + x) * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-650000000.0d0)) .or. (.not. (x <= 2.5d-81))) then
        tmp = (y + z) * x
    else
        tmp = (5.0d0 + x) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -650000000.0) || !(x <= 2.5e-81)) {
		tmp = (y + z) * x;
	} else {
		tmp = (5.0 + x) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -650000000.0) or not (x <= 2.5e-81):
		tmp = (y + z) * x
	else:
		tmp = (5.0 + x) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -650000000.0) || !(x <= 2.5e-81))
		tmp = Float64(Float64(y + z) * x);
	else
		tmp = Float64(Float64(5.0 + x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -650000000.0) || ~((x <= 2.5e-81)))
		tmp = (y + z) * x;
	else
		tmp = (5.0 + x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -650000000.0], N[Not[LessEqual[x, 2.5e-81]], $MachinePrecision]], N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision], N[(N[(5.0 + x), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5e8 or 2.4999999999999999e-81 < x

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right) + z \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right)} + z \cdot 5 \]

      3. lift-+.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y + z\right)} + z \cdot 5 \]

      4. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(y \cdot x + z \cdot x\right)} + z \cdot 5 \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{y \cdot x + \left(z \cdot x + z \cdot 5\right)} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot x + z \cdot 5\right) + y \cdot x} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(z \cdot x + \color{blue}{z \cdot 5}\right) + y \cdot x \]

      8. distribute-lft-out N/A

         \[\leadsto \color{blue}{z \cdot \left(x + 5\right)} + y \cdot x \]

      9. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x + 5, y \cdot x\right)} \]

      10. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{x + 5}, y \cdot x\right) \]

      11. lower-*.f64 99.2

          \[\leadsto \mathsf{fma}\left(z, x + 5, \color{blue}{y \cdot x}\right) \]

   4. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, x + 5, y \cdot x\right)} \]

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-+.f64 94.8

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

   7. Applied rewrites 94.8%

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

   if -6.5e8 < x < 2.4999999999999999e-81

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{5 \cdot z + x \cdot z} \]
   4. Step-by-step derivation

      1. distribute-rgt-in N/A

         \[\leadsto \color{blue}{z \cdot \left(5 + x\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

      4. lower-+.f64 72.9

         \[\leadsto \color{blue}{\left(5 + x\right)} \cdot z \]

   5. Applied rewrites 72.9%

      \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -650000000 \lor \neg \left(x \leq 2.5 \cdot 10^{-81}\right):\\ \;\;\;\;\left(y + z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(5 + x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+99} \lor \neg \left(y \leq 2.05 \cdot 10^{+36}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(5 + x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.5e+99) (not (<= y 2.05e+36))) (* y x) (* (+ 5.0 x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.5e+99) || !(y <= 2.05e+36)) {
		tmp = y * x;
	} else {
		tmp = (5.0 + x) * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-9.5d+99)) .or. (.not. (y <= 2.05d+36))) then
        tmp = y * x
    else
        tmp = (5.0d0 + x) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.5e+99) || !(y <= 2.05e+36)) {
		tmp = y * x;
	} else {
		tmp = (5.0 + x) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9.5e+99) or not (y <= 2.05e+36):
		tmp = y * x
	else:
		tmp = (5.0 + x) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.5e+99) || !(y <= 2.05e+36))
		tmp = Float64(y * x);
	else
		tmp = Float64(Float64(5.0 + x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -9.5e+99) || ~((y <= 2.05e+36)))
		tmp = y * x;
	else
		tmp = (5.0 + x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9.5e+99], N[Not[LessEqual[y, 2.05e+36]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(N[(5.0 + x), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.49999999999999908e99 or 2.05000000000000006e36 < y

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot x} \]

      2. lower-*.f64 73.0

         \[\leadsto \color{blue}{y \cdot x} \]

   5. Applied rewrites 73.0%

      \[\leadsto \color{blue}{y \cdot x} \]

   if -9.49999999999999908e99 < y < 2.05000000000000006e36

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{5 \cdot z + x \cdot z} \]
   4. Step-by-step derivation

      1. distribute-rgt-in N/A

         \[\leadsto \color{blue}{z \cdot \left(5 + x\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

      4. lower-+.f64 78.2

         \[\leadsto \color{blue}{\left(5 + x\right)} \cdot z \]

   5. Applied rewrites 78.2%

      \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+99} \lor \neg \left(y \leq 2.05 \cdot 10^{+36}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(5 + x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \lor \neg \left(x \leq 8200000000000\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;5 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.0) (not (<= x 8200000000000.0))) (* x z) (* 5.0 z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.0) || !(x <= 8200000000000.0)) {
		tmp = x * z;
	} else {
		tmp = 5.0 * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-5.0d0)) .or. (.not. (x <= 8200000000000.0d0))) then
        tmp = x * z
    else
        tmp = 5.0d0 * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.0) || !(x <= 8200000000000.0)) {
		tmp = x * z;
	} else {
		tmp = 5.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.0) or not (x <= 8200000000000.0):
		tmp = x * z
	else:
		tmp = 5.0 * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.0) || !(x <= 8200000000000.0))
		tmp = Float64(x * z);
	else
		tmp = Float64(5.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.0) || ~((x <= 8200000000000.0)))
		tmp = x * z;
	else
		tmp = 5.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.0], N[Not[LessEqual[x, 8200000000000.0]], $MachinePrecision]], N[(x * z), $MachinePrecision], N[(5.0 * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5 or 8.2e12 < x

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{5 \cdot z + x \cdot z} \]
   4. Step-by-step derivation

      1. distribute-rgt-in N/A

         \[\leadsto \color{blue}{z \cdot \left(5 + x\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

      4. lower-+.f64 46.6

         \[\leadsto \color{blue}{\left(5 + x\right)} \cdot z \]

   5. Applied rewrites 46.6%

      \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 45.6%

      \[\leadsto x \cdot \color{blue}{z} \]

   if -5 < x < 8.2e12

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{5 \cdot z} \]
   4. Step-by-step derivation

      1. lower-*.f64 67.2

         \[\leadsto \color{blue}{5 \cdot z} \]

   5. Applied rewrites 67.2%

      \[\leadsto \color{blue}{5 \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \lor \neg \left(x \leq 8200000000000\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;5 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, x, \left(x + 5\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma y x (* (+ x 5.0) z)))

C

double code(double x, double y, double z) {
	return fma(y, x, ((x + 5.0) * z));
}

Julia

function code(x, y, z)
	return fma(y, x, Float64(Float64(x + 5.0) * z))
end

Wolfram

code[x_, y_, z_] := N[(y * x + N[(N[(x + 5.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(y + z\right) + z \cdot 5 \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x \cdot \left(y + z\right) + z \cdot 5} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{z \cdot 5 + x \cdot \left(y + z\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{z \cdot 5} + x \cdot \left(y + z\right) \]

   4. lower-fma.f64 100.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, 5, x \cdot \left(y + z\right)\right)} \]

   5. lift-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{x \cdot \left(y + z\right)}\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(y + z\right) \cdot x}\right) \]

   7. lower-*.f64 100.0

      \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(y + z\right) \cdot x}\right) \]

   8. lift-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(y + z\right)} \cdot x\right) \]

   9. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(z + y\right)} \cdot x\right) \]

   10. lower-+.f64 100.0

       \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{\left(z + y\right)} \cdot x\right) \]

4. Applied rewrites 100.0%

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

   1. lift-fma.f64 N/A

      \[\leadsto \color{blue}{z \cdot 5 + \left(z + y\right) \cdot x} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(z + y\right) \cdot x + z \cdot 5} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(z + y\right) \cdot x} + z \cdot 5 \]

   4. *-commutative N/A

      \[\leadsto \color{blue}{x \cdot \left(z + y\right)} + z \cdot 5 \]

   5. lift-+.f64 N/A

      \[\leadsto x \cdot \color{blue}{\left(z + y\right)} + z \cdot 5 \]

   6. +-commutative N/A

      \[\leadsto x \cdot \color{blue}{\left(y + z\right)} + z \cdot 5 \]

   7. distribute-rgt-in N/A

      \[\leadsto \color{blue}{\left(y \cdot x + z \cdot x\right)} + z \cdot 5 \]

   8. lift-*.f64 N/A

      \[\leadsto \left(\color{blue}{y \cdot x} + z \cdot x\right) + z \cdot 5 \]

   9. associate-+r+ N/A

      \[\leadsto \color{blue}{y \cdot x + \left(z \cdot x + z \cdot 5\right)} \]

   10. distribute-lft-in N/A

       \[\leadsto y \cdot x + \color{blue}{z \cdot \left(x + 5\right)} \]

   11. lift-+.f64 N/A

       \[\leadsto y \cdot x + z \cdot \color{blue}{\left(x + 5\right)} \]

   12. lift-*.f64 N/A

       \[\leadsto \color{blue}{y \cdot x} + z \cdot \left(x + 5\right) \]

   13. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, z \cdot \left(x + 5\right)\right)} \]

   14. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{\left(x + 5\right) \cdot z}\right) \]

   15. lower-*.f64 99.5

       \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{\left(x + 5\right) \cdot z}\right) \]

6. Applied rewrites 99.5%

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

Alternative 11: 26.7% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[x \cdot \left(y + z\right) + z \cdot 5 \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{5 \cdot z + x \cdot z} \]
4. Step-by-step derivation

   1. distribute-rgt-in N/A

      \[\leadsto \color{blue}{z \cdot \left(5 + x\right)} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

   3. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

   4. lower-+.f64 58.1

      \[\leadsto \color{blue}{\left(5 + x\right)} \cdot z \]

5. Applied rewrites 58.1%

   \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

6. Taylor expanded in x around inf

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

8. Applied rewrites 22.7%

   \[\leadsto x \cdot \color{blue}{z} \]

9. Final simplification 22.7%

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

Developer Target 1: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + 5\right) \cdot z + x \cdot y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* (+ x 5.0) z) (* x y)))

C

double code(double x, double y, double z) {
	return ((x + 5.0) * z) + (x * y);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x + 5.0d0) * z) + (x * y)
end function

Java

public static double code(double x, double y, double z) {
	return ((x + 5.0) * z) + (x * y);
}

Python

def code(x, y, z):
	return ((x + 5.0) * z) + (x * y)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x + 5.0) * z) + Float64(x * y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x + 5.0) * z) + (x * y);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x + 5.0), $MachinePrecision] * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024352 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (* (+ x 5) z) (* x y)))

  (+ (* x (+ y z)) (* z 5.0)))