Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C

Percentage Accurate: 99.9% → 99.9%

Time: 3.6s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y z) :precision binary64 (+ (+ x (sin y)) (* z (cos y))))

C

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

Java

public static double code(double x, double y, double z) {
	return (x + Math.sin(y)) + (z * Math.cos(y));
}

Python

def code(x, y, z):
	return (x + math.sin(y)) + (z * math.cos(y))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (+ (+ x (sin y)) (* z (cos y))))

C

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

Java

public static double code(double x, double y, double z) {
	return (x + Math.sin(y)) + (z * Math.cos(y));
}

Python

def code(x, y, z):
	return (x + math.sin(y)) + (z * math.cos(y))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (fma (cos y) z (+ (sin y) x)))

C

double code(double x, double y, double z) {
	return fma(cos(y), z, (sin(y) + x));
}

Julia

function code(x, y, z)
	return fma(cos(y), z, Float64(sin(y) + x))
end

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. *-rgt-identity N/A

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

   5. lift-cos.f64 N/A

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

   6. sin-PI/2 N/A

      \[\leadsto z \cdot \left(\cos y \cdot \color{blue}{\sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)}\right) + \left(x + \sin y\right) \]

   7. lift-cos.f64 N/A

      \[\leadsto z \cdot \left(\color{blue}{\cos y} \cdot \sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)\right) + \left(x + \sin y\right) \]

   8. sin-PI/2 N/A

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

   9. *-rgt-identity N/A

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

   10. *-commutative N/A

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

   11. *-rgt-identity N/A

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

   12. lift-cos.f64 N/A

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

   13. sin-PI/2 N/A

       \[\leadsto \left(\cos y \cdot \color{blue}{\sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)}\right) \cdot z + \left(x + \sin y\right) \]

   14. lift-cos.f64 N/A

       \[\leadsto \left(\color{blue}{\cos y} \cdot \sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)\right) \cdot z + \left(x + \sin y\right) \]

   15. sin-PI/2 N/A

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

   16. *-rgt-identity N/A

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

   17. lower-fma.f64 99.9

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

   18. lift-+.f64 N/A

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

   19. +-commutative N/A

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

   20. lower-+.f64 99.9

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

3. Applied rewrites 99.9%

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

Alternative 2: 90.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x + y\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+183}:\\ \;\;\;\;\left(\sin y + z\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.45e+72)
   (fma (cos y) z (+ x y))
   (if (<= z 1.4e+183) (+ (+ (sin y) z) x) (fma (cos y) z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.45e+72) {
		tmp = fma(cos(y), z, (x + y));
	} else if (z <= 1.4e+183) {
		tmp = (sin(y) + z) + x;
	} else {
		tmp = fma(cos(y), z, sin(y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.45e+72)
		tmp = fma(cos(y), z, Float64(x + y));
	elseif (z <= 1.4e+183)
		tmp = Float64(Float64(sin(y) + z) + x);
	else
		tmp = fma(cos(y), z, sin(y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.45e+72], N[(N[Cos[y], $MachinePrecision] * z + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+183], N[(N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision] + x), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] * z + N[Sin[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.45000000000000003e72

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-rgt-identity N/A

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

      5. lift-cos.f64 N/A

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

      6. sin-PI/2 N/A

         \[\leadsto z \cdot \left(\cos y \cdot \color{blue}{\sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)}\right) + \left(x + \sin y\right) \]

      7. lift-cos.f64 N/A

         \[\leadsto z \cdot \left(\color{blue}{\cos y} \cdot \sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)\right) + \left(x + \sin y\right) \]

      8. sin-PI/2 N/A

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

      9. *-rgt-identity N/A

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

      10. *-commutative N/A

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

      11. *-rgt-identity N/A

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

      12. lift-cos.f64 N/A

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

      13. sin-PI/2 N/A

          \[\leadsto \left(\cos y \cdot \color{blue}{\sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)}\right) \cdot z + \left(x + \sin y\right) \]

      14. lift-cos.f64 N/A

          \[\leadsto \left(\color{blue}{\cos y} \cdot \sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)\right) \cdot z + \left(x + \sin y\right) \]

      15. sin-PI/2 N/A

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

      16. *-rgt-identity N/A

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

      17. lower-fma.f64 99.9

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in y around 0

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

      1. lower-+.f64 70.7

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

   6. Applied rewrites 70.7%

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

   if -2.45000000000000003e72 < z < 1.40000000000000009e183

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 82.0%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-+.f64 82.0

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

   6. Applied rewrites 82.0%

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

   if 1.40000000000000009e183 < z

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-rgt-identity N/A

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

      5. lift-cos.f64 N/A

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

      6. sin-PI/2 N/A

         \[\leadsto z \cdot \left(\cos y \cdot \color{blue}{\sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)}\right) + \left(x + \sin y\right) \]

      7. lift-cos.f64 N/A

         \[\leadsto z \cdot \left(\color{blue}{\cos y} \cdot \sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)\right) + \left(x + \sin y\right) \]

      8. sin-PI/2 N/A

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

      9. *-rgt-identity N/A

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

      10. *-commutative N/A

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

      11. *-rgt-identity N/A

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

      12. lift-cos.f64 N/A

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

      13. sin-PI/2 N/A

          \[\leadsto \left(\cos y \cdot \color{blue}{\sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)}\right) \cdot z + \left(x + \sin y\right) \]

      14. lift-cos.f64 N/A

          \[\leadsto \left(\color{blue}{\cos y} \cdot \sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)\right) \cdot z + \left(x + \sin y\right) \]

      15. sin-PI/2 N/A

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

      16. *-rgt-identity N/A

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

      17. lower-fma.f64 99.9

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around 0

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

      1. lower-sin.f64 59.7

         \[\leadsto \mathsf{fma}\left(\cos y, z, \sin y\right) \]

   6. Applied rewrites 59.7%

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

Alternative 3: 89.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\cos y, z, x + y\right)\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{+72}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+139}:\\ \;\;\;\;\left(\sin y + z\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (cos y) z (+ x y))))
   (if (<= z -2.45e+72) t_0 (if (<= z 9e+139) (+ (+ (sin y) z) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(cos(y), z, (x + y));
	double tmp;
	if (z <= -2.45e+72) {
		tmp = t_0;
	} else if (z <= 9e+139) {
		tmp = (sin(y) + z) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(cos(y), z, Float64(x + y))
	tmp = 0.0
	if (z <= -2.45e+72)
		tmp = t_0;
	elseif (z <= 9e+139)
		tmp = Float64(Float64(sin(y) + z) + x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z + N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.45e+72], t$95$0, If[LessEqual[z, 9e+139], N[(N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.45000000000000003e72 or 8.9999999999999999e139 < z

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-rgt-identity N/A

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

      5. lift-cos.f64 N/A

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

      6. sin-PI/2 N/A

         \[\leadsto z \cdot \left(\cos y \cdot \color{blue}{\sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)}\right) + \left(x + \sin y\right) \]

      7. lift-cos.f64 N/A

         \[\leadsto z \cdot \left(\color{blue}{\cos y} \cdot \sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)\right) + \left(x + \sin y\right) \]

      8. sin-PI/2 N/A

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

      9. *-rgt-identity N/A

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

      10. *-commutative N/A

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

      11. *-rgt-identity N/A

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

      12. lift-cos.f64 N/A

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

      13. sin-PI/2 N/A

          \[\leadsto \left(\cos y \cdot \color{blue}{\sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)}\right) \cdot z + \left(x + \sin y\right) \]

      14. lift-cos.f64 N/A

          \[\leadsto \left(\color{blue}{\cos y} \cdot \sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)\right) \cdot z + \left(x + \sin y\right) \]

      15. sin-PI/2 N/A

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

      16. *-rgt-identity N/A

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

      17. lower-fma.f64 99.9

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in y around 0

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

      1. lower-+.f64 70.7

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

   6. Applied rewrites 70.7%

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

   if -2.45000000000000003e72 < z < 8.9999999999999999e139

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 82.0%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-+.f64 82.0

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

   6. Applied rewrites 82.0%

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

Alternative 4: 86.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\cos y, z, y\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+197}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+183}:\\ \;\;\;\;\left(\sin y + z\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (cos y) z y)))
   (if (<= z -8e+197) t_0 (if (<= z 1.45e+183) (+ (+ (sin y) z) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(cos(y), z, y);
	double tmp;
	if (z <= -8e+197) {
		tmp = t_0;
	} else if (z <= 1.45e+183) {
		tmp = (sin(y) + z) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(cos(y), z, y)
	tmp = 0.0
	if (z <= -8e+197)
		tmp = t_0;
	elseif (z <= 1.45e+183)
		tmp = Float64(Float64(sin(y) + z) + x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z + y), $MachinePrecision]}, If[LessEqual[z, -8e+197], t$95$0, If[LessEqual[z, 1.45e+183], N[(N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.9999999999999996e197 or 1.45e183 < z

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-rgt-identity N/A

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

      5. lift-cos.f64 N/A

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

      6. sin-PI/2 N/A

         \[\leadsto z \cdot \left(\cos y \cdot \color{blue}{\sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)}\right) + \left(x + \sin y\right) \]

      7. lift-cos.f64 N/A

         \[\leadsto z \cdot \left(\color{blue}{\cos y} \cdot \sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)\right) + \left(x + \sin y\right) \]

      8. sin-PI/2 N/A

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

      9. *-rgt-identity N/A

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

      10. *-commutative N/A

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

      11. *-rgt-identity N/A

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

      12. lift-cos.f64 N/A

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

      13. sin-PI/2 N/A

          \[\leadsto \left(\cos y \cdot \color{blue}{\sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)}\right) \cdot z + \left(x + \sin y\right) \]

      14. lift-cos.f64 N/A

          \[\leadsto \left(\color{blue}{\cos y} \cdot \sin \left(\frac{\mathsf{PI}\left(\right)}{2}\right)\right) \cdot z + \left(x + \sin y\right) \]

      15. sin-PI/2 N/A

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

      16. *-rgt-identity N/A

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

      17. lower-fma.f64 99.9

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

      18. lift-+.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in y around 0

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

      1. lower-+.f64 70.7

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

   6. Applied rewrites 70.7%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\cos y, z, y\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 39.3%

      \[\leadsto \mathsf{fma}\left(\cos y, z, y\right) \]

   if -7.9999999999999996e197 < z < 1.45e183

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 82.0%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-+.f64 82.0

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

   6. Applied rewrites 82.0%

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

Alternative 5: 77.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -470000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-9}:\\ \;\;\;\;\sin y + z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{z}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -470000000.0)
   (+ x z)
   (if (<= x 3.7e-9) (+ (sin y) z) (* x (+ 1.0 (/ z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -470000000.0) {
		tmp = x + z;
	} else if (x <= 3.7e-9) {
		tmp = sin(y) + z;
	} else {
		tmp = x * (1.0 + (z / 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 <= (-470000000.0d0)) then
        tmp = x + z
    else if (x <= 3.7d-9) then
        tmp = sin(y) + z
    else
        tmp = x * (1.0d0 + (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -470000000.0) {
		tmp = x + z;
	} else if (x <= 3.7e-9) {
		tmp = Math.sin(y) + z;
	} else {
		tmp = x * (1.0 + (z / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -470000000.0:
		tmp = x + z
	elif x <= 3.7e-9:
		tmp = math.sin(y) + z
	else:
		tmp = x * (1.0 + (z / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -470000000.0)
		tmp = Float64(x + z);
	elseif (x <= 3.7e-9)
		tmp = Float64(sin(y) + z);
	else
		tmp = Float64(x * Float64(1.0 + Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -470000000.0)
		tmp = x + z;
	elseif (x <= 3.7e-9)
		tmp = sin(y) + z;
	else
		tmp = x * (1.0 + (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -470000000.0], N[(x + z), $MachinePrecision], If[LessEqual[x, 3.7e-9], N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision], N[(x * N[(1.0 + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.7e8

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 65.4

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

   4. Applied rewrites 65.4%

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

   if -4.7e8 < x < 3.7e-9

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 82.0%

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

   5. Taylor expanded in y around 0

      \[\leadsto \left(x + \color{blue}{y \cdot \left(1 + \frac{-1}{6} \cdot {y}^{2}\right)}\right) + z \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x + y \cdot \color{blue}{\left(1 + \frac{-1}{6} \cdot {y}^{2}\right)}\right) + z \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + y \cdot \left(1 + \color{blue}{\frac{-1}{6} \cdot {y}^{2}}\right)\right) + z \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x + y \cdot \left(1 + \frac{-1}{6} \cdot \color{blue}{{y}^{2}}\right)\right) + z \]

      4. lower-pow.f64 53.9

         \[\leadsto \left(x + y \cdot \left(1 + -0.16666666666666666 \cdot {y}^{\color{blue}{2}}\right)\right) + z \]

   7. Applied rewrites 53.9%

      \[\leadsto \left(x + \color{blue}{y \cdot \left(1 + -0.16666666666666666 \cdot {y}^{2}\right)}\right) + z \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\sin y} + z \]
   9. Step-by-step derivation

      1. lower-sin.f64 42.4

         \[\leadsto \sin y + z \]

   10. Applied rewrites 42.4%

       \[\leadsto \color{blue}{\sin y} + z \]

   if 3.7e-9 < x

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 65.4

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

   4. Applied rewrites 65.4%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 59.1

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

   7. Applied rewrites 59.1%

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

Alternative 6: 69.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11000000000000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.8:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \mathsf{fma}\left(-0.5, z, -0.16666666666666666 \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -11000000000000.0)
   (+ x z)
   (if (<= y 4.8)
     (+ x (+ z (* y (+ 1.0 (* y (fma -0.5 z (* -0.16666666666666666 y)))))))
     (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -11000000000000.0) {
		tmp = x + z;
	} else if (y <= 4.8) {
		tmp = x + (z + (y * (1.0 + (y * fma(-0.5, z, (-0.16666666666666666 * y))))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -11000000000000.0)
		tmp = Float64(x + z);
	elseif (y <= 4.8)
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * fma(-0.5, z, Float64(-0.16666666666666666 * y)))))));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -11000000000000.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 4.8], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(-0.5 * z + N[(-0.16666666666666666 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e13 or 4.79999999999999982 < y

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 65.4

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

   4. Applied rewrites 65.4%

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

   if -1.1e13 < y < 4.79999999999999982

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(z + y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \left(z + \color{blue}{y \cdot \left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x + \left(z + y \cdot \color{blue}{\left(1 + y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)\right)}\right) \]

      4. lower-+.f64 N/A

         \[\leadsto x + \left(z + y \cdot \left(1 + \color{blue}{y \cdot \left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)}\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto x + \left(z + y \cdot \left(1 + y \cdot \color{blue}{\left(\frac{-1}{2} \cdot z + \frac{-1}{6} \cdot y\right)}\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \left(z + y \cdot \left(1 + y \cdot \mathsf{fma}\left(\frac{-1}{2}, \color{blue}{z}, \frac{-1}{6} \cdot y\right)\right)\right) \]

      7. lower-*.f64 53.4

         \[\leadsto x + \left(z + y \cdot \left(1 + y \cdot \mathsf{fma}\left(-0.5, z, -0.16666666666666666 \cdot y\right)\right)\right) \]

   4. Applied rewrites 53.4%

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + y \cdot \mathsf{fma}\left(-0.5, z, -0.16666666666666666 \cdot y\right)\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 69.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+31}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 6.2:\\ \;\;\;\;\left(x + y \cdot \mathsf{fma}\left(-0.16666666666666666 \cdot y, y, 1\right)\right) + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.55e+31)
   (+ x z)
   (if (<= y 6.2)
     (+ (+ x (* y (fma (* -0.16666666666666666 y) y 1.0))) z)
     (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.55e+31) {
		tmp = x + z;
	} else if (y <= 6.2) {
		tmp = (x + (y * fma((-0.16666666666666666 * y), y, 1.0))) + z;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.55e+31)
		tmp = Float64(x + z);
	elseif (y <= 6.2)
		tmp = Float64(Float64(x + Float64(y * fma(Float64(-0.16666666666666666 * y), y, 1.0))) + z);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.55e+31], N[(x + z), $MachinePrecision], If[LessEqual[y, 6.2], N[(N[(x + N[(y * N[(N[(-0.16666666666666666 * y), $MachinePrecision] * y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5500000000000001e31 or 6.20000000000000018 < y

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 65.4

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

   4. Applied rewrites 65.4%

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

   if -1.5500000000000001e31 < y < 6.20000000000000018

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 82.0%

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

   5. Taylor expanded in y around 0

      \[\leadsto \left(x + \color{blue}{y \cdot \left(1 + \frac{-1}{6} \cdot {y}^{2}\right)}\right) + z \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x + y \cdot \color{blue}{\left(1 + \frac{-1}{6} \cdot {y}^{2}\right)}\right) + z \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + y \cdot \left(1 + \color{blue}{\frac{-1}{6} \cdot {y}^{2}}\right)\right) + z \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x + y \cdot \left(1 + \frac{-1}{6} \cdot \color{blue}{{y}^{2}}\right)\right) + z \]

      4. lower-pow.f64 53.9

         \[\leadsto \left(x + y \cdot \left(1 + -0.16666666666666666 \cdot {y}^{\color{blue}{2}}\right)\right) + z \]

   7. Applied rewrites 53.9%

      \[\leadsto \left(x + \color{blue}{y \cdot \left(1 + -0.16666666666666666 \cdot {y}^{2}\right)}\right) + z \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \left(x + y \cdot \left(1 + \color{blue}{\frac{-1}{6} \cdot {y}^{2}}\right)\right) + z \]

      2. +-commutative N/A

         \[\leadsto \left(x + y \cdot \left(\frac{-1}{6} \cdot {y}^{2} + \color{blue}{1}\right)\right) + z \]

      3. lift-*.f64 N/A

         \[\leadsto \left(x + y \cdot \left(\frac{-1}{6} \cdot {y}^{2} + 1\right)\right) + z \]

      4. lift-pow.f64 N/A

         \[\leadsto \left(x + y \cdot \left(\frac{-1}{6} \cdot {y}^{2} + 1\right)\right) + z \]

      5. unpow2 N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 53.9

          \[\leadsto \left(x + y \cdot \mathsf{fma}\left(-0.16666666666666666 \cdot y, y, 1\right)\right) + z \]

   9. Applied rewrites 53.9%

      \[\leadsto \left(x + y \cdot \mathsf{fma}\left(-0.16666666666666666 \cdot y, \color{blue}{y}, 1\right)\right) + z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 69.7% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+15}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 48000000000000:\\ \;\;\;\;y + \mathsf{fma}\left(\mathsf{fma}\left(y \cdot y, -0.5, 1\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.2e+15)
   (+ x z)
   (if (<= y 48000000000000.0)
     (+ y (fma (fma (* y y) -0.5 1.0) z x))
     (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2e+15) {
		tmp = x + z;
	} else if (y <= 48000000000000.0) {
		tmp = y + fma(fma((y * y), -0.5, 1.0), z, x);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.2e+15)
		tmp = Float64(x + z);
	elseif (y <= 48000000000000.0)
		tmp = Float64(y + fma(fma(Float64(y * y), -0.5, 1.0), z, x));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.2e+15], N[(x + z), $MachinePrecision], If[LessEqual[y, 48000000000000.0], N[(y + N[(N[(N[(y * y), $MachinePrecision] * -0.5 + 1.0), $MachinePrecision] * z + x), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e15 or 4.8e13 < y

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 65.4

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

   4. Applied rewrites 65.4%

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

   if -1.2e15 < y < 4.8e13

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(z + y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \left(z + \color{blue}{y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x + \left(z + y \cdot \color{blue}{\left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)}\right) \]

      4. lower-+.f64 N/A

         \[\leadsto x + \left(z + y \cdot \left(1 + \color{blue}{\frac{-1}{2} \cdot \left(y \cdot z\right)}\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto x + \left(z + y \cdot \left(1 + \frac{-1}{2} \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

      6. lower-*.f64 56.7

         \[\leadsto x + \left(z + y \cdot \left(1 + -0.5 \cdot \left(y \cdot \color{blue}{z}\right)\right)\right) \]

   4. Applied rewrites 56.7%

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + -0.5 \cdot \left(y \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto x + \color{blue}{\left(z + y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(z + y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) + \color{blue}{x} \]

      3. lift-+.f64 N/A

         \[\leadsto \left(z + y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) + x \]

      4. +-commutative N/A

         \[\leadsto \left(y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right) + z\right) + x \]

      5. lift-*.f64 N/A

         \[\leadsto \left(y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right) + z\right) + x \]

      6. lift-+.f64 N/A

         \[\leadsto \left(y \cdot \left(1 + \frac{-1}{2} \cdot \left(y \cdot z\right)\right) + z\right) + x \]

      7. distribute-lft-in N/A

         \[\leadsto \left(\left(y \cdot 1 + y \cdot \left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) + z\right) + x \]

      8. *-rgt-identity N/A

         \[\leadsto \left(\left(y + y \cdot \left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) + z\right) + x \]

      9. +-commutative N/A

         \[\leadsto \left(\left(y \cdot \left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right) + y\right) + z\right) + x \]

      10. +-commutative N/A

          \[\leadsto \left(\left(y + y \cdot \left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right)\right) + z\right) + x \]

      11. associate-+l+ N/A

          \[\leadsto \left(y + \left(y \cdot \left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right) + z\right)\right) + x \]

      12. associate-+l+ N/A

          \[\leadsto y + \color{blue}{\left(\left(y \cdot \left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right) + z\right) + x\right)} \]

      13. lower-+.f64 N/A

          \[\leadsto y + \color{blue}{\left(\left(y \cdot \left(\frac{-1}{2} \cdot \left(y \cdot z\right)\right) + z\right) + x\right)} \]

   6. Applied rewrites 55.8%

      \[\leadsto y + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y \cdot y, -0.5, 1\right), z, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 69.7% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+33}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 70000000000000:\\ \;\;\;\;x + \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.15e+33)
   (+ x z)
   (if (<= y 70000000000000.0) (+ x (+ y z)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.15e+33) {
		tmp = x + z;
	} else if (y <= 70000000000000.0) {
		tmp = x + (y + z);
	} else {
		tmp = 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 <= (-2.15d+33)) then
        tmp = x + z
    else if (y <= 70000000000000.0d0) then
        tmp = x + (y + z)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.15e+33) {
		tmp = x + z;
	} else if (y <= 70000000000000.0) {
		tmp = x + (y + z);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.15e+33:
		tmp = x + z
	elif y <= 70000000000000.0:
		tmp = x + (y + z)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.15e+33)
		tmp = Float64(x + z);
	elseif (y <= 70000000000000.0)
		tmp = Float64(x + Float64(y + z));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.15e+33)
		tmp = x + z;
	elseif (y <= 70000000000000.0)
		tmp = x + (y + z);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.15e+33], N[(x + z), $MachinePrecision], If[LessEqual[y, 70000000000000.0], N[(x + N[(y + z), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.15000000000000014e33 or 7e13 < y

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 65.4

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

   4. Applied rewrites 65.4%

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

   if -2.15000000000000014e33 < y < 7e13

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 61.1

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

   4. Applied rewrites 61.1%

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

Alternative 10: 67.5% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{-114}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-135}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.12e-114) (+ x z) (if (<= x 2.15e-135) (+ y z) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.12e-114) {
		tmp = x + z;
	} else if (x <= 2.15e-135) {
		tmp = y + z;
	} else {
		tmp = 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 <= (-1.12d-114)) then
        tmp = x + z
    else if (x <= 2.15d-135) then
        tmp = y + z
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.12e-114) {
		tmp = x + z;
	} else if (x <= 2.15e-135) {
		tmp = y + z;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.12e-114:
		tmp = x + z
	elif x <= 2.15e-135:
		tmp = y + z
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.12e-114)
		tmp = Float64(x + z);
	elseif (x <= 2.15e-135)
		tmp = Float64(y + z);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.12e-114)
		tmp = x + z;
	elseif (x <= 2.15e-135)
		tmp = y + z;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.12e-114], N[(x + z), $MachinePrecision], If[LessEqual[x, 2.15e-135], N[(y + z), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.11999999999999995e-114 or 2.14999999999999999e-135 < x

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 65.4

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

   4. Applied rewrites 65.4%

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

   if -1.11999999999999995e-114 < x < 2.14999999999999999e-135

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 82.0%

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

   5. Taylor expanded in y around 0

      \[\leadsto \left(x + \color{blue}{y \cdot \left(1 + \frac{-1}{6} \cdot {y}^{2}\right)}\right) + z \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x + y \cdot \color{blue}{\left(1 + \frac{-1}{6} \cdot {y}^{2}\right)}\right) + z \]

      2. lower-+.f64 N/A

         \[\leadsto \left(x + y \cdot \left(1 + \color{blue}{\frac{-1}{6} \cdot {y}^{2}}\right)\right) + z \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x + y \cdot \left(1 + \frac{-1}{6} \cdot \color{blue}{{y}^{2}}\right)\right) + z \]

      4. lower-pow.f64 53.9

         \[\leadsto \left(x + y \cdot \left(1 + -0.16666666666666666 \cdot {y}^{\color{blue}{2}}\right)\right) + z \]

   7. Applied rewrites 53.9%

      \[\leadsto \left(x + \color{blue}{y \cdot \left(1 + -0.16666666666666666 \cdot {y}^{2}\right)}\right) + z \]

   8. Taylor expanded in y around 0

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

      1. lower-+.f64 61.1

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

   10. Applied rewrites 61.1%

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

   11. Taylor expanded in x around 0

       \[\leadsto y + z \]
   12. Step-by-step derivation

   13. Applied rewrites 29.9%

       \[\leadsto y + z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 65.4% accurate, 19.6× speedup

Math

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

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%

   \[\left(x + \sin y\right) + z \cdot \cos y \]

2. Taylor expanded in y around 0

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

   1. lower-+.f64 65.4

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

4. Applied rewrites 65.4%

   \[\leadsto \color{blue}{x + z} \]
5. Add Preprocessing

Alternative 12: 26.4% accurate, 73.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.9%

   \[\left(x + \sin y\right) + z \cdot \cos y \]

2. Taylor expanded in y around 0

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

   1. lower-+.f64 65.4

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

4. Applied rewrites 65.4%

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

5. Taylor expanded in x around 0

   \[\leadsto z \]
6. Step-by-step derivation

7. Applied rewrites 26.4%

   \[\leadsto z \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025156 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))