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

Percentage Accurate: 99.9% → 99.9%

Time: 8.4s

Alternatives: 10

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. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. lift-sin.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift-cos.f64 N/A

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

   6. +-commutative N/A

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

   7. *-commutative N/A

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

   8. lower-fma.f64 N/A

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

   9. lift-cos.f64 N/A

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

   10. +-commutative N/A

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

   11. lower-+.f64 N/A

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

   12. lift-sin.f64 99.9

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

4. Applied rewrites 99.9%

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

Alternative 2: 81.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + \sin y\right) + z \cdot \cos y\\ \mathbf{if}\;t\_0 \leq -20:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t\_0 \leq -0.01:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-18}:\\ \;\;\;\;\left(z + y\right) + x\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (+ x (sin y)) (* z (cos y)))))
   (if (<= t_0 -20.0)
     (+ z x)
     (if (<= t_0 -0.01)
       (sin y)
       (if (<= t_0 2e-18) (+ (+ z y) x) (if (<= t_0 2.0) (sin y) (+ z x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + sin(y)) + (z * cos(y));
	double tmp;
	if (t_0 <= -20.0) {
		tmp = z + x;
	} else if (t_0 <= -0.01) {
		tmp = sin(y);
	} else if (t_0 <= 2e-18) {
		tmp = (z + y) + x;
	} else if (t_0 <= 2.0) {
		tmp = sin(y);
	} else {
		tmp = 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) :: t_0
    real(8) :: tmp
    t_0 = (x + sin(y)) + (z * cos(y))
    if (t_0 <= (-20.0d0)) then
        tmp = z + x
    else if (t_0 <= (-0.01d0)) then
        tmp = sin(y)
    else if (t_0 <= 2d-18) then
        tmp = (z + y) + x
    else if (t_0 <= 2.0d0) then
        tmp = sin(y)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + Math.sin(y)) + (z * Math.cos(y));
	double tmp;
	if (t_0 <= -20.0) {
		tmp = z + x;
	} else if (t_0 <= -0.01) {
		tmp = Math.sin(y);
	} else if (t_0 <= 2e-18) {
		tmp = (z + y) + x;
	} else if (t_0 <= 2.0) {
		tmp = Math.sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + math.sin(y)) + (z * math.cos(y))
	tmp = 0
	if t_0 <= -20.0:
		tmp = z + x
	elif t_0 <= -0.01:
		tmp = math.sin(y)
	elif t_0 <= 2e-18:
		tmp = (z + y) + x
	elif t_0 <= 2.0:
		tmp = math.sin(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + sin(y)) + Float64(z * cos(y)))
	tmp = 0.0
	if (t_0 <= -20.0)
		tmp = Float64(z + x);
	elseif (t_0 <= -0.01)
		tmp = sin(y);
	elseif (t_0 <= 2e-18)
		tmp = Float64(Float64(z + y) + x);
	elseif (t_0 <= 2.0)
		tmp = sin(y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + sin(y)) + (z * cos(y));
	tmp = 0.0;
	if (t_0 <= -20.0)
		tmp = z + x;
	elseif (t_0 <= -0.01)
		tmp = sin(y);
	elseif (t_0 <= 2e-18)
		tmp = (z + y) + x;
	elseif (t_0 <= 2.0)
		tmp = sin(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -20.0], N[(z + x), $MachinePrecision], If[LessEqual[t$95$0, -0.01], N[Sin[y], $MachinePrecision], If[LessEqual[t$95$0, 2e-18], N[(N[(z + y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$0, 2.0], N[Sin[y], $MachinePrecision], N[(z + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -20 or 2 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 80.7

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

   5. Applied rewrites 80.7%

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

   if -20 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -0.0100000000000000002 or 2.0000000000000001e-18 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 2

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-cos.f64 N/A

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

      5. lift-sin.f64 96.0

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

   5. Applied rewrites 96.0%

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

   6. Taylor expanded in z around 0

      \[\leadsto \sin y \]
   7. Step-by-step derivation

      1. lift-sin.f64 91.9

         \[\leadsto \sin y \]

   8. Applied rewrites 91.9%

      \[\leadsto \sin y \]

   if -0.0100000000000000002 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 2.0000000000000001e-18

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 99.9

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

   5. Applied rewrites 99.9%

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

Alternative 3: 83.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+27}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-78}:\\ \;\;\;\;\sin y + x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+152}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)))
   (if (<= z -7.2e+27)
     t_0
     (if (<= z 5e-78) (+ (sin y) x) (if (<= z 1.1e+152) (+ z x) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double tmp;
	if (z <= -7.2e+27) {
		tmp = t_0;
	} else if (z <= 5e-78) {
		tmp = sin(y) + x;
	} else if (z <= 1.1e+152) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cos(y) * z
    if (z <= (-7.2d+27)) then
        tmp = t_0
    else if (z <= 5d-78) then
        tmp = sin(y) + x
    else if (z <= 1.1d+152) then
        tmp = z + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cos(y) * z;
	double tmp;
	if (z <= -7.2e+27) {
		tmp = t_0;
	} else if (z <= 5e-78) {
		tmp = Math.sin(y) + x;
	} else if (z <= 1.1e+152) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cos(y) * z
	tmp = 0
	if z <= -7.2e+27:
		tmp = t_0
	elif z <= 5e-78:
		tmp = math.sin(y) + x
	elif z <= 1.1e+152:
		tmp = z + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	tmp = 0.0
	if (z <= -7.2e+27)
		tmp = t_0;
	elseif (z <= 5e-78)
		tmp = Float64(sin(y) + x);
	elseif (z <= 1.1e+152)
		tmp = Float64(z + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cos(y) * z;
	tmp = 0.0;
	if (z <= -7.2e+27)
		tmp = t_0;
	elseif (z <= 5e-78)
		tmp = sin(y) + x;
	elseif (z <= 1.1e+152)
		tmp = z + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -7.2e+27], t$95$0, If[LessEqual[z, 5e-78], N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.1e+152], N[(z + x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.19999999999999966e27 or 1.0999999999999999e152 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

         \[\leadsto \cos y \cdot \color{blue}{z} \]

      2. lower-*.f64 N/A

         \[\leadsto \cos y \cdot \color{blue}{z} \]

      3. lift-cos.f64 86.7

         \[\leadsto \cos y \cdot z \]

   5. Applied rewrites 86.7%

      \[\leadsto \color{blue}{\cos y \cdot z} \]

   if -7.19999999999999966e27 < z < 4.9999999999999996e-78

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lift-sin.f64 91.2

         \[\leadsto \sin y + x \]

   5. Applied rewrites 91.2%

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

   if 4.9999999999999996e-78 < z < 1.0999999999999999e152

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 79.8

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

   5. Applied rewrites 79.8%

      \[\leadsto \color{blue}{z + x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 94.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0135 \lor \neg \left(z \leq 5 \cdot 10^{-78}\right):\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.0135) (not (<= z 5e-78))) (fma (cos y) z x) (+ (sin y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0135) || !(z <= 5e-78)) {
		tmp = fma(cos(y), z, x);
	} else {
		tmp = sin(y) + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.0135) || !(z <= 5e-78))
		tmp = fma(cos(y), z, x);
	else
		tmp = Float64(sin(y) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.0135], N[Not[LessEqual[z, 5e-78]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * z + x), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0134999999999999998 or 4.9999999999999996e-78 < z

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-sin.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-cos.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-cos.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lift-sin.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 99.0%

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

   if -0.0134999999999999998 < z < 4.9999999999999996e-78

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lift-sin.f64 93.3

         \[\leadsto \sin y + x \]

   5. Applied rewrites 93.3%

      \[\leadsto \color{blue}{\sin y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0135 \lor \neg \left(z \leq 5 \cdot 10^{-78}\right):\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.023 \lor \neg \left(y \leq 4600000000\right):\\ \;\;\;\;\sin y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z \cdot y, -0.5, 1\right), y, z + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.023) (not (<= y 4600000000.0)))
   (+ (sin y) x)
   (fma (fma (* z y) -0.5 1.0) y (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.023) || !(y <= 4600000000.0)) {
		tmp = sin(y) + x;
	} else {
		tmp = fma(fma((z * y), -0.5, 1.0), y, (z + x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.023) || !(y <= 4600000000.0))
		tmp = Float64(sin(y) + x);
	else
		tmp = fma(fma(Float64(z * y), -0.5, 1.0), y, Float64(z + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.023], N[Not[LessEqual[y, 4600000000.0]], $MachinePrecision]], N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(z * y), $MachinePrecision] * -0.5 + 1.0), $MachinePrecision] * y + N[(z + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.023 or 4.6e9 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lift-sin.f64 68.7

         \[\leadsto \sin y + x \]

   5. Applied rewrites 68.7%

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

   if -0.023 < y < 4.6e9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 97.5

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

   5. Applied rewrites 97.5%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.023 \lor \neg \left(y \leq 4600000000\right):\\ \;\;\;\;\sin y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z \cdot y, -0.5, 1\right), y, z + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.0% accurate, 5.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -36 \lor \neg \left(y \leq 190000\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.16666666666666666, y, -0.5 \cdot z\right), y, 1\right), y, z + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -36.0) (not (<= y 190000.0)))
   (+ z x)
   (fma (fma (fma -0.16666666666666666 y (* -0.5 z)) y 1.0) y (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -36.0) || !(y <= 190000.0)) {
		tmp = z + x;
	} else {
		tmp = fma(fma(fma(-0.16666666666666666, y, (-0.5 * z)), y, 1.0), y, (z + x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -36.0) || !(y <= 190000.0))
		tmp = Float64(z + x);
	else
		tmp = fma(fma(fma(-0.16666666666666666, y, Float64(-0.5 * z)), y, 1.0), y, Float64(z + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -36.0], N[Not[LessEqual[y, 190000.0]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(N[(N[(-0.16666666666666666 * y + N[(-0.5 * z), $MachinePrecision]), $MachinePrecision] * y + 1.0), $MachinePrecision] * y + N[(z + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -36 or 1.9e5 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 49.5

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

   5. Applied rewrites 49.5%

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

   if -36 < y < 1.9e5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-+.f64 98.5

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

   5. Applied rewrites 98.5%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -36 \lor \neg \left(y \leq 190000\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.16666666666666666, y, -0.5 \cdot z\right), y, 1\right), y, z + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.9% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -36 \lor \neg \left(y \leq 190000\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z \cdot y, -0.5, 1\right), y, z + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -36.0) (not (<= y 190000.0)))
   (+ z x)
   (fma (fma (* z y) -0.5 1.0) y (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -36.0) || !(y <= 190000.0)) {
		tmp = z + x;
	} else {
		tmp = fma(fma((z * y), -0.5, 1.0), y, (z + x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -36.0) || !(y <= 190000.0))
		tmp = Float64(z + x);
	else
		tmp = fma(fma(Float64(z * y), -0.5, 1.0), y, Float64(z + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -36.0], N[Not[LessEqual[y, 190000.0]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(N[(N[(z * y), $MachinePrecision] * -0.5 + 1.0), $MachinePrecision] * y + N[(z + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -36 or 1.9e5 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 49.5

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

   5. Applied rewrites 49.5%

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

   if -36 < y < 1.9e5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 98.4

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

   5. Applied rewrites 98.4%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -36 \lor \neg \left(y \leq 190000\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z \cdot y, -0.5, 1\right), y, z + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.7% accurate, 16.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+28}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+150}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.9e+28) z (if (<= z 4e+150) x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e+28) {
		tmp = z;
	} else if (z <= 4e+150) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-1.9d+28)) then
        tmp = z
    else if (z <= 4d+150) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e+28) {
		tmp = z;
	} else if (z <= 4e+150) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.9e+28:
		tmp = z
	elif z <= 4e+150:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.9e+28)
		tmp = z;
	elseif (z <= 4e+150)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.9e+28)
		tmp = z;
	elseif (z <= 4e+150)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.9e+28], z, If[LessEqual[z, 4e+150], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e28 or 3.99999999999999992e150 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-cos.f64 N/A

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

      5. lift-sin.f64 86.7

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

   5. Applied rewrites 86.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 57.9%

      \[\leadsto z \]

   if -1.8999999999999999e28 < z < 3.99999999999999992e150

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 60.5%

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

Alternative 9: 66.0% accurate, 53.0× speedup

Math

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

FPCore

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

C

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

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 + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 71.8

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

5. Applied rewrites 71.8%

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

Alternative 10: 42.1% accurate, 212.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 43.7%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2025038 
(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))))