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

Percentage Accurate: 99.9% → 99.9%

Time: 4.4s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 90.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + \cos y\right) - z \cdot \sin y\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+31} \lor \neg \left(t\_0 \leq 20\right):\\ \;\;\;\;\mathsf{fma}\left(z, \frac{-\sin y}{x}, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ x (cos y)) (* z (sin y)))))
   (if (or (<= t_0 -5e+31) (not (<= t_0 20.0)))
     (* (fma z (/ (- (sin y)) x) 1.0) x)
     (+ (cos y) x))))

C

double code(double x, double y, double z) {
	double t_0 = (x + cos(y)) - (z * sin(y));
	double tmp;
	if ((t_0 <= -5e+31) || !(t_0 <= 20.0)) {
		tmp = fma(z, (-sin(y) / x), 1.0) * x;
	} else {
		tmp = cos(y) + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
	tmp = 0.0
	if ((t_0 <= -5e+31) || !(t_0 <= 20.0))
		tmp = Float64(fma(z, Float64(Float64(-sin(y)) / x), 1.0) * x);
	else
		tmp = Float64(cos(y) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -5e+31], N[Not[LessEqual[t$95$0, 20.0]], $MachinePrecision]], N[(N[(z * N[((-N[Sin[y], $MachinePrecision]) / x), $MachinePrecision] + 1.0), $MachinePrecision] * x), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -5.00000000000000027e31 or 20 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. div-add-rev N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lift-cos.f64 N/A

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

      9. lift-sin.f64 77.6

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

   5. Applied rewrites 77.6%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-cos.f64 N/A

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

      10. lift-sin.f64 86.2

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

   8. Applied rewrites 86.2%

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

   9. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(z, \frac{-1 \cdot \sin y}{x}, 1\right) \cdot x \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{neg}\left(\sin y\right)}{x}, 1\right) \cdot x \]

       2. lower-neg.f64 N/A

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

       3. lift-sin.f64 85.9

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

   11. Applied rewrites 85.9%

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

   if -5.00000000000000027e31 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 20

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lift-cos.f64 94.4

         \[\leadsto \cos y + x \]

   5. Applied rewrites 94.4%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + \cos y\right) - z \cdot \sin y \leq -5 \cdot 10^{+31} \lor \neg \left(\left(x + \cos y\right) - z \cdot \sin y \leq 20\right):\\ \;\;\;\;\mathsf{fma}\left(z, \frac{-\sin y}{x}, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + \cos y\right) - z \cdot \sin y\\ \mathbf{if}\;t\_0 \leq -20 \lor \neg \left(t\_0 \leq 0.996\right):\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ x (cos y)) (* z (sin y)))))
   (if (or (<= t_0 -20.0) (not (<= t_0 0.996))) (- x (fma z y -1.0)) (cos y))))

C

double code(double x, double y, double z) {
	double t_0 = (x + cos(y)) - (z * sin(y));
	double tmp;
	if ((t_0 <= -20.0) || !(t_0 <= 0.996)) {
		tmp = x - fma(z, y, -1.0);
	} else {
		tmp = cos(y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
	tmp = 0.0
	if ((t_0 <= -20.0) || !(t_0 <= 0.996))
		tmp = Float64(x - fma(z, y, -1.0));
	else
		tmp = cos(y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -20.0], N[Not[LessEqual[t$95$0, 0.996]], $MachinePrecision]], N[(x - N[(z * y + -1.0), $MachinePrecision]), $MachinePrecision], N[Cos[y], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -20 or 0.996 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. lower--.f64 N/A

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

      7. metadata-eval N/A

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

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

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

      9. *-lft-identity N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 72.9

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

   5. Applied rewrites 72.9%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 72.9

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

   7. Applied rewrites 72.9%

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

   if -20 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.996

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lift-cos.f64 98.1

         \[\leadsto \cos y + x \]

   5. Applied rewrites 98.1%

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

   6. Taylor expanded in x around 0

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

      1. lift-cos.f64 95.4

         \[\leadsto \cos y \]

   8. Applied rewrites 95.4%

      \[\leadsto \cos y \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + \cos y\right) - z \cdot \sin y \leq -20 \lor \neg \left(\left(x + \cos y\right) - z \cdot \sin y \leq 0.996\right):\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.62\right):\\ \;\;\;\;\mathsf{fma}\left(z, \frac{-\sin y}{x}, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 0.62)))
   (* (fma z (/ (- (sin y)) x) 1.0) x)
   (- (cos y) (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.0) || !(x <= 0.62)) {
		tmp = fma(z, (-sin(y) / x), 1.0) * x;
	} else {
		tmp = cos(y) - (z * sin(y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 0.62))
		tmp = Float64(fma(z, Float64(Float64(-sin(y)) / x), 1.0) * x);
	else
		tmp = Float64(cos(y) - Float64(z * sin(y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 0.62]], $MachinePrecision]], N[(N[(z * N[((-N[Sin[y], $MachinePrecision]) / x), $MachinePrecision] + 1.0), $MachinePrecision] * x), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 0.619999999999999996 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. div-add-rev N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lift-cos.f64 N/A

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

      9. lift-sin.f64 68.6

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

   5. Applied rewrites 68.6%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-cos.f64 N/A

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

      10. lift-sin.f64 99.9

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

   8. Applied rewrites 99.9%

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

   9. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(z, \frac{-1 \cdot \sin y}{x}, 1\right) \cdot x \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(z, \frac{\mathsf{neg}\left(\sin y\right)}{x}, 1\right) \cdot x \]

       2. lower-neg.f64 N/A

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

       3. lift-sin.f64 96.9

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

   11. Applied rewrites 96.9%

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

   if -1 < x < 0.619999999999999996

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. lift-cos.f64 98.6

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

   5. Applied rewrites 98.6%

      \[\leadsto \color{blue}{\cos y} - z \cdot \sin y \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.62\right):\\ \;\;\;\;\mathsf{fma}\left(z, \frac{-\sin y}{x}, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+109} \lor \neg \left(z \leq 1.15 \cdot 10^{+117}\right):\\ \;\;\;\;\left(-z\right) \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.4e+109) (not (<= z 1.15e+117)))
   (* (- z) (sin y))
   (+ (cos y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e+109) || !(z <= 1.15e+117)) {
		tmp = -z * sin(y);
	} else {
		tmp = cos(y) + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.4d+109)) .or. (.not. (z <= 1.15d+117))) then
        tmp = -z * sin(y)
    else
        tmp = cos(y) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e+109) || !(z <= 1.15e+117)) {
		tmp = -z * Math.sin(y);
	} else {
		tmp = Math.cos(y) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.4e+109) or not (z <= 1.15e+117):
		tmp = -z * math.sin(y)
	else:
		tmp = math.cos(y) + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.4e+109) || !(z <= 1.15e+117))
		tmp = Float64(Float64(-z) * sin(y));
	else
		tmp = Float64(cos(y) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.4e+109) || ~((z <= 1.15e+117)))
		tmp = -z * sin(y);
	else
		tmp = cos(y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.4e+109], N[Not[LessEqual[z, 1.15e+117]], $MachinePrecision]], N[((-z) * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4000000000000001e109 or 1.14999999999999994e117 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-neg-in N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lift-sin.f64 72.0

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

   5. Applied rewrites 72.0%

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

   if -1.4000000000000001e109 < z < 1.14999999999999994e117

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lift-cos.f64 93.4

         \[\leadsto \cos y + x \]

   5. Applied rewrites 93.4%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+109} \lor \neg \left(z \leq 1.15 \cdot 10^{+117}\right):\\ \;\;\;\;\left(-z\right) \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.36 \lor \neg \left(y \leq 640\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(0.16666666666666666 \cdot \left(z \cdot y\right) - 0.5\right) \cdot y - z, y, x - -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.36) (not (<= y 640.0)))
   (+ (cos y) x)
   (fma (- (* (- (* 0.16666666666666666 (* z y)) 0.5) y) z) y (- x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.36) || !(y <= 640.0)) {
		tmp = cos(y) + x;
	} else {
		tmp = fma(((((0.16666666666666666 * (z * y)) - 0.5) * y) - z), y, (x - -1.0));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.36) || !(y <= 640.0))
		tmp = Float64(cos(y) + x);
	else
		tmp = fma(Float64(Float64(Float64(Float64(0.16666666666666666 * Float64(z * y)) - 0.5) * y) - z), y, Float64(x - -1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.36], N[Not[LessEqual[y, 640.0]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(N[(N[(0.16666666666666666 * N[(z * y), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision] * y + N[(x - -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.35999999999999999 or 640 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lift-cos.f64 66.3

         \[\leadsto \cos y + x \]

   5. Applied rewrites 66.3%

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

   if -0.35999999999999999 < y < 640

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. +-commutative N/A

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

      15. metadata-eval N/A

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

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

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

      17. metadata-eval N/A

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

      18. metadata-eval N/A

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

   5. Applied rewrites 99.0%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.36 \lor \neg \left(y \leq 640\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(0.16666666666666666 \cdot \left(z \cdot y\right) - 0.5\right) \cdot y - z, y, x - -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.8% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \lor \neg \left(y \leq 3200\right):\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(0.16666666666666666 \cdot \left(z \cdot y\right) - 0.5\right) \cdot y - z, y, x - -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.4) (not (<= y 3200.0)))
   (- x -1.0)
   (fma (- (* (- (* 0.16666666666666666 (* z y)) 0.5) y) z) y (- x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.4) || !(y <= 3200.0)) {
		tmp = x - -1.0;
	} else {
		tmp = fma(((((0.16666666666666666 * (z * y)) - 0.5) * y) - z), y, (x - -1.0));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.4) || !(y <= 3200.0))
		tmp = Float64(x - -1.0);
	else
		tmp = fma(Float64(Float64(Float64(Float64(0.16666666666666666 * Float64(z * y)) - 0.5) * y) - z), y, Float64(x - -1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.4], N[Not[LessEqual[y, 3200.0]], $MachinePrecision]], N[(x - -1.0), $MachinePrecision], N[(N[(N[(N[(N[(0.16666666666666666 * N[(z * y), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision] * y + N[(x - -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4000000000000004 or 3200 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto x + \color{blue}{1} \]

      2. metadata-eval N/A

         \[\leadsto x + 1 \cdot \color{blue}{1} \]

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

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

      4. metadata-eval N/A

         \[\leadsto x - -1 \cdot 1 \]

      5. metadata-eval N/A

         \[\leadsto x - -1 \]

      6. lower--.f64 37.0

         \[\leadsto x - \color{blue}{-1} \]

   5. Applied rewrites 37.0%

      \[\leadsto \color{blue}{x - -1} \]

   if -5.4000000000000004 < y < 3200

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. +-commutative N/A

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

      15. metadata-eval N/A

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

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

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

      17. metadata-eval N/A

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

      18. metadata-eval N/A

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

   5. Applied rewrites 99.0%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \lor \neg \left(y \leq 3200\right):\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(0.16666666666666666 \cdot \left(z \cdot y\right) - 0.5\right) \cdot y - z, y, x - -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.4% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -16500 \lor \neg \left(y \leq 3 \cdot 10^{+71}\right):\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -16500.0) (not (<= y 3e+71))) (- x -1.0) (- x (fma z y -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -16500.0) || !(y <= 3e+71)) {
		tmp = x - -1.0;
	} else {
		tmp = x - fma(z, y, -1.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -16500.0) || !(y <= 3e+71))
		tmp = Float64(x - -1.0);
	else
		tmp = Float64(x - fma(z, y, -1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -16500.0], N[Not[LessEqual[y, 3e+71]], $MachinePrecision]], N[(x - -1.0), $MachinePrecision], N[(x - N[(z * y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -16500 or 3.00000000000000013e71 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto x + \color{blue}{1} \]

      2. metadata-eval N/A

         \[\leadsto x + 1 \cdot \color{blue}{1} \]

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

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

      4. metadata-eval N/A

         \[\leadsto x - -1 \cdot 1 \]

      5. metadata-eval N/A

         \[\leadsto x - -1 \]

      6. lower--.f64 36.6

         \[\leadsto x - \color{blue}{-1} \]

   5. Applied rewrites 36.6%

      \[\leadsto \color{blue}{x - -1} \]

   if -16500 < y < 3.00000000000000013e71

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. lower--.f64 N/A

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

      7. metadata-eval N/A

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

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

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

      9. *-lft-identity N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 93.4

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

   5. Applied rewrites 93.4%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 93.4

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

   7. Applied rewrites 93.4%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -16500 \lor \neg \left(y \leq 3 \cdot 10^{+71}\right):\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.6% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-8} \lor \neg \left(x \leq 8 \cdot 10^{-6}\right):\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.4e-8) (not (<= x 8e-6))) (- x -1.0) (- 1.0 (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4e-8) || !(x <= 8e-6)) {
		tmp = x - -1.0;
	} else {
		tmp = 1.0 - (z * y);
	}
	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 <= (-1.4d-8)) .or. (.not. (x <= 8d-6))) then
        tmp = x - (-1.0d0)
    else
        tmp = 1.0d0 - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4e-8) || !(x <= 8e-6)) {
		tmp = x - -1.0;
	} else {
		tmp = 1.0 - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.4e-8) or not (x <= 8e-6):
		tmp = x - -1.0
	else:
		tmp = 1.0 - (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.4e-8) || !(x <= 8e-6))
		tmp = Float64(x - -1.0);
	else
		tmp = Float64(1.0 - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.4e-8) || ~((x <= 8e-6)))
		tmp = x - -1.0;
	else
		tmp = 1.0 - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.4e-8], N[Not[LessEqual[x, 8e-6]], $MachinePrecision]], N[(x - -1.0), $MachinePrecision], N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4e-8 or 7.99999999999999964e-6 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto x + \color{blue}{1} \]

      2. metadata-eval N/A

         \[\leadsto x + 1 \cdot \color{blue}{1} \]

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

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

      4. metadata-eval N/A

         \[\leadsto x - -1 \cdot 1 \]

      5. metadata-eval N/A

         \[\leadsto x - -1 \]

      6. lower--.f64 85.9

         \[\leadsto x - \color{blue}{-1} \]

   5. Applied rewrites 85.9%

      \[\leadsto \color{blue}{x - -1} \]

   if -1.4e-8 < x < 7.99999999999999964e-6

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. lower--.f64 N/A

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

      7. metadata-eval N/A

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

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

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

      9. *-lft-identity N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 48.1

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

   5. Applied rewrites 48.1%

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

   6. Taylor expanded in x around 0

      \[\leadsto 1 - \color{blue}{y \cdot z} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto 1 - y \cdot \color{blue}{z} \]

      2. *-commutative N/A

         \[\leadsto 1 - z \cdot y \]

      3. lift-*.f64 48.1

         \[\leadsto 1 - z \cdot y \]

   8. Applied rewrites 48.1%

      \[\leadsto 1 - \color{blue}{z \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-8} \lor \neg \left(x \leq 8 \cdot 10^{-6}\right):\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.9% accurate, 15.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.7 \cdot 10^{+244}:\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 3.7e+244) (- x -1.0) (* (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 3.7e+244) {
		tmp = x - -1.0;
	} else {
		tmp = -z * y;
	}
	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 <= 3.7d+244) then
        tmp = x - (-1.0d0)
    else
        tmp = -z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 3.7e+244) {
		tmp = x - -1.0;
	} else {
		tmp = -z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 3.7e+244:
		tmp = x - -1.0
	else:
		tmp = -z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 3.7e+244)
		tmp = Float64(x - -1.0);
	else
		tmp = Float64(Float64(-z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 3.7e+244)
		tmp = x - -1.0;
	else
		tmp = -z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 3.7e+244], N[(x - -1.0), $MachinePrecision], N[((-z) * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.7000000000000002e244

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto x + \color{blue}{1} \]

      2. metadata-eval N/A

         \[\leadsto x + 1 \cdot \color{blue}{1} \]

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

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

      4. metadata-eval N/A

         \[\leadsto x - -1 \cdot 1 \]

      5. metadata-eval N/A

         \[\leadsto x - -1 \]

      6. lower--.f64 61.4

         \[\leadsto x - \color{blue}{-1} \]

   5. Applied rewrites 61.4%

      \[\leadsto \color{blue}{x - -1} \]

   if 3.7000000000000002e244 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-neg-in N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lift-sin.f64 93.7

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

   5. Applied rewrites 93.7%

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

   6. Taylor expanded in y around 0

      \[\leadsto \left(-z\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 49.0%

      \[\leadsto \left(-z\right) \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 62.5% accurate, 53.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

      \[\leadsto x + \color{blue}{1} \]

   2. metadata-eval N/A

      \[\leadsto x + 1 \cdot \color{blue}{1} \]

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

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

   4. metadata-eval N/A

      \[\leadsto x - -1 \cdot 1 \]

   5. metadata-eval N/A

      \[\leadsto x - -1 \]

   6. lower--.f64 58.3

      \[\leadsto x - \color{blue}{-1} \]

5. Applied rewrites 58.3%

   \[\leadsto \color{blue}{x - -1} \]
6. Add Preprocessing

Alternative 12: 43.4% 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%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 39.8%

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

Reproduce

herbie shell --seed 2025052 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))