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

Percentage Accurate: 99.9% → 99.9%

Time: 4.5s

Alternatives: 18

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. lift-+.f64 N/A

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

   2. 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

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

3. Applied rewrites 99.9%

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

Alternative 2: 95.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(x, \frac{z \cdot \cos y}{x}, x\right)\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{-14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-20}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma x (/ (* z (cos y)) x) x)))
   (if (<= x -9.6e-14) t_0 (if (<= x 8.2e-20) (fma (cos y) z (sin y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(x, ((z * cos(y)) / x), x);
	double tmp;
	if (x <= -9.6e-14) {
		tmp = t_0;
	} else if (x <= 8.2e-20) {
		tmp = fma(cos(y), z, sin(y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(x, Float64(Float64(z * cos(y)) / x), x)
	tmp = 0.0
	if (x <= -9.6e-14)
		tmp = t_0;
	elseif (x <= 8.2e-20)
		tmp = fma(cos(y), z, sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[x, -9.6e-14], t$95$0, If[LessEqual[x, 8.2e-20], N[(N[Cos[y], $MachinePrecision] * z + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.599999999999999e-14 or 8.2000000000000002e-20 < x

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. 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

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around inf

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

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lift-sin.f64 N/A

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

      10. lift-fma.f64 N/A

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

      11. lift-cos.f64 88.1

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

   6. Applied rewrites 88.1%

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

   7. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift-cos.f64 71.5

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

   9. Applied rewrites 71.5%

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

   if -9.599999999999999e-14 < x < 8.2000000000000002e-20

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\sin y + z \cdot \cos y} \]
   3. 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 58.7

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

   4. Applied rewrites 58.7%

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

Alternative 3: 90.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(x, \frac{z \cdot \cos y}{x}, x\right)\\ \mathbf{if}\;z \leq -460000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-5}:\\ \;\;\;\;\left(\sin y + z\right) + x\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+189}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma x (/ (* z (cos y)) x) x)))
   (if (<= z -460000000.0)
     t_0
     (if (<= z 7e-5)
       (+ (+ (sin y) z) x)
       (if (<= z 8.6e+189) t_0 (fma (cos y) z (+ x y)))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(x, ((z * cos(y)) / x), x);
	double tmp;
	if (z <= -460000000.0) {
		tmp = t_0;
	} else if (z <= 7e-5) {
		tmp = (sin(y) + z) + x;
	} else if (z <= 8.6e+189) {
		tmp = t_0;
	} else {
		tmp = fma(cos(y), z, (x + y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(x, Float64(Float64(z * cos(y)) / x), x)
	tmp = 0.0
	if (z <= -460000000.0)
		tmp = t_0;
	elseif (z <= 7e-5)
		tmp = Float64(Float64(sin(y) + z) + x);
	elseif (z <= 8.6e+189)
		tmp = t_0;
	else
		tmp = fma(cos(y), z, Float64(x + y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -460000000.0], t$95$0, If[LessEqual[z, 7e-5], N[(N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 8.6e+189], t$95$0, N[(N[Cos[y], $MachinePrecision] * z + N[(x + y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6e8 or 6.9999999999999994e-5 < z < 8.59999999999999995e189

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. 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

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around inf

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

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lift-sin.f64 N/A

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

      10. lift-fma.f64 N/A

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

      11. lift-cos.f64 88.1

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

   6. Applied rewrites 88.1%

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

   7. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift-cos.f64 71.5

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

   9. Applied rewrites 71.5%

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

   if -4.6e8 < z < 6.9999999999999994e-5

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 82.2%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-sin.f64 N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lift-sin.f64 82.2

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

   6. Applied rewrites 82.2%

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

   if 8.59999999999999995e189 < z

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. 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

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in y around 0

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

      1. lower-+.f64 70.8

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

   6. Applied rewrites 70.8%

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

Alternative 4: 89.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+144}:\\ \;\;\;\;\left(x + y\right) + t\_0\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+134}:\\ \;\;\;\;\left(\sin y + z\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -4.9e+144)
     (+ (+ x y) t_0)
     (if (<= z 1.7e+134) (+ (+ (sin y) z) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -4.9e+144) {
		tmp = (x + y) + t_0;
	} else if (z <= 1.7e+134) {
		tmp = (sin(y) + 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 = z * cos(y)
    if (z <= (-4.9d+144)) then
        tmp = (x + y) + t_0
    else if (z <= 1.7d+134) then
        tmp = (sin(y) + 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 = z * Math.cos(y);
	double tmp;
	if (z <= -4.9e+144) {
		tmp = (x + y) + t_0;
	} else if (z <= 1.7e+134) {
		tmp = (Math.sin(y) + z) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -4.9e+144:
		tmp = (x + y) + t_0
	elif z <= 1.7e+134:
		tmp = (math.sin(y) + z) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -4.9e+144)
		tmp = Float64(Float64(x + y) + t_0);
	elseif (z <= 1.7e+134)
		tmp = Float64(Float64(sin(y) + z) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -4.9e+144)
		tmp = (x + y) + t_0;
	elseif (z <= 1.7e+134)
		tmp = (sin(y) + z) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.9e+144], N[(N[(x + y), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[z, 1.7e+134], N[(N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.9e144

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 70.8%

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

   if -4.9e144 < z < 1.70000000000000009e134

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 82.2%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-sin.f64 N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lift-sin.f64 82.2

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

   6. Applied rewrites 82.2%

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

   if 1.70000000000000009e134 < z

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. 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

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around inf

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

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lift-sin.f64 N/A

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

      10. lift-fma.f64 N/A

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

      11. lift-cos.f64 88.1

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

   6. Applied rewrites 88.1%

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

   7. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift-sin.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-cos.f64 76.2

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

   9. Applied rewrites 76.2%

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

   10. Taylor expanded in z around inf

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

       1. *-commutative N/A

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

       2. +-commutative N/A

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

       3. +-commutative N/A

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

       4. lower-*.f64 N/A

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

       5. lift-cos.f64 42.8

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

   12. Applied rewrites 42.8%

       \[\leadsto \color{blue}{z \cdot \cos y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 89.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+144}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, x + y\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+134}:\\ \;\;\;\;\left(\sin y + z\right) + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.9e+144)
   (fma (cos y) z (+ x y))
   (if (<= z 1.7e+134) (+ (+ (sin y) z) x) (* z (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.9e+144) {
		tmp = fma(cos(y), z, (x + y));
	} else if (z <= 1.7e+134) {
		tmp = (sin(y) + z) + x;
	} else {
		tmp = z * cos(y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.9e+144)
		tmp = fma(cos(y), z, Float64(x + y));
	elseif (z <= 1.7e+134)
		tmp = Float64(Float64(sin(y) + z) + x);
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.9e+144], N[(N[Cos[y], $MachinePrecision] * z + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+134], N[(N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision] + x), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.9e144

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. 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

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in y around 0

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

      1. lower-+.f64 70.8

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

   6. Applied rewrites 70.8%

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

   if -4.9e144 < z < 1.70000000000000009e134

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 82.2%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-sin.f64 N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lift-sin.f64 82.2

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

   6. Applied rewrites 82.2%

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

   if 1.70000000000000009e134 < z

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. 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

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around inf

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

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lift-sin.f64 N/A

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

      10. lift-fma.f64 N/A

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

      11. lift-cos.f64 88.1

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

   6. Applied rewrites 88.1%

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

   7. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift-sin.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-cos.f64 76.2

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

   9. Applied rewrites 76.2%

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

   10. Taylor expanded in z around inf

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

       1. *-commutative N/A

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

       2. +-commutative N/A

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

       3. +-commutative N/A

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

       4. lower-*.f64 N/A

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

       5. lift-cos.f64 42.8

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

   12. Applied rewrites 42.8%

       \[\leadsto \color{blue}{z \cdot \cos y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 89.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+151}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+134}:\\ \;\;\;\;\left(\sin y + z\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -7.5e+151) t_0 (if (<= z 1.7e+134) (+ (+ (sin y) z) x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -7.5e+151) {
		tmp = t_0;
	} else if (z <= 1.7e+134) {
		tmp = (sin(y) + 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 = z * cos(y)
    if (z <= (-7.5d+151)) then
        tmp = t_0
    else if (z <= 1.7d+134) then
        tmp = (sin(y) + 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 = z * Math.cos(y);
	double tmp;
	if (z <= -7.5e+151) {
		tmp = t_0;
	} else if (z <= 1.7e+134) {
		tmp = (Math.sin(y) + z) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -7.5e+151:
		tmp = t_0
	elif z <= 1.7e+134:
		tmp = (math.sin(y) + z) + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -7.5e+151)
		tmp = t_0;
	elseif (z <= 1.7e+134)
		tmp = Float64(Float64(sin(y) + z) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -7.5e+151)
		tmp = t_0;
	elseif (z <= 1.7e+134)
		tmp = (sin(y) + z) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+151], t$95$0, If[LessEqual[z, 1.7e+134], N[(N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999977e151 or 1.70000000000000009e134 < z

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. 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

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around inf

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

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lift-sin.f64 N/A

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

      10. lift-fma.f64 N/A

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

      11. lift-cos.f64 88.1

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

   6. Applied rewrites 88.1%

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

   7. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift-sin.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-cos.f64 76.2

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

   9. Applied rewrites 76.2%

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

   10. Taylor expanded in z around inf

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

       1. *-commutative N/A

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

       2. +-commutative N/A

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

       3. +-commutative N/A

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

       4. lower-*.f64 N/A

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

       5. lift-cos.f64 42.8

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

   12. Applied rewrites 42.8%

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

   if -7.49999999999999977e151 < z < 1.70000000000000009e134

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 82.2%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-sin.f64 N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lift-sin.f64 82.2

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

   6. Applied rewrites 82.2%

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

Alternative 7: 84.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+151}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1150000000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-56}:\\ \;\;\;\;\sin y + x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+134}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -7.5e+151)
     t_0
     (if (<= z -1150000000.0)
       (+ z x)
       (if (<= z 1.85e-56) (+ (sin y) x) (if (<= z 1.7e+134) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -7.5e+151) {
		tmp = t_0;
	} else if (z <= -1150000000.0) {
		tmp = z + x;
	} else if (z <= 1.85e-56) {
		tmp = sin(y) + x;
	} else if (z <= 1.7e+134) {
		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 = z * cos(y)
    if (z <= (-7.5d+151)) then
        tmp = t_0
    else if (z <= (-1150000000.0d0)) then
        tmp = z + x
    else if (z <= 1.85d-56) then
        tmp = sin(y) + x
    else if (z <= 1.7d+134) 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 = z * Math.cos(y);
	double tmp;
	if (z <= -7.5e+151) {
		tmp = t_0;
	} else if (z <= -1150000000.0) {
		tmp = z + x;
	} else if (z <= 1.85e-56) {
		tmp = Math.sin(y) + x;
	} else if (z <= 1.7e+134) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -7.5e+151:
		tmp = t_0
	elif z <= -1150000000.0:
		tmp = z + x
	elif z <= 1.85e-56:
		tmp = math.sin(y) + x
	elif z <= 1.7e+134:
		tmp = z + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -7.5e+151)
		tmp = t_0;
	elseif (z <= -1150000000.0)
		tmp = Float64(z + x);
	elseif (z <= 1.85e-56)
		tmp = Float64(sin(y) + x);
	elseif (z <= 1.7e+134)
		tmp = Float64(z + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -7.5e+151)
		tmp = t_0;
	elseif (z <= -1150000000.0)
		tmp = z + x;
	elseif (z <= 1.85e-56)
		tmp = sin(y) + x;
	elseif (z <= 1.7e+134)
		tmp = z + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+151], t$95$0, If[LessEqual[z, -1150000000.0], N[(z + x), $MachinePrecision], If[LessEqual[z, 1.85e-56], N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.7e+134], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.49999999999999977e151 or 1.70000000000000009e134 < z

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. 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

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around inf

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

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lift-sin.f64 N/A

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

      10. lift-fma.f64 N/A

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

      11. lift-cos.f64 88.1

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

   6. Applied rewrites 88.1%

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

   7. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift-sin.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-cos.f64 76.2

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

   9. Applied rewrites 76.2%

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

   10. Taylor expanded in z around inf

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

       1. *-commutative N/A

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

       2. +-commutative N/A

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

       3. +-commutative N/A

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

       4. lower-*.f64 N/A

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

       5. lift-cos.f64 42.8

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

   12. Applied rewrites 42.8%

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

   if -7.49999999999999977e151 < z < -1.15e9 or 1.8500000000000001e-56 < z < 1.70000000000000009e134

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 66.2

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

   4. Applied rewrites 66.2%

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

   if -1.15e9 < z < 1.8500000000000001e-56

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. 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

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around inf

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

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lift-sin.f64 N/A

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

      10. lift-fma.f64 N/A

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

      11. lift-cos.f64 88.1

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

   6. Applied rewrites 88.1%

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

   7. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \sin y} \]
   8. 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 58.5

         \[\leadsto \sin y + x \]

   9. Applied rewrites 58.5%

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

Alternative 8: 80.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + \sin y\right) + z \cdot \cos y\\ \mathbf{if}\;t\_0 \leq -1000000000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t\_0 \leq -0.2:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;t\_0 \leq 10^{-12}:\\ \;\;\;\;\left(x + \mathsf{fma}\left(y \cdot y, -0.16666666666666666, 1\right) \cdot y\right) + z\\ \mathbf{elif}\;t\_0 \leq 1:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (+ x (sin y)) (* z (cos y)))))
   (if (<= t_0 -1000000000.0)
     (+ z x)
     (if (<= t_0 -0.2)
       (sin y)
       (if (<= t_0 1e-12)
         (+ (+ x (* (fma (* y y) -0.16666666666666666 1.0) y)) z)
         (if (<= t_0 1.0) (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 <= -1000000000.0) {
		tmp = z + x;
	} else if (t_0 <= -0.2) {
		tmp = sin(y);
	} else if (t_0 <= 1e-12) {
		tmp = (x + (fma((y * y), -0.16666666666666666, 1.0) * y)) + z;
	} else if (t_0 <= 1.0) {
		tmp = 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 <= -1000000000.0)
		tmp = Float64(z + x);
	elseif (t_0 <= -0.2)
		tmp = sin(y);
	elseif (t_0 <= 1e-12)
		tmp = Float64(Float64(x + Float64(fma(Float64(y * y), -0.16666666666666666, 1.0) * y)) + z);
	elseif (t_0 <= 1.0)
		tmp = sin(y);
	else
		tmp = Float64(z + x);
	end
	return 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, -1000000000.0], N[(z + x), $MachinePrecision], If[LessEqual[t$95$0, -0.2], N[Sin[y], $MachinePrecision], If[LessEqual[t$95$0, 1e-12], N[(N[(x + N[(N[(N[(y * y), $MachinePrecision] * -0.16666666666666666 + 1.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[t$95$0, 1.0], 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))) < -1e9 or 1 < (+.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. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 66.2

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

   4. Applied rewrites 66.2%

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

   if -1e9 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -0.20000000000000001 or 9.9999999999999998e-13 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 1

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. 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

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around inf

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

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lift-sin.f64 N/A

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

      10. lift-fma.f64 N/A

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

      11. lift-cos.f64 88.1

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

   6. Applied rewrites 88.1%

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

   7. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \sin y} \]
   8. 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 58.5

         \[\leadsto \sin y + x \]

   9. Applied rewrites 58.5%

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

   10. Taylor expanded in x around 0

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

       1. lift-sin.f64 18.2

          \[\leadsto \sin y \]

   12. Applied rewrites 18.2%

       \[\leadsto \sin y \]

   if -0.20000000000000001 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 9.9999999999999998e-13

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 82.2%

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

   5. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 54.7

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

   7. Applied rewrites 54.7%

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

Alternative 9: 79.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y + x\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-5}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z \cdot y, -0.5, 1\right), y, z + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (sin y) x)))
   (if (<= y -4.8e-5)
     t_0
     (if (<= y 3.7e-38) (fma (fma (* z y) -0.5 1.0) y (+ z x)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) + x;
	double tmp;
	if (y <= -4.8e-5) {
		tmp = t_0;
	} else if (y <= 3.7e-38) {
		tmp = fma(fma((z * y), -0.5, 1.0), y, (z + x));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) + x)
	tmp = 0.0
	if (y <= -4.8e-5)
		tmp = t_0;
	elseif (y <= 3.7e-38)
		tmp = fma(fma(Float64(z * y), -0.5, 1.0), y, Float64(z + x));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -4.8e-5], t$95$0, If[LessEqual[y, 3.7e-38], N[(N[(N[(z * y), $MachinePrecision] * -0.5 + 1.0), $MachinePrecision] * y + N[(z + x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8000000000000001e-5 or 3.7e-38 < y

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. 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

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around inf

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

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lift-sin.f64 N/A

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

      10. lift-fma.f64 N/A

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

      11. lift-cos.f64 88.1

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

   6. Applied rewrites 88.1%

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

   7. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \sin y} \]
   8. 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 58.5

         \[\leadsto \sin y + x \]

   9. Applied rewrites 58.5%

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

   if -4.8000000000000001e-5 < y < 3.7e-38

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 57.0

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

   4. Applied rewrites 57.0%

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

Alternative 10: 70.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6400:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 23000:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.16666666666666666, y, -0.5 \cdot z\right), y, 1\right), y, z\right) + x\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6400.0)
   (+ z x)
   (if (<= y 23000.0)
     (+ (fma (fma (fma -0.16666666666666666 y (* -0.5 z)) y 1.0) y z) x)
     (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6400.0) {
		tmp = z + x;
	} else if (y <= 23000.0) {
		tmp = fma(fma(fma(-0.16666666666666666, y, (-0.5 * z)), y, 1.0), y, z) + x;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6400.0)
		tmp = Float64(z + x);
	elseif (y <= 23000.0)
		tmp = Float64(fma(fma(fma(-0.16666666666666666, y, Float64(-0.5 * z)), y, 1.0), y, z) + x);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6400.0], N[(z + x), $MachinePrecision], If[LessEqual[y, 23000.0], N[(N[(N[(N[(-0.16666666666666666 * y + N[(-0.5 * z), $MachinePrecision]), $MachinePrecision] * y + 1.0), $MachinePrecision] * y + z), $MachinePrecision] + x), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6400 or 23000 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 66.2

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

   4. Applied rewrites 66.2%

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

   if -6400 < y < 23000

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. +-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. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 54.1

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

   4. Applied rewrites 54.1%

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

Alternative 11: 70.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5500:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 10600:\\ \;\;\;\;\left(x + \mathsf{fma}\left(y \cdot y, -0.16666666666666666, 1\right) \cdot y\right) + z\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5500.0)
   (+ z x)
   (if (<= y 10600.0)
     (+ (+ x (* (fma (* y y) -0.16666666666666666 1.0) y)) z)
     (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5500.0) {
		tmp = z + x;
	} else if (y <= 10600.0) {
		tmp = (x + (fma((y * y), -0.16666666666666666, 1.0) * y)) + z;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5500.0)
		tmp = Float64(z + x);
	elseif (y <= 10600.0)
		tmp = Float64(Float64(x + Float64(fma(Float64(y * y), -0.16666666666666666, 1.0) * y)) + z);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5500.0], N[(z + x), $MachinePrecision], If[LessEqual[y, 10600.0], N[(N[(x + N[(N[(N[(y * y), $MachinePrecision] * -0.16666666666666666 + 1.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5500 or 10600 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 66.2

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

   4. Applied rewrites 66.2%

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

   if -5500 < y < 10600

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 82.2%

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

   5. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 54.7

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

   7. Applied rewrites 54.7%

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

Alternative 12: 70.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3600000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 4.6:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z \cdot y, -0.5, 1\right), y, z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3600000.0)
   (+ z x)
   (if (<= y 4.6) (fma (fma (* z y) -0.5 1.0) y (+ z x)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3600000.0) {
		tmp = z + x;
	} else if (y <= 4.6) {
		tmp = fma(fma((z * y), -0.5, 1.0), y, (z + x));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3600000.0)
		tmp = Float64(z + x);
	elseif (y <= 4.6)
		tmp = fma(fma(Float64(z * y), -0.5, 1.0), y, Float64(z + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3600000.0], N[(z + x), $MachinePrecision], If[LessEqual[y, 4.6], N[(N[(N[(z * y), $MachinePrecision] * -0.5 + 1.0), $MachinePrecision] * y + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6e6 or 4.5999999999999996 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 66.2

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

   4. Applied rewrites 66.2%

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

   if -3.6e6 < y < 4.5999999999999996

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 57.0

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

   4. Applied rewrites 57.0%

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

Alternative 13: 70.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3600000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 4.6:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(y \cdot y, -0.5, 1\right), z, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3600000.0)
   (+ z x)
   (if (<= y 4.6) (fma (fma (* y y) -0.5 1.0) z (+ x y)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3600000.0) {
		tmp = z + x;
	} else if (y <= 4.6) {
		tmp = fma(fma((y * y), -0.5, 1.0), z, (x + y));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3600000.0)
		tmp = Float64(z + x);
	elseif (y <= 4.6)
		tmp = fma(fma(Float64(y * y), -0.5, 1.0), z, Float64(x + y));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3600000.0], N[(z + x), $MachinePrecision], If[LessEqual[y, 4.6], N[(N[(N[(y * y), $MachinePrecision] * -0.5 + 1.0), $MachinePrecision] * z + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6e6 or 4.5999999999999996 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 66.2

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

   4. Applied rewrites 66.2%

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

   if -3.6e6 < y < 4.5999999999999996

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 57.0

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

   4. Applied rewrites 57.0%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. +-commutative N/A

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

      10. distribute-lft-in N/A

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

      11. *-rgt-identity N/A

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

      12. *-commutative N/A

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

      15. associate-*r* N/A

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

      16. unpow2 N/A

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

      17. associate-*l* N/A

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

      18. associate-+r+ N/A

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

   6. Applied rewrites 56.3%

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

Alternative 14: 70.3% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+41}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 9.5:\\ \;\;\;\;\left(z + y\right) + x\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e+41) (+ z x) (if (<= y 9.5) (+ (+ z y) x) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+41) {
		tmp = z + x;
	} else if (y <= 9.5) {
		tmp = (z + y) + x;
	} 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) :: tmp
    if (y <= (-3.8d+41)) then
        tmp = z + x
    else if (y <= 9.5d0) then
        tmp = (z + y) + x
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+41) {
		tmp = z + x;
	} else if (y <= 9.5) {
		tmp = (z + y) + x;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e+41:
		tmp = z + x
	elif y <= 9.5:
		tmp = (z + y) + x
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e+41)
		tmp = Float64(z + x);
	elseif (y <= 9.5)
		tmp = Float64(Float64(z + y) + x);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.8e+41)
		tmp = z + x;
	elseif (y <= 9.5)
		tmp = (z + y) + x;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e+41], N[(z + x), $MachinePrecision], If[LessEqual[y, 9.5], N[(N[(z + y), $MachinePrecision] + x), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8000000000000001e41 or 9.5 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 66.2

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

   4. Applied rewrites 66.2%

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

   if -3.8000000000000001e41 < y < 9.5

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. +-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 61.6

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

   4. Applied rewrites 61.6%

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

Alternative 15: 68.1% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-150}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-154}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.9e-150) (+ z x) (if (<= x 1.22e-154) (+ z y) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.9e-150) {
		tmp = z + x;
	} else if (x <= 1.22e-154) {
		tmp = z + 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) :: tmp
    if (x <= (-4.9d-150)) then
        tmp = z + x
    else if (x <= 1.22d-154) then
        tmp = z + y
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.9e-150) {
		tmp = z + x;
	} else if (x <= 1.22e-154) {
		tmp = z + y;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.9e-150:
		tmp = z + x
	elif x <= 1.22e-154:
		tmp = z + y
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.9e-150)
		tmp = Float64(z + x);
	elseif (x <= 1.22e-154)
		tmp = Float64(z + y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.9e-150)
		tmp = z + x;
	elseif (x <= 1.22e-154)
		tmp = z + y;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.9e-150], N[(z + x), $MachinePrecision], If[LessEqual[x, 1.22e-154], N[(z + y), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8999999999999995e-150 or 1.22000000000000005e-154 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 66.2

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

   4. Applied rewrites 66.2%

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

   if -4.8999999999999995e-150 < x < 1.22000000000000005e-154

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\sin y + z \cdot \cos y} \]
   3. 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 58.7

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

   4. Applied rewrites 58.7%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto z + y \]

      2. lower-+.f64 29.5

         \[\leadsto z + y \]

   7. Applied rewrites 29.5%

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

Alternative 16: 50.7% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+50}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+50}:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.75e+50) (+ y x) (if (<= x 1.45e+50) (+ z y) (+ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.75e+50) {
		tmp = y + x;
	} else if (x <= 1.45e+50) {
		tmp = z + y;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.75d+50)) then
        tmp = y + x
    else if (x <= 1.45d+50) then
        tmp = z + y
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.75e+50) {
		tmp = y + x;
	} else if (x <= 1.45e+50) {
		tmp = z + y;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.75e+50:
		tmp = y + x
	elif x <= 1.45e+50:
		tmp = z + y
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.75e+50)
		tmp = Float64(y + x);
	elseif (x <= 1.45e+50)
		tmp = Float64(z + y);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.75e+50)
		tmp = y + x;
	elseif (x <= 1.45e+50)
		tmp = z + y;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.75e+50], N[(y + x), $MachinePrecision], If[LessEqual[x, 1.45e+50], N[(z + y), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75000000000000003e50 or 1.45e50 < x

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. 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

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around inf

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

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lift-sin.f64 N/A

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

      10. lift-fma.f64 N/A

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

      11. lift-cos.f64 88.1

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

   6. Applied rewrites 88.1%

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

   7. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \sin y} \]
   8. 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 58.5

         \[\leadsto \sin y + x \]

   9. Applied rewrites 58.5%

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

   10. Taylor expanded in y around 0

       \[\leadsto y + x \]
   11. Step-by-step derivation

   12. Applied rewrites 38.6%

       \[\leadsto y + x \]

   if -1.75000000000000003e50 < x < 1.45e50

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\sin y + z \cdot \cos y} \]
   3. 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 58.7

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

   4. Applied rewrites 58.7%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto z + y \]

      2. lower-+.f64 29.5

         \[\leadsto z + y \]

   7. Applied rewrites 29.5%

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

Alternative 17: 46.9% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+163}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+137}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.2e+163) z (if (<= z 3.8e+137) (+ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.2e+163) {
		tmp = z;
	} else if (z <= 3.8e+137) {
		tmp = y + 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 <= (-3.2d+163)) then
        tmp = z
    else if (z <= 3.8d+137) then
        tmp = y + 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 <= -3.2e+163) {
		tmp = z;
	} else if (z <= 3.8e+137) {
		tmp = y + x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.2e+163:
		tmp = z
	elif z <= 3.8e+137:
		tmp = y + x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.2e+163)
		tmp = z;
	elseif (z <= 3.8e+137)
		tmp = Float64(y + x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.2e+163)
		tmp = z;
	elseif (z <= 3.8e+137)
		tmp = y + x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.2e+163], z, If[LessEqual[z, 3.8e+137], N[(y + x), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1999999999999998e163 or 3.79999999999999963e137 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 66.2

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

   4. Applied rewrites 66.2%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 26.1%

      \[\leadsto z \]

   if -3.1999999999999998e163 < z < 3.79999999999999963e137

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. 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

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around inf

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

      1. distribute-lft-in N/A

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

      2. *-rgt-identity N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lift-sin.f64 N/A

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

      10. lift-fma.f64 N/A

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

      11. lift-cos.f64 88.1

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

   6. Applied rewrites 88.1%

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

   7. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \sin y} \]
   8. 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 58.5

         \[\leadsto \sin y + x \]

   9. Applied rewrites 58.5%

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

   10. Taylor expanded in y around 0

       \[\leadsto y + x \]
   11. Step-by-step derivation

   12. Applied rewrites 38.6%

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

Alternative 18: 26.1% accurate, 73.1× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 66.2

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

4. Applied rewrites 66.2%

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

5. Taylor expanded in x around 0

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

7. Applied rewrites 26.1%

   \[\leadsto z \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025136 
(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))))