Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B

Percentage Accurate: 99.8% → 99.8%

Time: 8.8s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

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

real(8) function code(x, y, z)
    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: 99.8% accurate, 1.0× speedup

Math

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

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

real(8) function code(x, y, z)
    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: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. lower-fma.f64 99.8

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 99.8

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

4. Applied rewrites 99.8%

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

5. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(\sin y, x, z \cdot \cos y\right) \]
6. Add Preprocessing

Alternative 2: 86.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+49}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(\sin y, x, 1 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -8.8e+49) t_0 (if (<= z 1.4e+51) (fma (sin y) x (* 1.0 z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -8.8e+49) {
		tmp = t_0;
	} else if (z <= 1.4e+51) {
		tmp = fma(sin(y), x, (1.0 * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -8.8e+49)
		tmp = t_0;
	elseif (z <= 1.4e+51)
		tmp = fma(sin(y), x, Float64(1.0 * z));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.8e+49], t$95$0, If[LessEqual[z, 1.4e+51], N[(N[Sin[y], $MachinePrecision] * x + N[(1.0 * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8000000000000003e49 or 1.40000000000000002e51 < z

   1. Initial program 99.8%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 88.1

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

   5. Applied rewrites 88.1%

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

   if -8.8000000000000003e49 < z < 1.40000000000000002e51

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 99.8

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 86.0%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(\sin y, x, 1 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \sin y\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+71}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 35000:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (sin y))))
   (if (<= x -3.9e+71) t_0 (if (<= x 35000.0) (* z (cos y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * sin(y);
	double tmp;
	if (x <= -3.9e+71) {
		tmp = t_0;
	} else if (x <= 35000.0) {
		tmp = z * cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * sin(y)
    if (x <= (-3.9d+71)) then
        tmp = t_0
    else if (x <= 35000.0d0) then
        tmp = z * cos(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.sin(y);
	double tmp;
	if (x <= -3.9e+71) {
		tmp = t_0;
	} else if (x <= 35000.0) {
		tmp = z * Math.cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.sin(y)
	tmp = 0
	if x <= -3.9e+71:
		tmp = t_0
	elif x <= 35000.0:
		tmp = z * math.cos(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * sin(y))
	tmp = 0.0
	if (x <= -3.9e+71)
		tmp = t_0;
	elseif (x <= 35000.0)
		tmp = Float64(z * cos(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * sin(y);
	tmp = 0.0;
	if (x <= -3.9e+71)
		tmp = t_0;
	elseif (x <= 35000.0)
		tmp = z * cos(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.9e+71], t$95$0, If[LessEqual[x, 35000.0], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.9000000000000001e71 or 35000 < x

   1. Initial program 99.8%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-sin.f64 71.3

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

   5. Applied rewrites 71.3%

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

   if -3.9000000000000001e71 < x < 35000

   1. Initial program 99.8%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 83.7

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

   5. Applied rewrites 83.7%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;x \leq 35000:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{-6}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 36000000:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(x \cdot y\right) \cdot -0.16666666666666666, y, x\right), y, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= y -1.15e-6)
     t_0
     (if (<= y 36000000.0)
       (fma (fma (* (* x y) -0.16666666666666666) y x) y z)
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (y <= -1.15e-6) {
		tmp = t_0;
	} else if (y <= 36000000.0) {
		tmp = fma(fma(((x * y) * -0.16666666666666666), y, x), y, z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (y <= -1.15e-6)
		tmp = t_0;
	elseif (y <= 36000000.0)
		tmp = fma(fma(Float64(Float64(x * y) * -0.16666666666666666), y, x), y, z);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e-6], t$95$0, If[LessEqual[y, 36000000.0], N[(N[(N[(N[(x * y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision] * y + x), $MachinePrecision] * y + z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e-6 or 3.6e7 < y

   1. Initial program 99.6%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 52.2

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

   5. Applied rewrites 52.2%

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

   if -1.15e-6 < y < 3.6e7

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-+ N/A

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

      7. lift-+.f64 N/A

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

      8. inv-pow N/A

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

      9. lower-pow.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 98.6

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

   7. Applied rewrites 98.6%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{6} \cdot \left(x \cdot y\right), y, x\right), y, z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 98.6%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-6}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq 36000000:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(x \cdot y\right) \cdot -0.16666666666666666, y, x\right), y, z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.4% accurate, 30.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \sin y + z \cdot \cos y \]
2. Add Preprocessing

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 44.8

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

5. Applied rewrites 44.8%

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

Alternative 6: 16.9% accurate, 35.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \sin y + z \cdot \cos y \]
2. Add Preprocessing

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 44.8

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

5. Applied rewrites 44.8%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 13.2%

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

9. Final simplification 13.2%

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

Reproduce

herbie shell --seed 2024248 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))