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

Percentage Accurate: 99.8% → 99.8%

Time: 6.4s

Alternatives: 7

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. fma-def 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 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]

Derivation

1. Initial program 99.8%

   \[x \cdot \sin y + z \cdot \cos y \]

2. Final simplification 99.8%

   \[\leadsto x \cdot \sin y + z \cdot \cos y \]

Alternative 3: 85.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-110} \lor \neg \left(x \leq 1.6 \cdot 10^{-92}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.2e-110) (not (<= x 1.6e-92)))
   (+ z (* x (sin y)))
   (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.2e-110) || !(x <= 1.6e-92)) {
		tmp = z + (x * sin(y));
	} else {
		tmp = z * cos(y);
	}
	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) :: tmp
    if ((x <= (-5.2d-110)) .or. (.not. (x <= 1.6d-92))) then
        tmp = z + (x * sin(y))
    else
        tmp = z * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.2e-110) || !(x <= 1.6e-92)) {
		tmp = z + (x * Math.sin(y));
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.2e-110) or not (x <= 1.6e-92):
		tmp = z + (x * math.sin(y))
	else:
		tmp = z * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.2e-110) || !(x <= 1.6e-92))
		tmp = Float64(z + Float64(x * sin(y)));
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.2e-110) || ~((x <= 1.6e-92)))
		tmp = z + (x * sin(y));
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.2e-110], N[Not[LessEqual[x, 1.6e-92]], $MachinePrecision]], N[(z + N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.19999999999999979e-110 or 1.5999999999999998e-92 < x

   1. Initial program 99.8%

      \[x \cdot \sin y + z \cdot \cos y \]

   2. Taylor expanded in y around 0 83.5%

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

   if -5.19999999999999979e-110 < x < 1.5999999999999998e-92

   1. Initial program 99.8%

      \[x \cdot \sin y + z \cdot \cos y \]

   2. Taylor expanded in x around 0 99.8%

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

      1. fma-def 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around inf 91.9%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-110} \lor \neg \left(x \leq 1.6 \cdot 10^{-92}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 4: 74.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0065 \lor \neg \left(y \leq 0.011\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right) + \left(z + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0065) (not (<= y 0.011)))
   (* z (cos y))
   (+ (* -0.5 (* z (* y y))) (+ z (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0065) || !(y <= 0.011)) {
		tmp = z * cos(y);
	} else {
		tmp = (-0.5 * (z * (y * y))) + (z + (x * y));
	}
	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) :: tmp
    if ((y <= (-0.0065d0)) .or. (.not. (y <= 0.011d0))) then
        tmp = z * cos(y)
    else
        tmp = ((-0.5d0) * (z * (y * y))) + (z + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0065) || !(y <= 0.011)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = (-0.5 * (z * (y * y))) + (z + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0065) or not (y <= 0.011):
		tmp = z * math.cos(y)
	else:
		tmp = (-0.5 * (z * (y * y))) + (z + (x * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0065) || !(y <= 0.011))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(Float64(-0.5 * Float64(z * Float64(y * y))) + Float64(z + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0065) || ~((y <= 0.011)))
		tmp = z * cos(y);
	else
		tmp = (-0.5 * (z * (y * y))) + (z + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0065], N[Not[LessEqual[y, 0.011]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[(-0.5 * N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0064999999999999997 or 0.010999999999999999 < y

   1. Initial program 99.6%

      \[x \cdot \sin y + z \cdot \cos y \]

   2. Taylor expanded in x around 0 99.6%

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

      1. fma-def 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around inf 54.4%

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

   if -0.0064999999999999997 < y < 0.010999999999999999

   1. Initial program 100.0%

      \[x \cdot \sin y + z \cdot \cos y \]

   2. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{-0.5 \cdot \left({y}^{2} \cdot z\right) + \left(y \cdot x + z\right)} \]
   3. Step-by-step derivation

      1. expm1-log1p-u 89.3%

         \[\leadsto -0.5 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({y}^{2} \cdot z\right)\right)} + \left(y \cdot x + z\right) \]

      2. expm1-udef 89.3%

         \[\leadsto -0.5 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left({y}^{2} \cdot z\right)} - 1\right)} + \left(y \cdot x + z\right) \]

      3. unpow2 89.3%

         \[\leadsto -0.5 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(y \cdot y\right)} \cdot z\right)} - 1\right) + \left(y \cdot x + z\right) \]

      4. associate-*l* 89.3%

         \[\leadsto -0.5 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{y \cdot \left(y \cdot z\right)}\right)} - 1\right) + \left(y \cdot x + z\right) \]

   4. Applied egg-rr 89.3%

      \[\leadsto -0.5 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(y \cdot \left(y \cdot z\right)\right)} - 1\right)} + \left(y \cdot x + z\right) \]
   5. Step-by-step derivation

      1. expm1-def 89.3%

         \[\leadsto -0.5 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(y \cdot z\right)\right)\right)} + \left(y \cdot x + z\right) \]

      2. expm1-log1p 100.0%

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

      3. *-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-*r* 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0065 \lor \neg \left(y \leq 0.011\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right) + \left(z + x \cdot y\right)\\ \end{array} \]

Alternative 5: 73.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{+141} \lor \neg \left(x \leq 1.55 \cdot 10^{+122}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.9e+141) (not (<= x 1.55e+122))) (* x (sin y)) (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.9e+141) || !(x <= 1.55e+122)) {
		tmp = x * sin(y);
	} else {
		tmp = z * cos(y);
	}
	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) :: tmp
    if ((x <= (-5.9d+141)) .or. (.not. (x <= 1.55d+122))) then
        tmp = x * sin(y)
    else
        tmp = z * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.9e+141) || !(x <= 1.55e+122)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.9e+141) or not (x <= 1.55e+122):
		tmp = x * math.sin(y)
	else:
		tmp = z * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.9e+141) || !(x <= 1.55e+122))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.9e+141) || ~((x <= 1.55e+122)))
		tmp = x * sin(y);
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.9e+141], N[Not[LessEqual[x, 1.55e+122]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.90000000000000029e141 or 1.54999999999999999e122 < x

   1. Initial program 99.8%

      \[x \cdot \sin y + z \cdot \cos y \]

   2. Taylor expanded in x around 0 99.8%

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

      1. fma-def 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around 0 78.5%

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

   if -5.90000000000000029e141 < x < 1.54999999999999999e122

   1. Initial program 99.8%

      \[x \cdot \sin y + z \cdot \cos y \]

   2. Taylor expanded in x around 0 99.8%

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

      1. fma-def 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around inf 78.1%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{+141} \lor \neg \left(x \leq 1.55 \cdot 10^{+122}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 6: 51.6% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \sin y + z \cdot \cos y \]

2. Taylor expanded in y around 0 51.8%

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

3. Final simplification 51.8%

   \[\leadsto z + x \cdot y \]

Alternative 7: 38.2% accurate, 207.0× 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

real(8) function code(x, y, z)
    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 99.8%

   \[x \cdot \sin y + z \cdot \cos y \]

2. Taylor expanded in x around 0 99.8%

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

   1. fma-def 99.8%

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

4. Simplified 99.8%

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

5. Taylor expanded in y around 0 39.9%

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

6. Final simplification 39.9%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023229 
(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))))