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

Percentage Accurate: 99.8% → 99.8%

Time: 7.0s

Alternatives: 9

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

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

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 99.8%

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

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. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

Alternative 3: 87.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+57} \lor \neg \left(z \leq 2.7 \cdot 10^{+29}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \sin y, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6e+57) (not (<= z 2.7e+29))) (* (cos y) z) (fma x (sin y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e+57) || !(z <= 2.7e+29)) {
		tmp = cos(y) * z;
	} else {
		tmp = fma(x, sin(y), z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6e+57) || !(z <= 2.7e+29))
		tmp = Float64(cos(y) * z);
	else
		tmp = fma(x, sin(y), z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6e+57], N[Not[LessEqual[z, 2.7e+29]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision], N[(x * N[Sin[y], $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.9999999999999999e57 or 2.7e29 < z

   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 89.7%

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

   if -5.9999999999999999e57 < z < 2.7e29

   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. Taylor expanded in y around 0 87.5%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+57} \lor \neg \left(z \leq 2.7 \cdot 10^{+29}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \sin y, z\right)\\ \end{array} \]

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 5: 87.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+57} \lor \neg \left(z \leq 2.2 \cdot 10^{+27}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z + \sin y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6e+57) (not (<= z 2.2e+27)))
   (* (cos y) z)
   (+ z (* (sin y) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e+57) || !(z <= 2.2e+27)) {
		tmp = cos(y) * z;
	} else {
		tmp = z + (sin(y) * x);
	}
	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 ((z <= (-6d+57)) .or. (.not. (z <= 2.2d+27))) then
        tmp = cos(y) * z
    else
        tmp = z + (sin(y) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e+57) || !(z <= 2.2e+27)) {
		tmp = Math.cos(y) * z;
	} else {
		tmp = z + (Math.sin(y) * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6e+57) or not (z <= 2.2e+27):
		tmp = math.cos(y) * z
	else:
		tmp = z + (math.sin(y) * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6e+57) || !(z <= 2.2e+27))
		tmp = Float64(cos(y) * z);
	else
		tmp = Float64(z + Float64(sin(y) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6e+57) || ~((z <= 2.2e+27)))
		tmp = cos(y) * z;
	else
		tmp = z + (sin(y) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6e+57], N[Not[LessEqual[z, 2.2e+27]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision], N[(z + N[(N[Sin[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.9999999999999999e57 or 2.1999999999999999e27 < z

   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 89.7%

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

   if -5.9999999999999999e57 < z < 2.1999999999999999e27

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 87.5%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+57} \lor \neg \left(z \leq 2.2 \cdot 10^{+27}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z + \sin y \cdot x\\ \end{array} \]

Alternative 6: 74.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.004 \lor \neg \left(y \leq 0.43\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.004) (not (<= y 0.43))) (* (cos y) z) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.004) || !(y <= 0.43)) {
		tmp = cos(y) * z;
	} else {
		tmp = z + (y * x);
	}
	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 <= (-0.004d0)) .or. (.not. (y <= 0.43d0))) then
        tmp = cos(y) * z
    else
        tmp = z + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.004) || !(y <= 0.43)) {
		tmp = Math.cos(y) * z;
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.004) or not (y <= 0.43):
		tmp = math.cos(y) * z
	else:
		tmp = z + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.004) || !(y <= 0.43))
		tmp = Float64(cos(y) * z);
	else
		tmp = Float64(z + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.004) || ~((y <= 0.43)))
		tmp = cos(y) * z;
	else
		tmp = z + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.004], N[Not[LessEqual[y, 0.43]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0040000000000000001 or 0.429999999999999993 < 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 99.6%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in z around inf 53.0%

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

   if -0.0040000000000000001 < y < 0.429999999999999993

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.4%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.004 \lor \neg \left(y \leq 0.43\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]

Alternative 7: 74.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-99} \lor \neg \left(z \leq 5 \cdot 10^{-144}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7e-99) (not (<= z 5e-144))) (* (cos y) z) (* (sin y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7e-99) || !(z <= 5e-144)) {
		tmp = cos(y) * z;
	} else {
		tmp = sin(y) * x;
	}
	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 ((z <= (-7d-99)) .or. (.not. (z <= 5d-144))) then
        tmp = cos(y) * z
    else
        tmp = sin(y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7e-99) || !(z <= 5e-144)) {
		tmp = Math.cos(y) * z;
	} else {
		tmp = Math.sin(y) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7e-99) or not (z <= 5e-144):
		tmp = math.cos(y) * z
	else:
		tmp = math.sin(y) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7e-99) || !(z <= 5e-144))
		tmp = Float64(cos(y) * z);
	else
		tmp = Float64(sin(y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7e-99) || ~((z <= 5e-144)))
		tmp = cos(y) * z;
	else
		tmp = sin(y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7e-99], N[Not[LessEqual[z, 5e-144]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.9999999999999997e-99 or 4.9999999999999998e-144 < z

   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 82.6%

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

   if -6.9999999999999997e-99 < z < 4.9999999999999998e-144

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.7%

      \[\leadsto \color{blue}{\cos y \cdot z + \sin y \cdot x} \]
   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 0 70.0%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-99} \lor \neg \left(z \leq 5 \cdot 10^{-144}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot x\\ \end{array} \]

Alternative 8: 53.1% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

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 + (y * x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 51.5%

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

3. Final simplification 51.5%

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

Alternative 9: 38.8% 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 43.1%

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

6. Final simplification 43.1%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023196 
(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))))