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

Percentage Accurate: 99.8% → 99.8%

Time: 7.5s

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, 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 2: 75.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \sin y\\ t_1 := z \cdot \cos y\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+191}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.00125:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-6}:\\ \;\;\;\;z + x \cdot y\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+245}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (sin y))) (t_1 (* z (cos y))))
   (if (<= y -1.3e+191)
     t_0
     (if (<= y -0.00125)
       t_1
       (if (<= y 5.2e-6) (+ z (* x y)) (if (<= y 2.2e+245) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * sin(y);
	double t_1 = z * cos(y);
	double tmp;
	if (y <= -1.3e+191) {
		tmp = t_0;
	} else if (y <= -0.00125) {
		tmp = t_1;
	} else if (y <= 5.2e-6) {
		tmp = z + (x * y);
	} else if (y <= 2.2e+245) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = x * sin(y)
    t_1 = z * cos(y)
    if (y <= (-1.3d+191)) then
        tmp = t_0
    else if (y <= (-0.00125d0)) then
        tmp = t_1
    else if (y <= 5.2d-6) then
        tmp = z + (x * y)
    else if (y <= 2.2d+245) then
        tmp = t_1
    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 t_1 = z * Math.cos(y);
	double tmp;
	if (y <= -1.3e+191) {
		tmp = t_0;
	} else if (y <= -0.00125) {
		tmp = t_1;
	} else if (y <= 5.2e-6) {
		tmp = z + (x * y);
	} else if (y <= 2.2e+245) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.sin(y)
	t_1 = z * math.cos(y)
	tmp = 0
	if y <= -1.3e+191:
		tmp = t_0
	elif y <= -0.00125:
		tmp = t_1
	elif y <= 5.2e-6:
		tmp = z + (x * y)
	elif y <= 2.2e+245:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * sin(y))
	t_1 = Float64(z * cos(y))
	tmp = 0.0
	if (y <= -1.3e+191)
		tmp = t_0;
	elseif (y <= -0.00125)
		tmp = t_1;
	elseif (y <= 5.2e-6)
		tmp = Float64(z + Float64(x * y));
	elseif (y <= 2.2e+245)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * sin(y);
	t_1 = z * cos(y);
	tmp = 0.0;
	if (y <= -1.3e+191)
		tmp = t_0;
	elseif (y <= -0.00125)
		tmp = t_1;
	elseif (y <= 5.2e-6)
		tmp = z + (x * y);
	elseif (y <= 2.2e+245)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+191], t$95$0, If[LessEqual[y, -0.00125], t$95$1, If[LessEqual[y, 5.2e-6], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+245], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3e191 or 2.2000000000000001e245 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 67.9%

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

   if -1.3e191 < y < -0.00125000000000000003 or 5.20000000000000019e-6 < y < 2.2000000000000001e245

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 69.2%

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

   if -0.00125000000000000003 < y < 5.20000000000000019e-6

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.3%

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

      1. +-commutative 99.3%

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

   4. Simplified 99.3%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+191}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;y \leq -0.00125:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-6}:\\ \;\;\;\;z + x \cdot y\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+245}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \]

Alternative 3: 75.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \sin y\\ t_1 := z \cdot \cos y\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+189}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.0013:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+242}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (sin y))) (t_1 (* z (cos y))))
   (if (<= y -4.4e+189)
     t_0
     (if (<= y -0.0013)
       t_1
       (if (<= y 7.6e-6) (fma x y z) (if (<= y 1.85e+242) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * sin(y);
	double t_1 = z * cos(y);
	double tmp;
	if (y <= -4.4e+189) {
		tmp = t_0;
	} else if (y <= -0.0013) {
		tmp = t_1;
	} else if (y <= 7.6e-6) {
		tmp = fma(x, y, z);
	} else if (y <= 1.85e+242) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * sin(y))
	t_1 = Float64(z * cos(y))
	tmp = 0.0
	if (y <= -4.4e+189)
		tmp = t_0;
	elseif (y <= -0.0013)
		tmp = t_1;
	elseif (y <= 7.6e-6)
		tmp = fma(x, y, z);
	elseif (y <= 1.85e+242)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+189], t$95$0, If[LessEqual[y, -0.0013], t$95$1, If[LessEqual[y, 7.6e-6], N[(x * y + z), $MachinePrecision], If[LessEqual[y, 1.85e+242], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4000000000000001e189 or 1.85e242 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 67.9%

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

   if -4.4000000000000001e189 < y < -0.0012999999999999999 or 7.6000000000000001e-6 < y < 1.85e242

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 69.2%

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

   if -0.0012999999999999999 < y < 7.6000000000000001e-6

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.3%

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

      1. +-commutative 99.3%

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

      2. fma-def 99.3%

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

   4. Simplified 99.3%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+189}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;y \leq -0.0013:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+242}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \]

Alternative 4: 75.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11500 \lor \neg \left(y \leq 0.032\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -11500.0) (not (<= y 0.032))) (* x (sin y)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -11500.0) || !(y <= 0.032)) {
		tmp = x * sin(y);
	} else {
		tmp = 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 <= (-11500.0d0)) .or. (.not. (y <= 0.032d0))) then
        tmp = x * sin(y)
    else
        tmp = z + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -11500.0) || !(y <= 0.032)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -11500.0) or not (y <= 0.032):
		tmp = x * math.sin(y)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -11500.0) || !(y <= 0.032))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -11500.0) || ~((y <= 0.032)))
		tmp = x * sin(y);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -11500.0], N[Not[LessEqual[y, 0.032]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -11500 or 0.032000000000000001 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 42.8%

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

   if -11500 < y < 0.032000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.6%

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

      1. +-commutative 97.6%

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

   4. Simplified 97.6%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11500 \lor \neg \left(y \leq 0.032\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]

Alternative 5: 41.2% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-52}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-108}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.55e-52) z (if (<= z 1.02e-108) (* x y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e-52) {
		tmp = z;
	} else if (z <= 1.02e-108) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	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 <= (-1.55d-52)) then
        tmp = z
    else if (z <= 1.02d-108) then
        tmp = x * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e-52) {
		tmp = z;
	} else if (z <= 1.02e-108) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.55e-52:
		tmp = z
	elif z <= 1.02e-108:
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.55e-52)
		tmp = z;
	elseif (z <= 1.02e-108)
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.55e-52)
		tmp = z;
	elseif (z <= 1.02e-108)
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.55e-52], z, If[LessEqual[z, 1.02e-108], N[(x * y), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5499999999999999e-52 or 1.02000000000000008e-108 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 53.9%

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

      1. +-commutative 53.9%

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

   4. Simplified 53.9%

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

   5. Taylor expanded in x around 0 48.8%

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

   if -1.5499999999999999e-52 < z < 1.02000000000000008e-108

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 75.3%

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

   3. Taylor expanded in y around 0 37.6%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-52}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-108}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 6: 52.7% 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 53.2%

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

   1. +-commutative 53.2%

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

4. Simplified 53.2%

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

5. Final simplification 53.2%

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

Alternative 7: 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 y around 0 53.2%

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

   1. +-commutative 53.2%

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

4. Simplified 53.2%

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

5. Taylor expanded in x around 0 38.7%

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

6. Final simplification 38.7%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023320 
(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))))