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

Percentage Accurate: 99.8% → 99.8%

Time: 6.7s

Alternatives: 8

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. *-commutative 99.9%

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

   3. fma-def 99.9%

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

4. Applied egg-rr 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 3: 74.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \sin y\\ \mathbf{if}\;y \leq -0.000175:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.0032:\\ \;\;\;\;z + y \cdot x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+209} \lor \neg \left(y \leq 1.02 \cdot 10^{+288}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (sin y))))
   (if (<= y -0.000175)
     t_0
     (if (<= y 0.0032)
       (+ z (* y x))
       (if (or (<= y 3.4e+209) (not (<= y 1.02e+288))) (* (cos y) z) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * sin(y);
	double tmp;
	if (y <= -0.000175) {
		tmp = t_0;
	} else if (y <= 0.0032) {
		tmp = z + (y * x);
	} else if ((y <= 3.4e+209) || !(y <= 1.02e+288)) {
		tmp = cos(y) * z;
	} 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 (y <= (-0.000175d0)) then
        tmp = t_0
    else if (y <= 0.0032d0) then
        tmp = z + (y * x)
    else if ((y <= 3.4d+209) .or. (.not. (y <= 1.02d+288))) then
        tmp = cos(y) * z
    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 (y <= -0.000175) {
		tmp = t_0;
	} else if (y <= 0.0032) {
		tmp = z + (y * x);
	} else if ((y <= 3.4e+209) || !(y <= 1.02e+288)) {
		tmp = Math.cos(y) * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.sin(y)
	tmp = 0
	if y <= -0.000175:
		tmp = t_0
	elif y <= 0.0032:
		tmp = z + (y * x)
	elif (y <= 3.4e+209) or not (y <= 1.02e+288):
		tmp = math.cos(y) * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * sin(y))
	tmp = 0.0
	if (y <= -0.000175)
		tmp = t_0;
	elseif (y <= 0.0032)
		tmp = Float64(z + Float64(y * x));
	elseif ((y <= 3.4e+209) || !(y <= 1.02e+288))
		tmp = Float64(cos(y) * z);
	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 (y <= -0.000175)
		tmp = t_0;
	elseif (y <= 0.0032)
		tmp = z + (y * x);
	elseif ((y <= 3.4e+209) || ~((y <= 1.02e+288)))
		tmp = cos(y) * z;
	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[y, -0.000175], t$95$0, If[LessEqual[y, 0.0032], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.4e+209], N[Not[LessEqual[y, 1.02e+288]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.74999999999999998e-4 or 3.3999999999999997e209 < y < 1.02000000000000003e288

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 66.7%

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

   if -1.74999999999999998e-4 < y < 0.00320000000000000015

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.7%

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

      1. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   if 0.00320000000000000015 < y < 3.3999999999999997e209 or 1.02000000000000003e288 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 59.8%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.000175:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;y \leq 0.0032:\\ \;\;\;\;z + y \cdot x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+209} \lor \neg \left(y \leq 1.02 \cdot 10^{+288}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-58} \lor \neg \left(x \leq 2.85 \cdot 10^{-105}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2e-58) (not (<= x 2.85e-105)))
   (+ z (* x (sin y)))
   (* (cos y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2e-58) || !(x <= 2.85e-105)) {
		tmp = z + (x * sin(y));
	} else {
		tmp = cos(y) * 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 ((x <= (-2d-58)) .or. (.not. (x <= 2.85d-105))) then
        tmp = z + (x * sin(y))
    else
        tmp = cos(y) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2e-58) || !(x <= 2.85e-105)) {
		tmp = z + (x * Math.sin(y));
	} else {
		tmp = Math.cos(y) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2e-58) or not (x <= 2.85e-105):
		tmp = z + (x * math.sin(y))
	else:
		tmp = math.cos(y) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2e-58) || !(x <= 2.85e-105))
		tmp = Float64(z + Float64(x * sin(y)));
	else
		tmp = Float64(cos(y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2e-58) || ~((x <= 2.85e-105)))
		tmp = z + (x * sin(y));
	else
		tmp = cos(y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2e-58], N[Not[LessEqual[x, 2.85e-105]], $MachinePrecision]], N[(z + N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0000000000000001e-58 or 2.84999999999999981e-105 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 91.4%

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

   if -2.0000000000000001e-58 < x < 2.84999999999999981e-105

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 92.7%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-58} \lor \neg \left(x \leq 2.85 \cdot 10^{-105}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-5} \lor \neg \left(y \leq 8.7 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.2e-5) (not (<= y 8.7e-23))) (* x (sin y)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.2e-5) || !(y <= 8.7e-23)) {
		tmp = x * sin(y);
	} 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 <= (-3.2d-5)) .or. (.not. (y <= 8.7d-23))) then
        tmp = x * sin(y)
    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 <= -3.2e-5) || !(y <= 8.7e-23)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.2e-5) or not (y <= 8.7e-23):
		tmp = x * math.sin(y)
	else:
		tmp = z + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.2e-5) || !(y <= 8.7e-23))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.2e-5) || ~((y <= 8.7e-23)))
		tmp = x * sin(y);
	else
		tmp = z + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.2e-5], N[Not[LessEqual[y, 8.7e-23]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999986e-5 or 8.7000000000000005e-23 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 57.3%

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

   if -3.19999999999999986e-5 < y < 8.7000000000000005e-23

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-5} \lor \neg \left(y \leq 8.7 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 40.8% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+174} \lor \neg \left(x \leq 5.2 \cdot 10^{+39}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.2e+174) (not (<= x 5.2e+39))) (* y x) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.2e+174) || !(x <= 5.2e+39)) {
		tmp = y * x;
	} 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 ((x <= (-8.2d+174)) .or. (.not. (x <= 5.2d+39))) 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 ((x <= -8.2e+174) || !(x <= 5.2e+39)) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.2e+174) or not (x <= 5.2e+39):
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.2e+174) || !(x <= 5.2e+39))
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.2e+174) || ~((x <= 5.2e+39)))
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.2e+174], N[Not[LessEqual[x, 5.2e+39]], $MachinePrecision]], N[(y * x), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -8.20000000000000061e174 or 5.2e39 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 76.6%

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

   4. Taylor expanded in y around 0 43.7%

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

   if -8.20000000000000061e174 < x < 5.2e39

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. fma-def 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 52.8%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+174} \lor \neg \left(x \leq 5.2 \cdot 10^{+39}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.5% 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 99.9%

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

3. Taylor expanded in y around 0 59.1%

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

   1. +-commutative 59.1%

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

5. Simplified 59.1%

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

6. Final simplification 59.1%

   \[\leadsto z + y \cdot x \]
7. Add Preprocessing

Alternative 8: 38.4% 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 99.9%

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

   1. +-commutative 99.9%

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

   2. *-commutative 99.9%

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

   3. fma-def 99.9%

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

4. Applied egg-rr 99.9%

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

5. Taylor expanded in y around 0 42.8%

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

6. Final simplification 42.8%

   \[\leadsto z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024019 
(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))))