Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3

Percentage Accurate: 99.8% → 99.8%

Time: 8.0s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. *-commutative 99.8%

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

   3. fma-def 99.8%

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

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 3: 85.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+70} \lor \neg \left(x \leq -1.85 \cdot 10^{+44} \lor \neg \left(x \leq -5.8 \cdot 10^{-18}\right) \land x \leq 2.7 \cdot 10^{+107}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.4e+70)
         (not
          (or (<= x -1.85e+44) (and (not (<= x -5.8e-18)) (<= x 2.7e+107)))))
   (* x (cos y))
   (+ x (* (sin y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.4e+70) || !((x <= -1.85e+44) || (!(x <= -5.8e-18) && (x <= 2.7e+107)))) {
		tmp = x * cos(y);
	} else {
		tmp = x + (sin(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 <= (-2.4d+70)) .or. (.not. (x <= (-1.85d+44)) .or. (.not. (x <= (-5.8d-18))) .and. (x <= 2.7d+107))) then
        tmp = x * cos(y)
    else
        tmp = x + (sin(y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.4e+70) || !((x <= -1.85e+44) || (!(x <= -5.8e-18) && (x <= 2.7e+107)))) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (Math.sin(y) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.4e+70) or not ((x <= -1.85e+44) or (not (x <= -5.8e-18) and (x <= 2.7e+107))):
		tmp = x * math.cos(y)
	else:
		tmp = x + (math.sin(y) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.4e+70) || !((x <= -1.85e+44) || (!(x <= -5.8e-18) && (x <= 2.7e+107))))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(sin(y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.4e+70) || ~(((x <= -1.85e+44) || (~((x <= -5.8e-18)) && (x <= 2.7e+107)))))
		tmp = x * cos(y);
	else
		tmp = x + (sin(y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.4e+70], N[Not[Or[LessEqual[x, -1.85e+44], And[N[Not[LessEqual[x, -5.8e-18]], $MachinePrecision], LessEqual[x, 2.7e+107]]]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.39999999999999987e70 or -1.85e44 < x < -5.8e-18 or 2.7000000000000001e107 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 93.8%

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

   if -2.39999999999999987e70 < x < -1.85e44 or -5.8e-18 < x < 2.7000000000000001e107

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 89.9%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+70} \lor \neg \left(x \leq -1.85 \cdot 10^{+44} \lor \neg \left(x \leq -5.8 \cdot 10^{-18}\right) \land x \leq 2.7 \cdot 10^{+107}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-18} \lor \neg \left(x \leq -1.25 \cdot 10^{-53} \lor \neg \left(x \leq -5.5 \cdot 10^{-134}\right) \land x \leq 4 \cdot 10^{-82}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.4e-18)
         (not (or (<= x -1.25e-53) (and (not (<= x -5.5e-134)) (<= x 4e-82)))))
   (* x (cos y))
   (* (sin y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.4e-18) || !((x <= -1.25e-53) || (!(x <= -5.5e-134) && (x <= 4e-82)))) {
		tmp = x * cos(y);
	} else {
		tmp = sin(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 <= (-3.4d-18)) .or. (.not. (x <= (-1.25d-53)) .or. (.not. (x <= (-5.5d-134))) .and. (x <= 4d-82))) then
        tmp = x * cos(y)
    else
        tmp = sin(y) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.4e-18) || !((x <= -1.25e-53) || (!(x <= -5.5e-134) && (x <= 4e-82)))) {
		tmp = x * Math.cos(y);
	} else {
		tmp = Math.sin(y) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.4e-18) or not ((x <= -1.25e-53) or (not (x <= -5.5e-134) and (x <= 4e-82))):
		tmp = x * math.cos(y)
	else:
		tmp = math.sin(y) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.4e-18) || !((x <= -1.25e-53) || (!(x <= -5.5e-134) && (x <= 4e-82))))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(sin(y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.4e-18) || ~(((x <= -1.25e-53) || (~((x <= -5.5e-134)) && (x <= 4e-82)))))
		tmp = x * cos(y);
	else
		tmp = sin(y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.4e-18], N[Not[Or[LessEqual[x, -1.25e-53], And[N[Not[LessEqual[x, -5.5e-134]], $MachinePrecision], LessEqual[x, 4e-82]]]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.40000000000000001e-18 or -1.25e-53 < x < -5.5000000000000002e-134 or 4e-82 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 82.8%

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

   if -3.40000000000000001e-18 < x < -1.25e-53 or -5.5000000000000002e-134 < x < 4e-82

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 76.8%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-18} \lor \neg \left(x \leq -1.25 \cdot 10^{-53} \lor \neg \left(x \leq -5.5 \cdot 10^{-134}\right) \land x \leq 4 \cdot 10^{-82}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0058 \lor \neg \left(y \leq 0.0055\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0058) (not (<= y 0.0055)))
   (* x (cos y))
   (+ x (* y (+ z (* y (* x -0.5)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0058) || !(y <= 0.0055)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (y * (z + (y * (x * -0.5))));
	}
	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 <= (-0.0058d0)) .or. (.not. (y <= 0.0055d0))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * (z + (y * (x * (-0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0058) || !(y <= 0.0055)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * (z + (y * (x * -0.5))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0058) or not (y <= 0.0055):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * (z + (y * (x * -0.5))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0058) || !(y <= 0.0055))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * Float64(z + Float64(y * Float64(x * -0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0058) || ~((y <= 0.0055)))
		tmp = x * cos(y);
	else
		tmp = x + (y * (z + (y * (x * -0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0058], N[Not[LessEqual[y, 0.0055]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z + N[(y * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0058 or 0.0054999999999999997 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 52.2%

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

   if -0.0058 < y < 0.0054999999999999997

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.4%

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

      1. associate-*r* 99.4%

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

      2. unpow2 99.4%

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

      3. associate-*r* 99.4%

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

      4. *-commutative 99.4%

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

      5. distribute-rgt-out 99.4%

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

      6. *-commutative 99.4%

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

   5. Simplified 99.4%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0058 \lor \neg \left(y \leq 0.0055\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 42.4% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-166}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.4e-139) x (if (<= x 1.3e-166) (* y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.4e-139) {
		tmp = x;
	} else if (x <= 1.3e-166) {
		tmp = y * z;
	} else {
		tmp = 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 (x <= (-6.4d-139)) then
        tmp = x
    else if (x <= 1.3d-166) then
        tmp = y * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.4e-139) {
		tmp = x;
	} else if (x <= 1.3e-166) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.4e-139:
		tmp = x
	elif x <= 1.3e-166:
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.4e-139)
		tmp = x;
	elseif (x <= 1.3e-166)
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.4e-139)
		tmp = x;
	elseif (x <= 1.3e-166)
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.4e-139], x, If[LessEqual[x, 1.3e-166], N[(y * z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.3999999999999999e-139 or 1.29999999999999995e-166 < x

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-def 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0 40.5%

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

   if -6.3999999999999999e-139 < x < 1.29999999999999995e-166

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 54.8%

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

   4. Taylor expanded in x around 0 36.1%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-166}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.9% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around 0 47.3%

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

4. Final simplification 47.3%

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

Alternative 8: 39.7% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. *-commutative 99.8%

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

   3. fma-def 99.8%

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

4. Applied egg-rr 99.8%

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

5. Taylor expanded in y around 0 35.8%

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

6. Final simplification 35.8%

   \[\leadsto x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024041 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))