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

Percentage Accurate: 99.8% → 99.8%

Time: 7.3s

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, 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]

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 2: 86.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-144} \lor \neg \left(z \leq 1.12 \cdot 10^{-57}\right):\\ \;\;\;\;x + z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4e-144) (not (<= z 1.12e-57)))
   (+ x (* z (sin y)))
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4e-144) || !(z <= 1.12e-57)) {
		tmp = x + (z * sin(y));
	} else {
		tmp = x * 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 ((z <= (-4d-144)) .or. (.not. (z <= 1.12d-57))) then
        tmp = x + (z * sin(y))
    else
        tmp = x * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4e-144) || !(z <= 1.12e-57)) {
		tmp = x + (z * Math.sin(y));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4e-144) or not (z <= 1.12e-57):
		tmp = x + (z * math.sin(y))
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4e-144) || !(z <= 1.12e-57))
		tmp = Float64(x + Float64(z * sin(y)));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4e-144) || ~((z <= 1.12e-57)))
		tmp = x + (z * sin(y));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4e-144], N[Not[LessEqual[z, 1.12e-57]], $MachinePrecision]], N[(x + N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9999999999999998e-144 or 1.12e-57 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 91.1%

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

   if -3.9999999999999998e-144 < z < 1.12e-57

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 91.4%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-144} \lor \neg \left(z \leq 1.12 \cdot 10^{-57}\right):\\ \;\;\;\;x + z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 3: 74.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0108 \lor \neg \left(y \leq 0.015\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0108) (not (<= y 0.015))) (* x (cos y)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0108) || !(y <= 0.015)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (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 ((y <= (-0.0108d0)) .or. (.not. (y <= 0.015d0))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0108) || !(y <= 0.015)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0108) or not (y <= 0.015):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0108) || !(y <= 0.015))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0108) || ~((y <= 0.015)))
		tmp = x * cos(y);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0108], N[Not[LessEqual[y, 0.015]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.010800000000000001 or 0.014999999999999999 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 47.9%

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

   if -0.010800000000000001 < y < 0.014999999999999999

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.0%

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

      1. +-commutative 99.0%

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

   4. Simplified 99.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0108 \lor \neg \left(y \leq 0.015\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 4: 74.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0132:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq 54000000000:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.0132)
   (* x (cos y))
   (if (<= y 54000000000.0) (+ x (* y z)) (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.0132) {
		tmp = x * cos(y);
	} else if (y <= 54000000000.0) {
		tmp = x + (y * z);
	} else {
		tmp = z * sin(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 <= (-0.0132d0)) then
        tmp = x * cos(y)
    else if (y <= 54000000000.0d0) then
        tmp = x + (y * z)
    else
        tmp = z * sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.0132) {
		tmp = x * Math.cos(y);
	} else if (y <= 54000000000.0) {
		tmp = x + (y * z);
	} else {
		tmp = z * Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.0132:
		tmp = x * math.cos(y)
	elif y <= 54000000000.0:
		tmp = x + (y * z)
	else:
		tmp = z * math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.0132)
		tmp = Float64(x * cos(y));
	elseif (y <= 54000000000.0)
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(z * sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.0132)
		tmp = x * cos(y);
	elseif (y <= 54000000000.0)
		tmp = x + (y * z);
	else
		tmp = z * sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.0132], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 54000000000.0], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0132

   1. Initial program 99.5%

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

   2. Taylor expanded in x around inf 51.4%

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

   if -0.0132 < y < 5.4e10

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.7%

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

      1. +-commutative 97.7%

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

   4. Simplified 97.7%

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

   if 5.4e10 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 59.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0132:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq 54000000000:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \sin y\\ \end{array} \]

Alternative 5: 74.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.019:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq 54000000000:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.019)
   (* x (cos y))
   (if (<= y 54000000000.0) (fma y z x) (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.019) {
		tmp = x * cos(y);
	} else if (y <= 54000000000.0) {
		tmp = fma(y, z, x);
	} else {
		tmp = z * sin(y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.019)
		tmp = Float64(x * cos(y));
	elseif (y <= 54000000000.0)
		tmp = fma(y, z, x);
	else
		tmp = Float64(z * sin(y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.019], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 54000000000.0], N[(y * z + x), $MachinePrecision], N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0189999999999999995

   1. Initial program 99.5%

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

   2. Taylor expanded in x around inf 51.4%

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

   if -0.0189999999999999995 < y < 5.4e10

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.7%

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

      1. +-commutative 97.7%

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

      2. fma-def 97.8%

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

   4. Simplified 97.8%

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

   if 5.4e10 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 59.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.019:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq 54000000000:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \sin y\\ \end{array} \]

Alternative 6: 41.3% accurate, 18.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-198} \lor \neg \left(x \leq -4.1 \cdot 10^{-257}\right) \land x \leq 4.1 \cdot 10^{-114}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.2e-130)
   x
   (if (or (<= x -8e-198) (and (not (<= x -4.1e-257)) (<= x 4.1e-114)))
     (* y z)
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e-130) {
		tmp = x;
	} else if ((x <= -8e-198) || (!(x <= -4.1e-257) && (x <= 4.1e-114))) {
		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 <= (-4.2d-130)) then
        tmp = x
    else if ((x <= (-8d-198)) .or. (.not. (x <= (-4.1d-257))) .and. (x <= 4.1d-114)) 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 <= -4.2e-130) {
		tmp = x;
	} else if ((x <= -8e-198) || (!(x <= -4.1e-257) && (x <= 4.1e-114))) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.2e-130:
		tmp = x
	elif (x <= -8e-198) or (not (x <= -4.1e-257) and (x <= 4.1e-114)):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.2e-130)
		tmp = x;
	elseif ((x <= -8e-198) || (!(x <= -4.1e-257) && (x <= 4.1e-114)))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.2e-130)
		tmp = x;
	elseif ((x <= -8e-198) || (~((x <= -4.1e-257)) && (x <= 4.1e-114)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.2e-130], x, If[Or[LessEqual[x, -8e-198], And[N[Not[LessEqual[x, -4.1e-257]], $MachinePrecision], LessEqual[x, 4.1e-114]]], N[(y * z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.20000000000000004e-130 or -7.9999999999999993e-198 < x < -4.0999999999999997e-257 or 4.0999999999999997e-114 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 76.1%

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

   3. Taylor expanded in y around 0 55.9%

      \[\leadsto \color{blue}{x + \left(-0.16666666666666666 \cdot \left({y}^{3} \cdot z\right) + y \cdot z\right)} \]

   4. Taylor expanded in x around inf 52.7%

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

   if -4.20000000000000004e-130 < x < -7.9999999999999993e-198 or -4.0999999999999997e-257 < x < 4.0999999999999997e-114

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 58.0%

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

      1. +-commutative 58.0%

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

   4. Simplified 58.0%

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

   5. Taylor expanded in y around inf 42.1%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-198} \lor \neg \left(x \leq -4.1 \cdot 10^{-257}\right) \land x \leq 4.1 \cdot 10^{-114}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 53.0% 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. Taylor expanded in y around 0 57.2%

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

   1. +-commutative 57.2%

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

4. Simplified 57.2%

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

5. Final simplification 57.2%

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

Alternative 8: 39.8% 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. Taylor expanded in y around 0 80.5%

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

3. Taylor expanded in y around 0 56.2%

   \[\leadsto \color{blue}{x + \left(-0.16666666666666666 \cdot \left({y}^{3} \cdot z\right) + y \cdot z\right)} \]

4. Taylor expanded in x around inf 43.4%

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

5. Final simplification 43.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023322 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))