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

Percentage Accurate: 99.8% → 99.8%

Time: 3.4s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (- (* 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)
use fmin_fmax_functions
    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]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x * (cos(y))) - (z * (sin(y)))
END code

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (- (* 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)
use fmin_fmax_functions
    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]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x * (cos(y))) - (z * (sin(y)))
END code

Alternative 1: 86.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} t_0 := x \cdot 1 - z \cdot \sin y\\ \mathbf{if}\;z \leq -1.5998878487717716 \cdot 10^{-87}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.3906905842088115 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (- (* x 1.0) (* z (sin y)))))
  (if (<= z -1.5998878487717716e-87)
    t_0
    (if (<= z 1.3906905842088115e-61) (* x (cos y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * 1.0) - (z * sin(y));
	double tmp;
	if (z <= -1.5998878487717716e-87) {
		tmp = t_0;
	} else if (z <= 1.3906905842088115e-61) {
		tmp = x * cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    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 * 1.0d0) - (z * sin(y))
    if (z <= (-1.5998878487717716d-87)) then
        tmp = t_0
    else if (z <= 1.3906905842088115d-61) then
        tmp = x * cos(y)
    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 * 1.0) - (z * Math.sin(y));
	double tmp;
	if (z <= -1.5998878487717716e-87) {
		tmp = t_0;
	} else if (z <= 1.3906905842088115e-61) {
		tmp = x * Math.cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * 1.0) - (z * math.sin(y))
	tmp = 0
	if z <= -1.5998878487717716e-87:
		tmp = t_0
	elif z <= 1.3906905842088115e-61:
		tmp = x * math.cos(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * 1.0) - Float64(z * sin(y)))
	tmp = 0.0
	if (z <= -1.5998878487717716e-87)
		tmp = t_0;
	elseif (z <= 1.3906905842088115e-61)
		tmp = Float64(x * cos(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * 1.0) - (z * sin(y));
	tmp = 0.0;
	if (z <= -1.5998878487717716e-87)
		tmp = t_0;
	elseif (z <= 1.3906905842088115e-61)
		tmp = x * cos(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5998878487717716e-87], t$95$0, If[LessEqual[z, 1.3906905842088115e-61], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = ((x * (1)) - (z * (sin(y)))) IN
		LET tmp_1 = IF (z <= (139069058420881154967487957630223034015355744194129779251587240099952514292987109389899646542932568675618170646032168982972712282179196417877818123690699010641669275401000049896538257598876953125e-255)) THEN (x * (cos(y))) ELSE t_0 ENDIF IN
		LET tmp = IF (z <= (-159988784877177164685523371169830722870522374072384409119026858684832480050318864005140114871679013601761552483193181404403016128515199488354968070059220853336754264519220820635743157089849151568897638446024723319315030689580225953250192105770111083984375e-341)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -1.5998878487717716e-87 or 1.3906905842088115e-61 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0

      \[\leadsto x \cdot 1 - z \cdot \sin y \]
   3. Step-by-step derivation

   4. Applied rewrites 77.3%

      \[\leadsto x \cdot 1 - z \cdot \sin y \]

   if -1.5998878487717716e-87 < z < 1.3906905842088115e-61

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(\cos y + -1 \cdot \frac{z \cdot \sin y}{x}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 92.2%

      \[\leadsto x \cdot \left(\cos y + -1 \cdot \frac{z \cdot \sin y}{x}\right) \]

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \cos y \]
   6. Step-by-step derivation

   7. Applied rewrites 61.0%

      \[\leadsto x \cdot \cos y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 74.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_0 := x \cdot \cos y\\ \mathbf{if}\;x \leq -1.2014353339475216 \cdot 10^{-53}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.3907246641268288 \cdot 10^{-133}:\\ \;\;\;\;-\sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* x (cos y))))
  (if (<= x -1.2014353339475216e-53)
    t_0
    (if (<= x 1.3907246641268288e-133) (- (* (sin y) z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * cos(y);
	double tmp;
	if (x <= -1.2014353339475216e-53) {
		tmp = t_0;
	} else if (x <= 1.3907246641268288e-133) {
		tmp = -(sin(y) * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    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 * cos(y)
    if (x <= (-1.2014353339475216d-53)) then
        tmp = t_0
    else if (x <= 1.3907246641268288d-133) then
        tmp = -(sin(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.cos(y);
	double tmp;
	if (x <= -1.2014353339475216e-53) {
		tmp = t_0;
	} else if (x <= 1.3907246641268288e-133) {
		tmp = -(Math.sin(y) * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.cos(y)
	tmp = 0
	if x <= -1.2014353339475216e-53:
		tmp = t_0
	elif x <= 1.3907246641268288e-133:
		tmp = -(math.sin(y) * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	tmp = 0.0
	if (x <= -1.2014353339475216e-53)
		tmp = t_0;
	elseif (x <= 1.3907246641268288e-133)
		tmp = Float64(-Float64(sin(y) * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * cos(y);
	tmp = 0.0;
	if (x <= -1.2014353339475216e-53)
		tmp = t_0;
	elseif (x <= 1.3907246641268288e-133)
		tmp = -(sin(y) * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2014353339475216e-53], t$95$0, If[LessEqual[x, 1.3907246641268288e-133], (-N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), t$95$0]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = (x * (cos(y))) IN
		LET tmp_1 = IF (x <= (13907246641268287719553288589367698732274009277678938853341083963550402305825730272558285284260707557226592286720658421468340914383077588215032524302117800378662076704866440675793204111827833749549383931163536547600078549247750976353053708772891633938598045310131695191357079148094045872458853184477607279647119117250357415993544663024295005016028881072998046875e-494)) THEN (- ((sin(y)) * z)) ELSE t_0 ENDIF IN
		LET tmp = IF (x <= (-1201435333947521567179383940228922831410793169252770766996959593329040310462231836384689301534482831918011668944531164721304996863097958037513990348088555037975311279296875e-224)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -1.2014353339475216e-53 or 1.3907246641268288e-133 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(\cos y + -1 \cdot \frac{z \cdot \sin y}{x}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 92.2%

      \[\leadsto x \cdot \left(\cos y + -1 \cdot \frac{z \cdot \sin y}{x}\right) \]

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \cos y \]
   6. Step-by-step derivation

   7. Applied rewrites 61.0%

      \[\leadsto x \cdot \cos y \]

   if -1.2014353339475216e-53 < x < 1.3907246641268288e-133

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto -1 \cdot \left(z \cdot \sin y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 40.4%

      \[\leadsto -1 \cdot \left(z \cdot \sin y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 40.4%

      \[\leadsto -\sin y \cdot z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 73.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_0 := x \cdot \cos y\\ \mathbf{if}\;y \leq -0.0037539651929508304:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.2681731775064146:\\ \;\;\;\;x + y \cdot \left(y \cdot \mathsf{fma}\left(-0.5, x, 0.16666666666666666 \cdot \left(y \cdot z\right)\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* x (cos y))))
  (if (<= y -0.0037539651929508304)
    t_0
    (if (<= y 0.2681731775064146)
      (+
       x
       (* y (- (* y (fma -0.5 x (* 0.16666666666666666 (* y z)))) z)))
      t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * cos(y);
	double tmp;
	if (y <= -0.0037539651929508304) {
		tmp = t_0;
	} else if (y <= 0.2681731775064146) {
		tmp = x + (y * ((y * fma(-0.5, x, (0.16666666666666666 * (y * z)))) - z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	tmp = 0.0
	if (y <= -0.0037539651929508304)
		tmp = t_0;
	elseif (y <= 0.2681731775064146)
		tmp = Float64(x + Float64(y * Float64(Float64(y * fma(-0.5, x, Float64(0.16666666666666666 * Float64(y * z)))) - z)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.0037539651929508304], t$95$0, If[LessEqual[y, 0.2681731775064146], N[(x + N[(y * N[(N[(y * N[(-0.5 * x + N[(0.16666666666666666 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = (x * (cos(y))) IN
		LET tmp_1 = IF (y <= (268173177506414617266017330621252767741680145263671875e-54)) THEN (x + (y * ((y * (((-5e-1) * x) + ((1666666666666666574148081281236954964697360992431640625e-55) * (y * z)))) - z))) ELSE t_0 ENDIF IN
		LET tmp = IF (y <= (-37539651929508303929150514477441902272403240203857421875e-58)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -0.0037539651929508304 or 0.26817317750641462 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(\cos y + -1 \cdot \frac{z \cdot \sin y}{x}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 92.2%

      \[\leadsto x \cdot \left(\cos y + -1 \cdot \frac{z \cdot \sin y}{x}\right) \]

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \cos y \]
   6. Step-by-step derivation

   7. Applied rewrites 61.0%

      \[\leadsto x \cdot \cos y \]

   if -0.0037539651929508304 < y < 0.26817317750641462

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0

      \[\leadsto x + y \cdot \left(y \cdot \left(\frac{-1}{2} \cdot x + \frac{1}{6} \cdot \left(y \cdot z\right)\right) - z\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 51.5%

      \[\leadsto x + y \cdot \left(y \cdot \mathsf{fma}\left(-0.5, x, 0.16666666666666666 \cdot \left(y \cdot z\right)\right) - z\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 52.7% accurate, 11.6× speedup

Math

\[x - z \cdot y \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (- x (* z y)))

C

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

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x - (z * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	x - (z * y)
END code

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0

   \[\leadsto x + -1 \cdot \left(y \cdot z\right) \]
3. Step-by-step derivation

4. Applied rewrites 52.7%

   \[\leadsto x + -1 \cdot \left(y \cdot z\right) \]
5. Step-by-step derivation

6. Applied rewrites 52.7%

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

Alternative 5: 39.5% accurate, 19.2× speedup

Math

\[x \cdot 1 \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (* x 1.0))

C

double code(double x, double y, double z) {
	return x * 1.0;
}

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return x * 1.0;
}

Python

def code(x, y, z):
	return x * 1.0

Julia

function code(x, y, z)
	return Float64(x * 1.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * 1.0;
end

Wolfram

code[x_, y_, z_] := N[(x * 1.0), $MachinePrecision]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	x * (1)
END code

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in x around inf

   \[\leadsto x \cdot \left(\cos y + -1 \cdot \frac{z \cdot \sin y}{x}\right) \]
3. Step-by-step derivation

4. Applied rewrites 92.2%

   \[\leadsto x \cdot \left(\cos y + -1 \cdot \frac{z \cdot \sin y}{x}\right) \]

5. Taylor expanded in x around inf

   \[\leadsto x \cdot \cos y \]
6. Step-by-step derivation

7. Applied rewrites 61.0%

   \[\leadsto x \cdot \cos y \]

8. Taylor expanded in y around 0

   \[\leadsto x \cdot 1 \]
9. Step-by-step derivation

10. Applied rewrites 39.5%

    \[\leadsto x \cdot 1 \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))