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

Percentage Accurate: 99.8% → 99.8%

Time: 8.4s

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(N[Cos[y], $MachinePrecision] * x + 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. Step-by-step derivation

   1. *-commutative 99.8%

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

   2. fma-neg 99.8%

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

   3. distribute-rgt-neg-in 99.8%

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

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 3: 74.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot \left(-z\right)\\ t_1 := \cos y \cdot x\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+84}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.015:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.23:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+126} \lor \neg \left(y \leq 7 \cdot 10^{+221}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) (- z))) (t_1 (* (cos y) x)))
   (if (<= y -5.2e+84)
     t_0
     (if (<= y -5.8e+21)
       t_1
       (if (<= y -0.015)
         t_0
         (if (<= y 0.23)
           (- x (* y z))
           (if (or (<= y 8.8e+126) (not (<= y 7e+221))) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * -z;
	double t_1 = cos(y) * x;
	double tmp;
	if (y <= -5.2e+84) {
		tmp = t_0;
	} else if (y <= -5.8e+21) {
		tmp = t_1;
	} else if (y <= -0.015) {
		tmp = t_0;
	} else if (y <= 0.23) {
		tmp = x - (y * z);
	} else if ((y <= 8.8e+126) || !(y <= 7e+221)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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 = sin(y) * -z
    t_1 = cos(y) * x
    if (y <= (-5.2d+84)) then
        tmp = t_0
    else if (y <= (-5.8d+21)) then
        tmp = t_1
    else if (y <= (-0.015d0)) then
        tmp = t_0
    else if (y <= 0.23d0) then
        tmp = x - (y * z)
    else if ((y <= 8.8d+126) .or. (.not. (y <= 7d+221))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) * -z;
	double t_1 = Math.cos(y) * x;
	double tmp;
	if (y <= -5.2e+84) {
		tmp = t_0;
	} else if (y <= -5.8e+21) {
		tmp = t_1;
	} else if (y <= -0.015) {
		tmp = t_0;
	} else if (y <= 0.23) {
		tmp = x - (y * z);
	} else if ((y <= 8.8e+126) || !(y <= 7e+221)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * -z
	t_1 = math.cos(y) * x
	tmp = 0
	if y <= -5.2e+84:
		tmp = t_0
	elif y <= -5.8e+21:
		tmp = t_1
	elif y <= -0.015:
		tmp = t_0
	elif y <= 0.23:
		tmp = x - (y * z)
	elif (y <= 8.8e+126) or not (y <= 7e+221):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * Float64(-z))
	t_1 = Float64(cos(y) * x)
	tmp = 0.0
	if (y <= -5.2e+84)
		tmp = t_0;
	elseif (y <= -5.8e+21)
		tmp = t_1;
	elseif (y <= -0.015)
		tmp = t_0;
	elseif (y <= 0.23)
		tmp = Float64(x - Float64(y * z));
	elseif ((y <= 8.8e+126) || !(y <= 7e+221))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * -z;
	t_1 = cos(y) * x;
	tmp = 0.0;
	if (y <= -5.2e+84)
		tmp = t_0;
	elseif (y <= -5.8e+21)
		tmp = t_1;
	elseif (y <= -0.015)
		tmp = t_0;
	elseif (y <= 0.23)
		tmp = x - (y * z);
	elseif ((y <= 8.8e+126) || ~((y <= 7e+221)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -5.2e+84], t$95$0, If[LessEqual[y, -5.8e+21], t$95$1, If[LessEqual[y, -0.015], t$95$0, If[LessEqual[y, 0.23], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8.8e+126], N[Not[LessEqual[y, 7e+221]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2000000000000002e84 or -5.8e21 < y < -0.014999999999999999 or 0.23000000000000001 < y < 8.79999999999999994e126 or 7.0000000000000003e221 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 63.2%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \sin y\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 63.2%

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

      2. *-commutative 63.2%

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

      3. distribute-rgt-neg-in 63.2%

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

   5. Simplified 63.2%

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

   if -5.2000000000000002e84 < y < -5.8e21 or 8.79999999999999994e126 < y < 7.0000000000000003e221

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 70.1%

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

   if -0.014999999999999999 < y < 0.23000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.0%

      \[\leadsto \color{blue}{x + -1 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 99.0%

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

      2. unsub-neg 99.0%

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

   5. Simplified 99.0%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+84}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+21}:\\ \;\;\;\;\cos y \cdot x\\ \mathbf{elif}\;y \leq -0.015:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 0.23:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+126} \lor \neg \left(y \leq 7 \cdot 10^{+221}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot \left(-z\right)\\ t_1 := \cos y \cdot x\\ \mathbf{if}\;y \leq -5 \cdot 10^{+83}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1850:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7900000000000:\\ \;\;\;\;t_1 - y \cdot z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+125} \lor \neg \left(y \leq 3.6 \cdot 10^{+220}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) (- z))) (t_1 (* (cos y) x)))
   (if (<= y -5e+83)
     t_0
     (if (<= y -9e+22)
       t_1
       (if (<= y -1850.0)
         t_0
         (if (<= y 7900000000000.0)
           (- t_1 (* y z))
           (if (or (<= y 3.1e+125) (not (<= y 3.6e+220))) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * -z;
	double t_1 = cos(y) * x;
	double tmp;
	if (y <= -5e+83) {
		tmp = t_0;
	} else if (y <= -9e+22) {
		tmp = t_1;
	} else if (y <= -1850.0) {
		tmp = t_0;
	} else if (y <= 7900000000000.0) {
		tmp = t_1 - (y * z);
	} else if ((y <= 3.1e+125) || !(y <= 3.6e+220)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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 = sin(y) * -z
    t_1 = cos(y) * x
    if (y <= (-5d+83)) then
        tmp = t_0
    else if (y <= (-9d+22)) then
        tmp = t_1
    else if (y <= (-1850.0d0)) then
        tmp = t_0
    else if (y <= 7900000000000.0d0) then
        tmp = t_1 - (y * z)
    else if ((y <= 3.1d+125) .or. (.not. (y <= 3.6d+220))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) * -z;
	double t_1 = Math.cos(y) * x;
	double tmp;
	if (y <= -5e+83) {
		tmp = t_0;
	} else if (y <= -9e+22) {
		tmp = t_1;
	} else if (y <= -1850.0) {
		tmp = t_0;
	} else if (y <= 7900000000000.0) {
		tmp = t_1 - (y * z);
	} else if ((y <= 3.1e+125) || !(y <= 3.6e+220)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * -z
	t_1 = math.cos(y) * x
	tmp = 0
	if y <= -5e+83:
		tmp = t_0
	elif y <= -9e+22:
		tmp = t_1
	elif y <= -1850.0:
		tmp = t_0
	elif y <= 7900000000000.0:
		tmp = t_1 - (y * z)
	elif (y <= 3.1e+125) or not (y <= 3.6e+220):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * Float64(-z))
	t_1 = Float64(cos(y) * x)
	tmp = 0.0
	if (y <= -5e+83)
		tmp = t_0;
	elseif (y <= -9e+22)
		tmp = t_1;
	elseif (y <= -1850.0)
		tmp = t_0;
	elseif (y <= 7900000000000.0)
		tmp = Float64(t_1 - Float64(y * z));
	elseif ((y <= 3.1e+125) || !(y <= 3.6e+220))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * -z;
	t_1 = cos(y) * x;
	tmp = 0.0;
	if (y <= -5e+83)
		tmp = t_0;
	elseif (y <= -9e+22)
		tmp = t_1;
	elseif (y <= -1850.0)
		tmp = t_0;
	elseif (y <= 7900000000000.0)
		tmp = t_1 - (y * z);
	elseif ((y <= 3.1e+125) || ~((y <= 3.6e+220)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -5e+83], t$95$0, If[LessEqual[y, -9e+22], t$95$1, If[LessEqual[y, -1850.0], t$95$0, If[LessEqual[y, 7900000000000.0], N[(t$95$1 - N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.1e+125], N[Not[LessEqual[y, 3.6e+220]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.00000000000000029e83 or -8.9999999999999996e22 < y < -1850 or 7.9e12 < y < 3.1e125 or 3.60000000000000019e220 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 64.1%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \sin y\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 64.1%

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

      2. *-commutative 64.1%

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

      3. distribute-rgt-neg-in 64.1%

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

   5. Simplified 64.1%

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

   if -5.00000000000000029e83 < y < -8.9999999999999996e22 or 3.1e125 < y < 3.60000000000000019e220

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 70.1%

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

   if -1850 < y < 7.9e12

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.0%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+83}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+22}:\\ \;\;\;\;\cos y \cdot x\\ \mathbf{elif}\;y \leq -1850:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 7900000000000:\\ \;\;\;\;\cos y \cdot x - y \cdot z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+125} \lor \neg \left(y \leq 3.6 \cdot 10^{+220}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00082 \lor \neg \left(y \leq 0.0065\right):\\ \;\;\;\;\cos y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00082) (not (<= y 0.0065))) (* (cos y) x) (- x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00082) || !(y <= 0.0065)) {
		tmp = cos(y) * x;
	} 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 <= (-0.00082d0)) .or. (.not. (y <= 0.0065d0))) then
        tmp = cos(y) * x
    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 <= -0.00082) || !(y <= 0.0065)) {
		tmp = Math.cos(y) * x;
	} else {
		tmp = x - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00082) or not (y <= 0.0065):
		tmp = math.cos(y) * x
	else:
		tmp = x - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00082) || !(y <= 0.0065))
		tmp = Float64(cos(y) * x);
	else
		tmp = Float64(x - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.00082) || ~((y <= 0.0065)))
		tmp = cos(y) * x;
	else
		tmp = x - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00082], N[Not[LessEqual[y, 0.0065]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.1999999999999998e-4 or 0.0064999999999999997 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 46.8%

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

   if -8.1999999999999998e-4 < y < 0.0064999999999999997

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.5%

      \[\leadsto \color{blue}{x + -1 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

   5. Simplified 99.5%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00082 \lor \neg \left(y \leq 0.0065\right):\\ \;\;\;\;\cos y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.9% accurate, 14.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+217} \lor \neg \left(z \leq 6.6 \cdot 10^{+183}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.7e+217) (not (<= z 6.6e+183))) (* y (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.7e+217) || !(z <= 6.6e+183)) {
		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 ((z <= (-3.7d+217)) .or. (.not. (z <= 6.6d+183))) 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 ((z <= -3.7e+217) || !(z <= 6.6e+183)) {
		tmp = y * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.7e+217) or not (z <= 6.6e+183):
		tmp = y * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.7e+217) || !(z <= 6.6e+183))
		tmp = Float64(y * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.7e+217) || ~((z <= 6.6e+183)))
		tmp = y * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.7e+217], N[Not[LessEqual[z, 6.6e+183]], $MachinePrecision]], N[(y * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.70000000000000011e217 or 6.60000000000000019e183 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 52.4%

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

   4. Taylor expanded in x around 0 40.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 40.2%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

      2. neg-mul-1 40.2%

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

   6. Simplified 40.2%

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

   if -3.70000000000000011e217 < z < 6.60000000000000019e183

   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%

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

      2. fma-neg 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0 45.6%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+217} \lor \neg \left(z \leq 6.6 \cdot 10^{+183}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.8% 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 51.0%

   \[\leadsto \color{blue}{x + -1 \cdot \left(y \cdot z\right)} \]
4. Step-by-step derivation

   1. mul-1-neg 51.0%

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

   2. unsub-neg 51.0%

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

5. Simplified 51.0%

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

6. Final simplification 51.0%

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

Alternative 8: 38.8% 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. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative 99.8%

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

   2. fma-neg 99.8%

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

   3. distribute-rgt-neg-in 99.8%

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

4. Applied egg-rr 99.8%

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

5. Taylor expanded in y around 0 40.5%

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

6. Final simplification 40.5%

   \[\leadsto x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024020 
(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))))