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

Percentage Accurate: 99.8% → 99.8%

Time: 6.7s

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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 74.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ t_1 := x \cdot \cos y\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+56}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.0011:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.215:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))) (t_1 (* x (cos y))))
   (if (<= y -1.55e+56)
     t_0
     (if (<= y -0.0011)
       t_1
       (if (<= y 0.215) (+ x (* y z)) (if (<= y 9.2e+43) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double t_1 = x * cos(y);
	double tmp;
	if (y <= -1.55e+56) {
		tmp = t_0;
	} else if (y <= -0.0011) {
		tmp = t_1;
	} else if (y <= 0.215) {
		tmp = x + (y * z);
	} else if (y <= 9.2e+43) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = z * sin(y)
    t_1 = x * cos(y)
    if (y <= (-1.55d+56)) then
        tmp = t_0
    else if (y <= (-0.0011d0)) then
        tmp = t_1
    else if (y <= 0.215d0) then
        tmp = x + (y * z)
    else if (y <= 9.2d+43) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double t_1 = x * Math.cos(y);
	double tmp;
	if (y <= -1.55e+56) {
		tmp = t_0;
	} else if (y <= -0.0011) {
		tmp = t_1;
	} else if (y <= 0.215) {
		tmp = x + (y * z);
	} else if (y <= 9.2e+43) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	t_1 = x * math.cos(y)
	tmp = 0
	if y <= -1.55e+56:
		tmp = t_0
	elif y <= -0.0011:
		tmp = t_1
	elif y <= 0.215:
		tmp = x + (y * z)
	elif y <= 9.2e+43:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	t_1 = Float64(x * cos(y))
	tmp = 0.0
	if (y <= -1.55e+56)
		tmp = t_0;
	elseif (y <= -0.0011)
		tmp = t_1;
	elseif (y <= 0.215)
		tmp = Float64(x + Float64(y * z));
	elseif (y <= 9.2e+43)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	t_1 = x * cos(y);
	tmp = 0.0;
	if (y <= -1.55e+56)
		tmp = t_0;
	elseif (y <= -0.0011)
		tmp = t_1;
	elseif (y <= 0.215)
		tmp = x + (y * z);
	elseif (y <= 9.2e+43)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+56], t$95$0, If[LessEqual[y, -0.0011], t$95$1, If[LessEqual[y, 0.215], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e+43], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55000000000000002e56 or 9.200000000000001e43 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 67.3%

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

   if -1.55000000000000002e56 < y < -0.00110000000000000007 or 0.214999999999999997 < y < 9.200000000000001e43

   1. Initial program 99.8%

      \[x \cdot \cos y + z \cdot \sin y \]
   2. 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. add-sqr-sqrt 36.5%

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

      4. associate-*r* 36.6%

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

      5. fma-def 36.6%

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

   3. Applied egg-rr 36.6%

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

   4. Taylor expanded in z around 0 77.1%

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

   if -0.00110000000000000007 < y < 0.214999999999999997

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.5%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+56}:\\ \;\;\;\;z \cdot \sin y\\ \mathbf{elif}\;y \leq -0.0011:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq 0.215:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \sin y\\ \end{array} \]

Alternative 3: 83.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+127}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+192}:\\ \;\;\;\;x + z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;t_0 + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))))
   (if (<= x -1.15e+127)
     t_0
     (if (<= x 7.2e+192) (+ x (* z (sin y))) (+ t_0 (* y z))))))

C

double code(double x, double y, double z) {
	double t_0 = x * cos(y);
	double tmp;
	if (x <= -1.15e+127) {
		tmp = t_0;
	} else if (x <= 7.2e+192) {
		tmp = x + (z * sin(y));
	} else {
		tmp = t_0 + (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) :: t_0
    real(8) :: tmp
    t_0 = x * cos(y)
    if (x <= (-1.15d+127)) then
        tmp = t_0
    else if (x <= 7.2d+192) then
        tmp = x + (z * sin(y))
    else
        tmp = t_0 + (y * z)
    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 <= -1.15e+127) {
		tmp = t_0;
	} else if (x <= 7.2e+192) {
		tmp = x + (z * Math.sin(y));
	} else {
		tmp = t_0 + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.cos(y)
	tmp = 0
	if x <= -1.15e+127:
		tmp = t_0
	elif x <= 7.2e+192:
		tmp = x + (z * math.sin(y))
	else:
		tmp = t_0 + (y * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	tmp = 0.0
	if (x <= -1.15e+127)
		tmp = t_0;
	elseif (x <= 7.2e+192)
		tmp = Float64(x + Float64(z * sin(y)));
	else
		tmp = Float64(t_0 + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * cos(y);
	tmp = 0.0;
	if (x <= -1.15e+127)
		tmp = t_0;
	elseif (x <= 7.2e+192)
		tmp = x + (z * sin(y));
	else
		tmp = t_0 + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+127], t$95$0, If[LessEqual[x, 7.2e+192], N[(x + N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1500000000000001e127

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. add-sqr-sqrt 39.4%

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

      4. associate-*r* 39.4%

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

      5. fma-def 39.4%

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

   3. Applied egg-rr 39.4%

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

   4. Taylor expanded in z around 0 90.0%

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

   if -1.1500000000000001e127 < x < 7.2000000000000004e192

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 86.2%

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

   if 7.2000000000000004e192 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.7%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+192}:\\ \;\;\;\;x + z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y + y \cdot z\\ \end{array} \]

Alternative 4: 84.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+128} \lor \neg \left(x \leq 6.5 \cdot 10^{+192}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.8e+128) (not (<= x 6.5e+192)))
   (* x (cos y))
   (+ x (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.8e+128) || !(x <= 6.5e+192)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (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 ((x <= (-4.8d+128)) .or. (.not. (x <= 6.5d+192))) then
        tmp = x * cos(y)
    else
        tmp = x + (z * sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.8e+128) || !(x <= 6.5e+192)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.8e+128) or not (x <= 6.5e+192):
		tmp = x * math.cos(y)
	else:
		tmp = x + (z * math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.8e+128) || !(x <= 6.5e+192))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(z * sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.8e+128) || ~((x <= 6.5e+192)))
		tmp = x * cos(y);
	else
		tmp = x + (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.8e+128], N[Not[LessEqual[x, 6.5e+192]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8000000000000004e128 or 6.50000000000000033e192 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. add-sqr-sqrt 41.2%

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

      4. associate-*r* 41.2%

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

      5. fma-def 41.2%

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

   3. Applied egg-rr 41.2%

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

   4. Taylor expanded in z around 0 92.5%

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

   if -4.8000000000000004e128 < x < 6.50000000000000033e192

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 86.2%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+128} \lor \neg \left(x \leq 6.5 \cdot 10^{+192}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \]

Alternative 5: 75.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.011 \lor \neg \left(y \leq 0.00145\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.011) (not (<= y 0.00145))) (* z (sin y)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.011) || !(y <= 0.00145)) {
		tmp = z * sin(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 <= (-0.011d0)) .or. (.not. (y <= 0.00145d0))) then
        tmp = z * sin(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 <= -0.011) || !(y <= 0.00145)) {
		tmp = z * Math.sin(y);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.011) or not (y <= 0.00145):
		tmp = z * math.sin(y)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.011) || !(y <= 0.00145))
		tmp = Float64(z * sin(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 <= -0.011) || ~((y <= 0.00145)))
		tmp = z * sin(y);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.011], N[Not[LessEqual[y, 0.00145]], $MachinePrecision]], N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.010999999999999999 or 0.00145 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 60.4%

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

   if -0.010999999999999999 < y < 0.00145

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.011 \lor \neg \left(y \leq 0.00145\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 6: 42.1% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+175}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+144}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.6e+175) (* y z) (if (<= z 2.3e+144) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.6e+175) {
		tmp = y * z;
	} else if (z <= 2.3e+144) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-4.6d+175)) then
        tmp = y * z
    else if (z <= 2.3d+144) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.6e+175) {
		tmp = y * z;
	} else if (z <= 2.3e+144) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.6e+175:
		tmp = y * z
	elif z <= 2.3e+144:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.6e+175)
		tmp = Float64(y * z);
	elseif (z <= 2.3e+144)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.6e+175)
		tmp = y * z;
	elseif (z <= 2.3e+144)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.6e+175], N[(y * z), $MachinePrecision], If[LessEqual[z, 2.3e+144], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5999999999999999e175 or 2.3000000000000001e144 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 85.6%

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

   3. Taylor expanded in y around 0 31.1%

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

   if -4.5999999999999999e175 < z < 2.3000000000000001e144

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.4%

         \[\leadsto x \cdot \cos y + \color{blue}{\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}} \]

      2. pow3 99.4%

         \[\leadsto x \cdot \cos y + \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]

   3. Applied egg-rr 99.4%

      \[\leadsto x \cdot \cos y + \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]

   4. Taylor expanded in y around 0 77.5%

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

   5. Taylor expanded in x around inf 52.7%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+175}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+144}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 7: 52.2% 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 99.9%

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

2. Taylor expanded in y around 0 55.4%

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

3. Final simplification 55.4%

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

Alternative 8: 38.9% 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 99.9%

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

   1. add-cube-cbrt 99.1%

      \[\leadsto x \cdot \cos y + \color{blue}{\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}} \]

   2. pow3 99.1%

      \[\leadsto x \cdot \cos y + \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]

3. Applied egg-rr 99.1%

   \[\leadsto x \cdot \cos y + \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]

4. Taylor expanded in y around 0 82.2%

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

5. Taylor expanded in x around inf 43.2%

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

6. Final simplification 43.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023200 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))