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

Percentage Accurate: 99.8% → 99.8%

Time: 8.2s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. *-commutative 99.8%

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

   3. fma-def 99.8%

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

3. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 3: 74.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \sin y\\ t_1 := \cos y \cdot z\\ \mathbf{if}\;y \leq -1.16 \cdot 10^{+67}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.028:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.00039:\\ \;\;\;\;z + \left(-0.5 \cdot \left(z \cdot {y}^{2}\right) + y \cdot x\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+88}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (sin y))) (t_1 (* (cos y) z)))
   (if (<= y -1.16e+67)
     t_0
     (if (<= y -0.028)
       t_1
       (if (<= y 0.00039)
         (+ z (+ (* -0.5 (* z (pow y 2.0))) (* y x)))
         (if (<= y 4.1e+88) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * sin(y);
	double t_1 = cos(y) * z;
	double tmp;
	if (y <= -1.16e+67) {
		tmp = t_0;
	} else if (y <= -0.028) {
		tmp = t_1;
	} else if (y <= 0.00039) {
		tmp = z + ((-0.5 * (z * pow(y, 2.0))) + (y * x));
	} else if (y <= 4.1e+88) {
		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 = x * sin(y)
    t_1 = cos(y) * z
    if (y <= (-1.16d+67)) then
        tmp = t_0
    else if (y <= (-0.028d0)) then
        tmp = t_1
    else if (y <= 0.00039d0) then
        tmp = z + (((-0.5d0) * (z * (y ** 2.0d0))) + (y * x))
    else if (y <= 4.1d+88) 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 = x * Math.sin(y);
	double t_1 = Math.cos(y) * z;
	double tmp;
	if (y <= -1.16e+67) {
		tmp = t_0;
	} else if (y <= -0.028) {
		tmp = t_1;
	} else if (y <= 0.00039) {
		tmp = z + ((-0.5 * (z * Math.pow(y, 2.0))) + (y * x));
	} else if (y <= 4.1e+88) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.sin(y)
	t_1 = math.cos(y) * z
	tmp = 0
	if y <= -1.16e+67:
		tmp = t_0
	elif y <= -0.028:
		tmp = t_1
	elif y <= 0.00039:
		tmp = z + ((-0.5 * (z * math.pow(y, 2.0))) + (y * x))
	elif y <= 4.1e+88:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * sin(y))
	t_1 = Float64(cos(y) * z)
	tmp = 0.0
	if (y <= -1.16e+67)
		tmp = t_0;
	elseif (y <= -0.028)
		tmp = t_1;
	elseif (y <= 0.00039)
		tmp = Float64(z + Float64(Float64(-0.5 * Float64(z * (y ^ 2.0))) + Float64(y * x)));
	elseif (y <= 4.1e+88)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * sin(y);
	t_1 = cos(y) * z;
	tmp = 0.0;
	if (y <= -1.16e+67)
		tmp = t_0;
	elseif (y <= -0.028)
		tmp = t_1;
	elseif (y <= 0.00039)
		tmp = z + ((-0.5 * (z * (y ^ 2.0))) + (y * x));
	elseif (y <= 4.1e+88)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[y, -1.16e+67], t$95$0, If[LessEqual[y, -0.028], t$95$1, If[LessEqual[y, 0.00039], N[(z + N[(N[(-0.5 * N[(z * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+88], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15999999999999994e67 or 3.89999999999999993e-4 < y < 4.10000000000000028e88

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 63.5%

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

   if -1.15999999999999994e67 < y < -0.0280000000000000006 or 4.10000000000000028e88 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 64.5%

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

   if -0.0280000000000000006 < y < 3.89999999999999993e-4

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;y \leq -0.028:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;y \leq 0.00039:\\ \;\;\;\;z + \left(-0.5 \cdot \left(z \cdot {y}^{2}\right) + y \cdot x\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]

Alternative 4: 73.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \sin y\\ t_1 := \cos y \cdot z\\ \mathbf{if}\;y \leq -4 \cdot 10^{+66}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.00043:\\ \;\;\;\;z + y \cdot x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+88}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (sin y))) (t_1 (* (cos y) z)))
   (if (<= y -4e+66)
     t_0
     (if (<= y -5.5e-8)
       t_1
       (if (<= y 0.00043) (+ z (* y x)) (if (<= y 3.1e+88) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * sin(y);
	double t_1 = cos(y) * z;
	double tmp;
	if (y <= -4e+66) {
		tmp = t_0;
	} else if (y <= -5.5e-8) {
		tmp = t_1;
	} else if (y <= 0.00043) {
		tmp = z + (y * x);
	} else if (y <= 3.1e+88) {
		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 = x * sin(y)
    t_1 = cos(y) * z
    if (y <= (-4d+66)) then
        tmp = t_0
    else if (y <= (-5.5d-8)) then
        tmp = t_1
    else if (y <= 0.00043d0) then
        tmp = z + (y * x)
    else if (y <= 3.1d+88) 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 = x * Math.sin(y);
	double t_1 = Math.cos(y) * z;
	double tmp;
	if (y <= -4e+66) {
		tmp = t_0;
	} else if (y <= -5.5e-8) {
		tmp = t_1;
	} else if (y <= 0.00043) {
		tmp = z + (y * x);
	} else if (y <= 3.1e+88) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.sin(y)
	t_1 = math.cos(y) * z
	tmp = 0
	if y <= -4e+66:
		tmp = t_0
	elif y <= -5.5e-8:
		tmp = t_1
	elif y <= 0.00043:
		tmp = z + (y * x)
	elif y <= 3.1e+88:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * sin(y))
	t_1 = Float64(cos(y) * z)
	tmp = 0.0
	if (y <= -4e+66)
		tmp = t_0;
	elseif (y <= -5.5e-8)
		tmp = t_1;
	elseif (y <= 0.00043)
		tmp = Float64(z + Float64(y * x));
	elseif (y <= 3.1e+88)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * sin(y);
	t_1 = cos(y) * z;
	tmp = 0.0;
	if (y <= -4e+66)
		tmp = t_0;
	elseif (y <= -5.5e-8)
		tmp = t_1;
	elseif (y <= 0.00043)
		tmp = z + (y * x);
	elseif (y <= 3.1e+88)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[y, -4e+66], t$95$0, If[LessEqual[y, -5.5e-8], t$95$1, If[LessEqual[y, 0.00043], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+88], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.99999999999999978e66 or 4.29999999999999989e-4 < y < 3.1000000000000001e88

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 63.5%

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

   if -3.99999999999999978e66 < y < -5.5000000000000003e-8 or 3.1000000000000001e88 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 65.7%

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

   if -5.5000000000000003e-8 < y < 4.29999999999999989e-4

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.5%

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

      1. *-commutative 99.5%

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

   4. Simplified 99.5%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;y \leq 0.00043:\\ \;\;\;\;z + y \cdot x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]

Alternative 5: 73.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -42000 \lor \neg \left(y \leq 0.00175\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -42000.0) (not (<= y 0.00175))) (* x (sin y)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -42000.0) || !(y <= 0.00175)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (y * 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 ((y <= (-42000.0d0)) .or. (.not. (y <= 0.00175d0))) then
        tmp = x * sin(y)
    else
        tmp = z + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -42000.0) || !(y <= 0.00175)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -42000.0) or not (y <= 0.00175):
		tmp = x * math.sin(y)
	else:
		tmp = z + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -42000.0) || !(y <= 0.00175))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -42000.0) || ~((y <= 0.00175)))
		tmp = x * sin(y);
	else
		tmp = z + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -42000.0], N[Not[LessEqual[y, 0.00175]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -42000 or 0.00175000000000000004 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 52.2%

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

   if -42000 < y < 0.00175000000000000004

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.9%

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

      1. *-commutative 97.9%

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

   4. Simplified 97.9%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -42000 \lor \neg \left(y \leq 0.00175\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]

Alternative 6: 41.1% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-82}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-172}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.2e-82) z (if (<= z 4e-172) (* y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.2e-82) {
		tmp = z;
	} else if (z <= 4e-172) {
		tmp = y * x;
	} else {
		tmp = 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 <= (-1.2d-82)) then
        tmp = z
    else if (z <= 4d-172) then
        tmp = y * x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.2e-82) {
		tmp = z;
	} else if (z <= 4e-172) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.2e-82:
		tmp = z
	elif z <= 4e-172:
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.2e-82)
		tmp = z;
	elseif (z <= 4e-172)
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.2e-82)
		tmp = z;
	elseif (z <= 4e-172)
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.2e-82], z, If[LessEqual[z, 4e-172], N[(y * x), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000004e-82 or 4.0000000000000002e-172 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. fma-def 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in y around 0 46.3%

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

   if -1.20000000000000004e-82 < z < 4.0000000000000002e-172

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 58.2%

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

      1. *-commutative 58.2%

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

   4. Simplified 58.2%

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

   5. Taylor expanded in z around 0 44.6%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-82}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-172}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 7: 51.7% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 54.4%

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

   1. *-commutative 54.4%

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

4. Simplified 54.4%

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

5. Final simplification 54.4%

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

Alternative 8: 38.2% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. *-commutative 99.8%

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

   3. fma-def 99.8%

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

3. Applied egg-rr 99.8%

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

4. Taylor expanded in y around 0 36.5%

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

5. Final simplification 36.5%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023311 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))