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

Percentage Accurate: 99.8% → 99.8%

Time: 6.2s

Alternatives: 9

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. +-commutative 99.7%

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

   2. *-commutative 99.7%

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

   3. fma-def 99.8%

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

3. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

2. Final simplification 99.7%

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

Alternative 3: 75.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot z\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+253}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.052:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-12}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) z)))
   (if (<= y -3.9e+253)
     t_0
     (if (<= y -0.052) (* x (cos y)) (if (<= y 3.4e-12) (+ x (* y z)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * z;
	double tmp;
	if (y <= -3.9e+253) {
		tmp = t_0;
	} else if (y <= -0.052) {
		tmp = x * cos(y);
	} else if (y <= 3.4e-12) {
		tmp = x + (y * z);
	} 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) :: tmp
    t_0 = sin(y) * z
    if (y <= (-3.9d+253)) then
        tmp = t_0
    else if (y <= (-0.052d0)) then
        tmp = x * cos(y)
    else if (y <= 3.4d-12) then
        tmp = x + (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 = Math.sin(y) * z;
	double tmp;
	if (y <= -3.9e+253) {
		tmp = t_0;
	} else if (y <= -0.052) {
		tmp = x * Math.cos(y);
	} else if (y <= 3.4e-12) {
		tmp = x + (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * z
	tmp = 0
	if y <= -3.9e+253:
		tmp = t_0
	elif y <= -0.052:
		tmp = x * math.cos(y)
	elif y <= 3.4e-12:
		tmp = x + (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * z)
	tmp = 0.0
	if (y <= -3.9e+253)
		tmp = t_0;
	elseif (y <= -0.052)
		tmp = Float64(x * cos(y));
	elseif (y <= 3.4e-12)
		tmp = Float64(x + Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * z;
	tmp = 0.0;
	if (y <= -3.9e+253)
		tmp = t_0;
	elseif (y <= -0.052)
		tmp = x * cos(y);
	elseif (y <= 3.4e-12)
		tmp = x + (y * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[y, -3.9e+253], t$95$0, If[LessEqual[y, -0.052], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-12], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9000000000000001e253 or 3.4000000000000001e-12 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 63.0%

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

   if -3.9000000000000001e253 < y < -0.0519999999999999976

   1. Initial program 99.4%

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

   2. Taylor expanded in x around inf 57.4%

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

   if -0.0519999999999999976 < y < 3.4000000000000001e-12

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. +-commutative 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+253}:\\ \;\;\;\;\sin y \cdot z\\ \mathbf{elif}\;y \leq -0.052:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-12}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot z\\ \end{array} \]

Alternative 4: 75.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot z\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+253}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.000155:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) z)))
   (if (<= y -3.6e+253)
     t_0
     (if (<= y -0.000155) (* x (cos y)) (if (<= y 3.4e-12) (fma y z x) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * z;
	double tmp;
	if (y <= -3.6e+253) {
		tmp = t_0;
	} else if (y <= -0.000155) {
		tmp = x * cos(y);
	} else if (y <= 3.4e-12) {
		tmp = fma(y, z, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * z)
	tmp = 0.0
	if (y <= -3.6e+253)
		tmp = t_0;
	elseif (y <= -0.000155)
		tmp = Float64(x * cos(y));
	elseif (y <= 3.4e-12)
		tmp = fma(y, z, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[y, -3.6e+253], t$95$0, If[LessEqual[y, -0.000155], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-12], N[(y * z + x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6e253 or 3.4000000000000001e-12 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 63.0%

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

   if -3.6e253 < y < -1.55e-4

   1. Initial program 99.4%

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

   2. Taylor expanded in x around inf 57.4%

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

   if -1.55e-4 < y < 3.4000000000000001e-12

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-def 100.0%

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

   4. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z, x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+253}:\\ \;\;\;\;\sin y \cdot z\\ \mathbf{elif}\;y \leq -0.000155:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot z\\ \end{array} \]

Alternative 5: 85.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-9} \lor \neg \left(x \leq 6.2 \cdot 10^{+38}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.55e-9) (not (<= x 6.2e+38)))
   (* x (cos y))
   (+ x (* (sin y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.55e-9) || !(x <= 6.2e+38)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (sin(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 ((x <= (-1.55d-9)) .or. (.not. (x <= 6.2d+38))) then
        tmp = x * cos(y)
    else
        tmp = x + (sin(y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.55e-9) || !(x <= 6.2e+38)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (Math.sin(y) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.55e-9) or not (x <= 6.2e+38):
		tmp = x * math.cos(y)
	else:
		tmp = x + (math.sin(y) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.55e-9) || !(x <= 6.2e+38))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(sin(y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.55e-9) || ~((x <= 6.2e+38)))
		tmp = x * cos(y);
	else
		tmp = x + (sin(y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.55e-9], N[Not[LessEqual[x, 6.2e+38]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000002e-9 or 6.20000000000000035e38 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 85.9%

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

   if -1.55000000000000002e-9 < x < 6.20000000000000035e38

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 93.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-9} \lor \neg \left(x \leq 6.2 \cdot 10^{+38}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y \cdot z\\ \end{array} \]

Alternative 6: 74.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00032 \lor \neg \left(y \leq 0.029\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00032) (not (<= y 0.029))) (* x (cos y)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00032) || !(y <= 0.029)) {
		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 <= (-0.00032d0)) .or. (.not. (y <= 0.029d0))) 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 <= -0.00032) || !(y <= 0.029)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00032) or not (y <= 0.029):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00032) || !(y <= 0.029))
		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 <= -0.00032) || ~((y <= 0.029)))
		tmp = x * cos(y);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00032], N[Not[LessEqual[y, 0.029]], $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 < -3.20000000000000026e-4 or 0.0290000000000000015 < y

   1. Initial program 99.5%

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

   2. Taylor expanded in x around inf 49.1%

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

   if -3.20000000000000026e-4 < y < 0.0290000000000000015

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.5%

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

      1. +-commutative 99.5%

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

   4. Simplified 99.5%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00032 \lor \neg \left(y \leq 0.029\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 7: 40.5% accurate, 18.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-155} \lor \neg \left(x \leq -7.5 \cdot 10^{-227}\right) \land x \leq 3.2 \cdot 10^{-35}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.8e-138)
   x
   (if (or (<= x -1.25e-155) (and (not (<= x -7.5e-227)) (<= x 3.2e-35)))
     (* y z)
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.8e-138) {
		tmp = x;
	} else if ((x <= -1.25e-155) || (!(x <= -7.5e-227) && (x <= 3.2e-35))) {
		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 <= (-7.8d-138)) then
        tmp = x
    else if ((x <= (-1.25d-155)) .or. (.not. (x <= (-7.5d-227))) .and. (x <= 3.2d-35)) 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 <= -7.8e-138) {
		tmp = x;
	} else if ((x <= -1.25e-155) || (!(x <= -7.5e-227) && (x <= 3.2e-35))) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.8e-138:
		tmp = x
	elif (x <= -1.25e-155) or (not (x <= -7.5e-227) and (x <= 3.2e-35)):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.8e-138)
		tmp = x;
	elseif ((x <= -1.25e-155) || (!(x <= -7.5e-227) && (x <= 3.2e-35)))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.8e-138)
		tmp = x;
	elseif ((x <= -1.25e-155) || (~((x <= -7.5e-227)) && (x <= 3.2e-35)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.8e-138], x, If[Or[LessEqual[x, -1.25e-155], And[N[Not[LessEqual[x, -7.5e-227]], $MachinePrecision], LessEqual[x, 3.2e-35]]], N[(y * z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.7999999999999999e-138 or -1.25e-155 < x < -7.49999999999999988e-227 or 3.1999999999999998e-35 < x

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-def 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in y around 0 46.9%

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

   if -7.7999999999999999e-138 < x < -1.25e-155 or -7.49999999999999988e-227 < x < 3.1999999999999998e-35

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 59.8%

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

      1. +-commutative 59.8%

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

   4. Simplified 59.8%

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

   5. Taylor expanded in y around inf 43.2%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-155} \lor \neg \left(x \leq -7.5 \cdot 10^{-227}\right) \land x \leq 3.2 \cdot 10^{-35}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 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 99.7%

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

2. Taylor expanded in y around 0 54.0%

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

   1. +-commutative 54.0%

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

4. Simplified 54.0%

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

5. Final simplification 54.0%

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

Alternative 9: 38.3% 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 99.7%

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

   1. +-commutative 99.7%

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

   2. *-commutative 99.7%

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

   3. fma-def 99.8%

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

3. Applied egg-rr 99.8%

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

4. Taylor expanded in y around 0 38.3%

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

5. Final simplification 38.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023332 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))