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

Percentage Accurate: 99.8% → 99.8%

Time: 8.5s

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, 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]

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 2: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+96} \lor \neg \left(z \leq 2.7 \cdot 10^{+141}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\sin y, x, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.4e+96) (not (<= z 2.7e+141)))
   (* z (cos y))
   (fma (sin y) x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.4e+96) || !(z <= 2.7e+141)) {
		tmp = z * cos(y);
	} else {
		tmp = fma(sin(y), x, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.4e+96) || !(z <= 2.7e+141))
		tmp = Float64(z * cos(y));
	else
		tmp = fma(sin(y), x, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.4e+96], N[Not[LessEqual[z, 2.7e+141]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] * x + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3999999999999998e96 or 2.7000000000000001e141 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 75.0%

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

      1. *-commutative 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in x around 0 90.1%

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

   if -4.3999999999999998e96 < z < 2.7000000000000001e141

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 90.3%

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

      1. *-commutative 90.3%

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

      2. fma-def 90.3%

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

   5. Applied egg-rr 90.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, x, z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+96} \lor \neg \left(z \leq 2.7 \cdot 10^{+141}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\sin y, x, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \sin y\\ \mathbf{if}\;y \leq -0.0019:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.9 \cdot 10^{-16}:\\ \;\;\;\;z + x \cdot y\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{+131} \lor \neg \left(y \leq 3 \cdot 10^{+156}\right) \land y \leq 4.8 \cdot 10^{+248}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (sin y))))
   (if (<= y -0.0019)
     t_0
     (if (<= y 7.9e-16)
       (+ z (* x y))
       (if (or (<= y 3.15e+131) (and (not (<= y 3e+156)) (<= y 4.8e+248)))
         (* z (cos y))
         t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * sin(y);
	double tmp;
	if (y <= -0.0019) {
		tmp = t_0;
	} else if (y <= 7.9e-16) {
		tmp = z + (x * y);
	} else if ((y <= 3.15e+131) || (!(y <= 3e+156) && (y <= 4.8e+248))) {
		tmp = z * cos(y);
	} 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 = x * sin(y)
    if (y <= (-0.0019d0)) then
        tmp = t_0
    else if (y <= 7.9d-16) then
        tmp = z + (x * y)
    else if ((y <= 3.15d+131) .or. (.not. (y <= 3d+156)) .and. (y <= 4.8d+248)) then
        tmp = z * cos(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.sin(y);
	double tmp;
	if (y <= -0.0019) {
		tmp = t_0;
	} else if (y <= 7.9e-16) {
		tmp = z + (x * y);
	} else if ((y <= 3.15e+131) || (!(y <= 3e+156) && (y <= 4.8e+248))) {
		tmp = z * Math.cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.sin(y)
	tmp = 0
	if y <= -0.0019:
		tmp = t_0
	elif y <= 7.9e-16:
		tmp = z + (x * y)
	elif (y <= 3.15e+131) or (not (y <= 3e+156) and (y <= 4.8e+248)):
		tmp = z * math.cos(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * sin(y))
	tmp = 0.0
	if (y <= -0.0019)
		tmp = t_0;
	elseif (y <= 7.9e-16)
		tmp = Float64(z + Float64(x * y));
	elseif ((y <= 3.15e+131) || (!(y <= 3e+156) && (y <= 4.8e+248)))
		tmp = Float64(z * cos(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * sin(y);
	tmp = 0.0;
	if (y <= -0.0019)
		tmp = t_0;
	elseif (y <= 7.9e-16)
		tmp = z + (x * y);
	elseif ((y <= 3.15e+131) || (~((y <= 3e+156)) && (y <= 4.8e+248)))
		tmp = z * cos(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.0019], t$95$0, If[LessEqual[y, 7.9e-16], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.15e+131], And[N[Not[LessEqual[y, 3e+156]], $MachinePrecision], LessEqual[y, 4.8e+248]]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0019 or 3.14999999999999998e131 < y < 3e156 or 4.8e248 < y

   1. Initial program 99.5%

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

      1. add-cube-cbrt 98.4%

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

      2. pow3 98.4%

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

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in y around 0 66.6%

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

   6. Taylor expanded in z around 0 64.6%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \sin y\right)} \]
   7. Step-by-step derivation

      1. pow-base-1 64.6%

         \[\leadsto \color{blue}{1} \cdot \left(x \cdot \sin y\right) \]

      2. *-lft-identity 64.6%

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

   8. Simplified 64.6%

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

   if -0.0019 < y < 7.9000000000000002e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 99.1%

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

   if 7.9000000000000002e-16 < y < 3.14999999999999998e131 or 3e156 < y < 4.8e248

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 46.3%

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

      1. *-commutative 46.3%

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

   5. Simplified 46.3%

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

   6. Taylor expanded in x around 0 64.4%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0019:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;y \leq 7.9 \cdot 10^{-16}:\\ \;\;\;\;z + x \cdot y\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{+131} \lor \neg \left(y \leq 3 \cdot 10^{+156}\right) \land y \leq 4.8 \cdot 10^{+248}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+96} \lor \neg \left(z \leq 2.9 \cdot 10^{+140}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.8e+96) (not (<= z 2.9e+140)))
   (* z (cos y))
   (+ (* x (sin y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e+96) || !(z <= 2.9e+140)) {
		tmp = z * 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 ((z <= (-1.8d+96)) .or. (.not. (z <= 2.9d+140))) then
        tmp = z * 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 ((z <= -1.8e+96) || !(z <= 2.9e+140)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = (x * Math.sin(y)) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.8e+96) or not (z <= 2.9e+140):
		tmp = z * math.cos(y)
	else:
		tmp = (x * math.sin(y)) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.8e+96) || !(z <= 2.9e+140))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(Float64(x * sin(y)) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.8e+96) || ~((z <= 2.9e+140)))
		tmp = z * cos(y);
	else
		tmp = (x * sin(y)) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.8e+96], N[Not[LessEqual[z, 2.9e+140]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.80000000000000007e96 or 2.8999999999999999e140 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 75.0%

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

      1. *-commutative 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in x around 0 90.1%

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

   if -1.80000000000000007e96 < z < 2.8999999999999999e140

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 90.3%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+96} \lor \neg \left(z \leq 2.9 \cdot 10^{+140}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y + z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0076 \lor \neg \left(y \leq 550\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0076) (not (<= y 550.0))) (* x (sin y)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0076) || !(y <= 550.0)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (x * 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 ((y <= (-0.0076d0)) .or. (.not. (y <= 550.0d0))) then
        tmp = x * sin(y)
    else
        tmp = z + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0076) || !(y <= 550.0)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0076) or not (y <= 550.0):
		tmp = x * math.sin(y)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0076) || !(y <= 550.0))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0076) || ~((y <= 550.0)))
		tmp = x * sin(y);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0076], N[Not[LessEqual[y, 550.0]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00759999999999999998 or 550 < y

   1. Initial program 99.6%

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

      1. add-cube-cbrt 98.6%

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

      2. pow3 98.6%

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

   4. Applied egg-rr 98.6%

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

   5. Taylor expanded in y around 0 61.1%

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

   6. Taylor expanded in z around 0 58.0%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot \sin y\right)} \]
   7. Step-by-step derivation

      1. pow-base-1 58.0%

         \[\leadsto \color{blue}{1} \cdot \left(x \cdot \sin y\right) \]

      2. *-lft-identity 58.0%

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

   8. Simplified 58.0%

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

   if -0.00759999999999999998 < y < 550

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 97.7%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0076 \lor \neg \left(y \leq 550\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.4% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+149} \lor \neg \left(x \leq 2.45 \cdot 10^{+113}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.4e+149) (not (<= x 2.45e+113))) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.4e+149) || !(x <= 2.45e+113)) {
		tmp = x * y;
	} 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 ((x <= (-4.4d+149)) .or. (.not. (x <= 2.45d+113))) then
        tmp = x * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.4e+149) || !(x <= 2.45e+113)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.4e+149) or not (x <= 2.45e+113):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.4e+149) || !(x <= 2.45e+113))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.4e+149) || ~((x <= 2.45e+113)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.4e+149], N[Not[LessEqual[x, 2.45e+113]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -4.4e149 or 2.45000000000000011e113 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 47.1%

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

      1. *-commutative 47.1%

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

   5. Simplified 47.1%

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

   6. Taylor expanded in y around inf 32.5%

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

   if -4.4e149 < x < 2.45000000000000011e113

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 73.6%

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

   4. Taylor expanded in x around 0 49.3%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+149} \lor \neg \left(x \leq 2.45 \cdot 10^{+113}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.0% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around 0 63.8%

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

   1. *-commutative 63.8%

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

5. Simplified 63.8%

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

6. Taylor expanded in y around 0 52.1%

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

7. Final simplification 52.1%

   \[\leadsto z + x \cdot y \]
8. Add Preprocessing

Alternative 8: 38.5% 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. Add Preprocessing

3. Taylor expanded in y around 0 80.0%

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

4. Taylor expanded in x around 0 38.8%

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

5. Final simplification 38.8%

   \[\leadsto z \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024023 
(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))))