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

Percentage Accurate: 99.8% → 99.8%

Time: 9.4s

Alternatives: 10

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. cancel-sign-sub-inv 99.8%

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

   2. +-commutative 99.8%

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

   3. distribute-lft-neg-out 99.8%

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

   4. distribute-rgt-neg-in 99.8%

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

   5. sin-neg 99.8%

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

   6. fma-def 99.8%

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

   7. sin-neg 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{-114} \lor \neg \left(z \leq 6.6 \cdot 10^{-160}\right):\\ \;\;\;\;\mathsf{fma}\left(z, -\sin y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.3e-114) (not (<= z 6.6e-160)))
   (fma z (- (sin y)) x)
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.3e-114) || !(z <= 6.6e-160)) {
		tmp = fma(z, -sin(y), x);
	} else {
		tmp = x * cos(y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.3e-114) || !(z <= 6.6e-160))
		tmp = fma(z, Float64(-sin(y)), x);
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.3e-114], N[Not[LessEqual[z, 6.6e-160]], $MachinePrecision]], N[(z * (-N[Sin[y], $MachinePrecision]) + x), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.30000000000000014e-114 or 6.6e-160 < z

   1. Initial program 99.9%

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

      1. cancel-sign-sub-inv 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-lft-neg-out 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. sin-neg 99.9%

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

      6. fma-def 99.9%

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

      7. sin-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 85.6%

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

   if -6.30000000000000014e-114 < z < 6.6e-160

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 94.3%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{-114} \lor \neg \left(z \leq 6.6 \cdot 10^{-160}\right):\\ \;\;\;\;\mathsf{fma}\left(z, -\sin y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 3: 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]

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 4: 73.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ t_1 := \sin y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+66}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.0068:\\ \;\;\;\;x - z \cdot y\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+88}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))) (t_1 (* (sin y) (- z))))
   (if (<= y -3.8e+66)
     t_0
     (if (<= y -5.5e-8)
       t_1
       (if (<= y 0.0068) (- x (* z y)) (if (<= y 3.7e+88) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * cos(y);
	double t_1 = sin(y) * -z;
	double tmp;
	if (y <= -3.8e+66) {
		tmp = t_0;
	} else if (y <= -5.5e-8) {
		tmp = t_1;
	} else if (y <= 0.0068) {
		tmp = x - (z * y);
	} else if (y <= 3.7e+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 * cos(y)
    t_1 = sin(y) * -z
    if (y <= (-3.8d+66)) then
        tmp = t_0
    else if (y <= (-5.5d-8)) then
        tmp = t_1
    else if (y <= 0.0068d0) then
        tmp = x - (z * y)
    else if (y <= 3.7d+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.cos(y);
	double t_1 = Math.sin(y) * -z;
	double tmp;
	if (y <= -3.8e+66) {
		tmp = t_0;
	} else if (y <= -5.5e-8) {
		tmp = t_1;
	} else if (y <= 0.0068) {
		tmp = x - (z * y);
	} else if (y <= 3.7e+88) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.cos(y)
	t_1 = math.sin(y) * -z
	tmp = 0
	if y <= -3.8e+66:
		tmp = t_0
	elif y <= -5.5e-8:
		tmp = t_1
	elif y <= 0.0068:
		tmp = x - (z * y)
	elif y <= 3.7e+88:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	t_1 = Float64(sin(y) * Float64(-z))
	tmp = 0.0
	if (y <= -3.8e+66)
		tmp = t_0;
	elseif (y <= -5.5e-8)
		tmp = t_1;
	elseif (y <= 0.0068)
		tmp = Float64(x - Float64(z * y));
	elseif (y <= 3.7e+88)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * cos(y);
	t_1 = sin(y) * -z;
	tmp = 0.0;
	if (y <= -3.8e+66)
		tmp = t_0;
	elseif (y <= -5.5e-8)
		tmp = t_1;
	elseif (y <= 0.0068)
		tmp = x - (z * y);
	elseif (y <= 3.7e+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[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[y, -3.8e+66], t$95$0, If[LessEqual[y, -5.5e-8], t$95$1, If[LessEqual[y, 0.0068], N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e+88], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000002e66 or 0.00679999999999999962 < y < 3.69999999999999994e88

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 63.1%

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

   if -3.8000000000000002e66 < y < -5.5000000000000003e-8 or 3.69999999999999994e88 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 66.0%

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

      1. neg-mul-1 66.0%

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

      2. distribute-rgt-neg-in 66.0%

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

   4. Simplified 66.0%

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

   if -5.5000000000000003e-8 < y < 0.00679999999999999962

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.6%

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

      1. mul-1-neg 99.6%

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

      2. unsub-neg 99.6%

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

   4. Simplified 99.6%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 0.0068:\\ \;\;\;\;x - z \cdot y\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \end{array} \]

Alternative 5: 73.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ t_1 := \sin y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -3.15 \cdot 10^{+66}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.0068:\\ \;\;\;\;\mathsf{fma}\left(-z, y, x\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+88}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))) (t_1 (* (sin y) (- z))))
   (if (<= y -3.15e+66)
     t_0
     (if (<= y -5.5e-8)
       t_1
       (if (<= y 0.0068) (fma (- z) y x) (if (<= y 3.5e+88) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * cos(y);
	double t_1 = sin(y) * -z;
	double tmp;
	if (y <= -3.15e+66) {
		tmp = t_0;
	} else if (y <= -5.5e-8) {
		tmp = t_1;
	} else if (y <= 0.0068) {
		tmp = fma(-z, y, x);
	} else if (y <= 3.5e+88) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	t_1 = Float64(sin(y) * Float64(-z))
	tmp = 0.0
	if (y <= -3.15e+66)
		tmp = t_0;
	elseif (y <= -5.5e-8)
		tmp = t_1;
	elseif (y <= 0.0068)
		tmp = fma(Float64(-z), y, x);
	elseif (y <= 3.5e+88)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[y, -3.15e+66], t$95$0, If[LessEqual[y, -5.5e-8], t$95$1, If[LessEqual[y, 0.0068], N[((-z) * y + x), $MachinePrecision], If[LessEqual[y, 3.5e+88], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1499999999999999e66 or 0.00679999999999999962 < y < 3.4999999999999998e88

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 63.1%

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

   if -3.1499999999999999e66 < y < -5.5000000000000003e-8 or 3.4999999999999998e88 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 66.0%

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

      1. neg-mul-1 66.0%

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

      2. distribute-rgt-neg-in 66.0%

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

   4. Simplified 66.0%

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

   if -5.5000000000000003e-8 < y < 0.00679999999999999962

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.6%

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

      1. mul-1-neg 99.6%

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

      2. unsub-neg 99.6%

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

   4. Simplified 99.6%

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

      1. sub-neg 99.6%

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

      2. +-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. distribute-lft-neg-in 99.6%

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

      5. fma-def 99.6%

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

   6. Applied egg-rr 99.6%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-8}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 0.0068:\\ \;\;\;\;\mathsf{fma}\left(-z, y, x\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \end{array} \]

Alternative 6: 85.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-114} \lor \neg \left(z \leq 7.2 \cdot 10^{-160}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.8e-114) (not (<= z 7.2e-160)))
   (- x (* z (sin y)))
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.8e-114) || !(z <= 7.2e-160)) {
		tmp = x - (z * sin(y));
	} else {
		tmp = x * cos(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 ((z <= (-7.8d-114)) .or. (.not. (z <= 7.2d-160))) then
        tmp = x - (z * sin(y))
    else
        tmp = x * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.8e-114) || !(z <= 7.2e-160)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.8e-114) or not (z <= 7.2e-160):
		tmp = x - (z * math.sin(y))
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.8e-114) || !(z <= 7.2e-160))
		tmp = Float64(x - Float64(z * sin(y)));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.8e-114) || ~((z <= 7.2e-160)))
		tmp = x - (z * sin(y));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.8e-114], N[Not[LessEqual[z, 7.2e-160]], $MachinePrecision]], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.80000000000000003e-114 or 7.1999999999999994e-160 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 85.6%

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

   if -7.80000000000000003e-114 < z < 7.1999999999999994e-160

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 94.3%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-114} \lor \neg \left(z \leq 7.2 \cdot 10^{-160}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 7: 73.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -42000 \lor \neg \left(y \leq 0.0068\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -42000.0) (not (<= y 0.0068))) (* x (cos y)) (- x (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -42000.0) || !(y <= 0.0068)) {
		tmp = x * cos(y);
	} else {
		tmp = x - (z * 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 <= (-42000.0d0)) .or. (.not. (y <= 0.0068d0))) then
        tmp = x * cos(y)
    else
        tmp = x - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -42000.0) || !(y <= 0.0068)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -42000.0) or not (y <= 0.0068):
		tmp = x * math.cos(y)
	else:
		tmp = x - (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -42000.0) || !(y <= 0.0068))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -42000.0) || ~((y <= 0.0068)))
		tmp = x * cos(y);
	else
		tmp = x - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -42000.0], N[Not[LessEqual[y, 0.0068]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -42000 or 0.00679999999999999962 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 51.8%

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

   if -42000 < y < 0.00679999999999999962

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.9%

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

      1. mul-1-neg 97.9%

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

      2. unsub-neg 97.9%

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

   4. Simplified 97.9%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -42000 \lor \neg \left(y \leq 0.0068\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot y\\ \end{array} \]

Alternative 8: 38.5% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.8 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 2.8e+27) x (* z (- y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.8e+27) {
		tmp = x;
	} else {
		tmp = z * -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 (z <= 2.8d+27) then
        tmp = x
    else
        tmp = z * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.8e+27) {
		tmp = x;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2.8e+27:
		tmp = x
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2.8e+27)
		tmp = x;
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 2.8e+27)
		tmp = x;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2.8e+27], x, N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.7999999999999999e27

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 58.2%

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

      1. mul-1-neg 58.2%

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

      2. unsub-neg 58.2%

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

   4. Simplified 58.2%

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

   5. Taylor expanded in x around inf 48.7%

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

   if 2.7999999999999999e27 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 38.7%

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

      1. mul-1-neg 38.7%

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

      2. unsub-neg 38.7%

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

   4. Simplified 38.7%

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

   5. Taylor expanded in x around 0 27.3%

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

      1. mul-1-neg 27.3%

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

      2. distribute-rgt-neg-in 27.3%

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

   7. Simplified 27.3%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.8 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]

Alternative 9: 51.8% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 54.2%

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

   1. mul-1-neg 54.2%

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

   2. unsub-neg 54.2%

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

4. Simplified 54.2%

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

5. Final simplification 54.2%

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

Alternative 10: 38.6% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 54.2%

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

   1. mul-1-neg 54.2%

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

   2. unsub-neg 54.2%

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

4. Simplified 54.2%

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

5. Taylor expanded in x around inf 41.8%

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

6. Final simplification 41.8%

   \[\leadsto x \]

Reproduce

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