Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B

Percentage Accurate: 100.0% → 100.0%

Time: 3.5s

Alternatives: 5

Speedup: 1.0×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot z \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot z \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot z \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - x\right) \cdot z \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 76.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+257} \lor \neg \left(z \leq -3.9 \cdot 10^{+200} \lor \neg \left(z \leq -1.2 \cdot 10^{+169}\right) \land \left(z \leq -2.25 \cdot 10^{+115} \lor \neg \left(z \leq 4.1 \cdot 10^{+18}\right) \land z \leq 5 \cdot 10^{+122}\right)\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.8e+257)
         (not
          (or (<= z -3.9e+200)
              (and (not (<= z -1.2e+169))
                   (or (<= z -2.25e+115)
                       (and (not (<= z 4.1e+18)) (<= z 5e+122)))))))
   (+ x (* y z))
   (* x (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e+257) || !((z <= -3.9e+200) || (!(z <= -1.2e+169) && ((z <= -2.25e+115) || (!(z <= 4.1e+18) && (z <= 5e+122)))))) {
		tmp = x + (y * z);
	} else {
		tmp = x * -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 <= (-5.8d+257)) .or. (.not. (z <= (-3.9d+200)) .or. (.not. (z <= (-1.2d+169))) .and. (z <= (-2.25d+115)) .or. (.not. (z <= 4.1d+18)) .and. (z <= 5d+122))) then
        tmp = x + (y * z)
    else
        tmp = x * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e+257) || !((z <= -3.9e+200) || (!(z <= -1.2e+169) && ((z <= -2.25e+115) || (!(z <= 4.1e+18) && (z <= 5e+122)))))) {
		tmp = x + (y * z);
	} else {
		tmp = x * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.8e+257) or not ((z <= -3.9e+200) or (not (z <= -1.2e+169) and ((z <= -2.25e+115) or (not (z <= 4.1e+18) and (z <= 5e+122))))):
		tmp = x + (y * z)
	else:
		tmp = x * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.8e+257) || !((z <= -3.9e+200) || (!(z <= -1.2e+169) && ((z <= -2.25e+115) || (!(z <= 4.1e+18) && (z <= 5e+122))))))
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.8e+257) || ~(((z <= -3.9e+200) || (~((z <= -1.2e+169)) && ((z <= -2.25e+115) || (~((z <= 4.1e+18)) && (z <= 5e+122)))))))
		tmp = x + (y * z);
	else
		tmp = x * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.8e+257], N[Not[Or[LessEqual[z, -3.9e+200], And[N[Not[LessEqual[z, -1.2e+169]], $MachinePrecision], Or[LessEqual[z, -2.25e+115], And[N[Not[LessEqual[z, 4.1e+18]], $MachinePrecision], LessEqual[z, 5e+122]]]]]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7999999999999998e257 or -3.90000000000000019e200 < z < -1.1999999999999999e169 or -2.24999999999999982e115 < z < 4.1e18 or 4.99999999999999989e122 < z

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 89.4%

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

      1. *-commutative 89.4%

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

   5. Simplified 89.4%

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

   if -5.7999999999999998e257 < z < -3.90000000000000019e200 or -1.1999999999999999e169 < z < -2.24999999999999982e115 or 4.1e18 < z < 4.99999999999999989e122

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 70.8%

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

      1. mul-1-neg 70.8%

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

      2. distribute-lft-neg-out 70.8%

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

      3. *-commutative 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in z around inf 70.8%

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

      1. associate-*r* 70.8%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot z} \]

      2. mul-1-neg 70.8%

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

   8. Simplified 70.8%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+257} \lor \neg \left(z \leq -3.9 \cdot 10^{+200} \lor \neg \left(z \leq -1.2 \cdot 10^{+169}\right) \land \left(z \leq -2.25 \cdot 10^{+115} \lor \neg \left(z \leq 4.1 \cdot 10^{+18}\right) \land z \leq 5 \cdot 10^{+122}\right)\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+132} \lor \neg \left(x \leq 1.1 \cdot 10^{+182}\right):\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.8e+132) (not (<= x 1.1e+182))) (- x (* x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e+132) || !(x <= 1.1e+182)) {
		tmp = x - (x * z);
	} 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 ((x <= (-3.8d+132)) .or. (.not. (x <= 1.1d+182))) then
        tmp = x - (x * z)
    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 ((x <= -3.8e+132) || !(x <= 1.1e+182)) {
		tmp = x - (x * z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.8e+132) or not (x <= 1.1e+182):
		tmp = x - (x * z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.8e+132) || !(x <= 1.1e+182))
		tmp = Float64(x - Float64(x * z));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.8e+132) || ~((x <= 1.1e+182)))
		tmp = x - (x * z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.8e+132], N[Not[LessEqual[x, 1.1e+182]], $MachinePrecision]], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.80000000000000006e132 or 1.09999999999999998e182 < x

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 93.4%

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

      1. mul-1-neg 93.4%

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

      2. distribute-lft-neg-out 93.4%

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

      3. *-commutative 93.4%

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

   5. Simplified 93.4%

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

      1. distribute-rgt-neg-out 93.4%

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

      2. unsub-neg 93.4%

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

      3. *-commutative 93.4%

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

   7. Applied egg-rr 93.4%

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

   if -3.80000000000000006e132 < x < 1.09999999999999998e182

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 85.2%

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

      1. *-commutative 85.2%

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

   5. Simplified 85.2%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+132} \lor \neg \left(x \leq 1.1 \cdot 10^{+182}\right):\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \lor \neg \left(z \leq 6800000000000\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.2) (not (<= z 6800000000000.0))) (* x (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.2) || !(z <= 6800000000000.0)) {
		tmp = x * -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 ((z <= (-5.2d0)) .or. (.not. (z <= 6800000000000.0d0))) then
        tmp = x * -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.2) || !(z <= 6800000000000.0)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.2) or not (z <= 6800000000000.0):
		tmp = x * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.2) || !(z <= 6800000000000.0))
		tmp = Float64(x * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.2) || ~((z <= 6800000000000.0)))
		tmp = x * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.2], N[Not[LessEqual[z, 6800000000000.0]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.20000000000000018 or 6.8e12 < z

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 50.1%

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

      1. mul-1-neg 50.1%

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

      2. distribute-lft-neg-out 50.1%

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

      3. *-commutative 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in z around inf 50.1%

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

      1. associate-*r* 50.1%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot z} \]

      2. mul-1-neg 50.1%

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

   8. Simplified 50.1%

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

   if -5.20000000000000018 < z < 6.8e12

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 61.0%

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

      1. mul-1-neg 61.0%

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

      2. distribute-lft-neg-out 61.0%

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

      3. *-commutative 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in z around 0 60.7%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \lor \neg \left(z \leq 6800000000000\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 36.4% accurate, 7.0× 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 100.0%

   \[x + \left(y - x\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in y around 0 55.7%

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

   1. mul-1-neg 55.7%

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

   2. distribute-lft-neg-out 55.7%

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

   3. *-commutative 55.7%

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

5. Simplified 55.7%

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

6. Taylor expanded in z around 0 32.7%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024108 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))