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

Percentage Accurate: 100.0% → 100.0%

Time: 3.2s

Alternatives: 5

Speedup: 1.0×

• 22.0% 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. Final simplification 100.0%

   \[\leadsto x + \left(y - x\right) \cdot z \]

Alternative 2: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+234} \lor \neg \left(z \leq -3.2 \cdot 10^{+85}\right) \land z \leq 6.8 \cdot 10^{+20}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.2e+234) (and (not (<= z -3.2e+85)) (<= z 6.8e+20)))
   (+ x (* y z))
   (* z (- x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.2e+234) || (!(z <= -3.2e+85) && (z <= 6.8e+20))) {
		tmp = x + (y * z);
	} else {
		tmp = z * -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 <= (-3.2d+234)) .or. (.not. (z <= (-3.2d+85))) .and. (z <= 6.8d+20)) then
        tmp = x + (y * z)
    else
        tmp = z * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.2e+234) || (!(z <= -3.2e+85) && (z <= 6.8e+20))) {
		tmp = x + (y * z);
	} else {
		tmp = z * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.2e+234) or (not (z <= -3.2e+85) and (z <= 6.8e+20)):
		tmp = x + (y * z)
	else:
		tmp = z * -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.2e+234) || (!(z <= -3.2e+85) && (z <= 6.8e+20)))
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(z * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.2e+234) || (~((z <= -3.2e+85)) && (z <= 6.8e+20)))
		tmp = x + (y * z);
	else
		tmp = z * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.2e+234], And[N[Not[LessEqual[z, -3.2e+85]], $MachinePrecision], LessEqual[z, 6.8e+20]]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(z * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999992e234 or -3.20000000000000018e85 < z < 6.8e20

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in y around inf 93.2%

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

      1. *-commutative 93.2%

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

   4. Simplified 93.2%

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

   if -3.19999999999999992e234 < z < -3.20000000000000018e85 or 6.8e20 < z

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in y around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. distribute-lft-neg-out 67.7%

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

      3. *-commutative 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in z around inf 67.7%

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

      1. associate-*r* 67.7%

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

      2. mul-1-neg 67.7%

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

   7. Simplified 67.7%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+234} \lor \neg \left(z \leq -3.2 \cdot 10^{+85}\right) \land z \leq 6.8 \cdot 10^{+20}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+44} \lor \neg \left(x \leq 3.45 \cdot 10^{+44}\right):\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.2e+44) (not (<= x 3.45e+44))) (- x (* x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.2e+44) || !(x <= 3.45e+44)) {
		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 <= (-5.2d+44)) .or. (.not. (x <= 3.45d+44))) 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 <= -5.2e+44) || !(x <= 3.45e+44)) {
		tmp = x - (x * z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.2e+44) or not (x <= 3.45e+44):
		tmp = x - (x * z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.2e+44) || !(x <= 3.45e+44))
		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 <= -5.2e+44) || ~((x <= 3.45e+44)))
		tmp = x - (x * z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.2e+44], N[Not[LessEqual[x, 3.45e+44]], $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 < -5.1999999999999998e44 or 3.4499999999999999e44 < x

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in y around 0 91.3%

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

      1. mul-1-neg 91.3%

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

      2. distribute-lft-neg-out 91.3%

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

      3. *-commutative 91.3%

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

   4. Simplified 91.3%

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

      1. distribute-rgt-neg-out 91.3%

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

      2. unsub-neg 91.3%

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

      3. *-commutative 91.3%

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

   6. Applied egg-rr 91.3%

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

   if -5.1999999999999998e44 < x < 3.4499999999999999e44

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in y around inf 88.3%

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

      1. *-commutative 88.3%

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

   4. Simplified 88.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+44} \lor \neg \left(x \leq 3.45 \cdot 10^{+44}\right):\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 4: 59.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -14000000000 \lor \neg \left(z \leq 3.3 \cdot 10^{+17}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -14000000000.0) (not (<= z 3.3e+17))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -14000000000.0) || !(z <= 3.3e+17)) {
		tmp = z * -x;
	} 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 <= (-14000000000.0d0)) .or. (.not. (z <= 3.3d+17))) then
        tmp = z * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -14000000000.0) || !(z <= 3.3e+17)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -14000000000.0) or not (z <= 3.3e+17):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -14000000000.0) || !(z <= 3.3e+17))
		tmp = Float64(z * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -14000000000.0) || ~((z <= 3.3e+17)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -14000000000.0], N[Not[LessEqual[z, 3.3e+17]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e10 or 3.3e17 < z

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in y around 0 55.9%

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

      1. mul-1-neg 55.9%

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

      2. distribute-lft-neg-out 55.9%

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

      3. *-commutative 55.9%

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

   4. Simplified 55.9%

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

   5. Taylor expanded in z around inf 55.9%

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

      1. associate-*r* 55.9%

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

      2. mul-1-neg 55.9%

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

   7. Simplified 55.9%

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

   if -1.4e10 < z < 3.3e17

   1. Initial program 100.0%

      \[x + \left(y - x\right) \cdot z \]

   2. Taylor expanded in y around 0 63.6%

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

      1. mul-1-neg 63.6%

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

      2. distribute-lft-neg-out 63.6%

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

      3. *-commutative 63.6%

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

   4. Simplified 63.6%

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

   5. Taylor expanded in z around 0 62.8%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -14000000000 \lor \neg \left(z \leq 3.3 \cdot 10^{+17}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 36.5% 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. Taylor expanded in y around 0 60.1%

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

   1. mul-1-neg 60.1%

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

   2. distribute-lft-neg-out 60.1%

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

   3. *-commutative 60.1%

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

4. Simplified 60.1%

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

5. Taylor expanded in z around 0 35.8%

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

6. Final simplification 35.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023310 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))