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

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

Alternatives: 5

Speedup: 1.0×

• 20.8% 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: 85.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-55} \lor \neg \left(y \leq -4.4 \cdot 10^{-97}\right) \land \left(y \leq -9.2 \cdot 10^{-132} \lor \neg \left(y \leq 3.6 \cdot 10^{+42}\right)\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.5e-55)
         (and (not (<= y -4.4e-97))
              (or (<= y -9.2e-132) (not (<= y 3.6e+42)))))
   (+ x (* y z))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.5e-55) || (!(y <= -4.4e-97) && ((y <= -9.2e-132) || !(y <= 3.6e+42)))) {
		tmp = x + (y * z);
	} else {
		tmp = x * (1.0 - 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 <= (-2.5d-55)) .or. (.not. (y <= (-4.4d-97))) .and. (y <= (-9.2d-132)) .or. (.not. (y <= 3.6d+42))) then
        tmp = x + (y * z)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.5e-55) || (!(y <= -4.4e-97) && ((y <= -9.2e-132) || !(y <= 3.6e+42)))) {
		tmp = x + (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.5e-55) or (not (y <= -4.4e-97) and ((y <= -9.2e-132) or not (y <= 3.6e+42))):
		tmp = x + (y * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.5e-55) || (!(y <= -4.4e-97) && ((y <= -9.2e-132) || !(y <= 3.6e+42))))
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.5e-55) || (~((y <= -4.4e-97)) && ((y <= -9.2e-132) || ~((y <= 3.6e+42)))))
		tmp = x + (y * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.5e-55], And[N[Not[LessEqual[y, -4.4e-97]], $MachinePrecision], Or[LessEqual[y, -9.2e-132], N[Not[LessEqual[y, 3.6e+42]], $MachinePrecision]]]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5000000000000001e-55 or -4.3999999999999998e-97 < y < -9.20000000000000012e-132 or 3.6000000000000001e42 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 91.4%

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

      1. *-commutative 91.4%

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

   5. Simplified 91.4%

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

   if -2.5000000000000001e-55 < y < -4.3999999999999998e-97 or -9.20000000000000012e-132 < y < 3.6000000000000001e42

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 90.0%

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

      1. mul-1-neg 90.0%

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

      2. unsub-neg 90.0%

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

   5. Simplified 90.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-55} \lor \neg \left(y \leq -4.4 \cdot 10^{-97}\right) \land \left(y \leq -9.2 \cdot 10^{-132} \lor \neg \left(y \leq 3.6 \cdot 10^{+42}\right)\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot z\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{-55}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-132} \lor \neg \left(y \leq 4 \cdot 10^{+42}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y z))))
   (if (<= y -1.65e-55)
     t_0
     (if (<= y -4e-97)
       (* x (- 1.0 z))
       (if (or (<= y -9.2e-132) (not (<= y 4e+42))) t_0 (- x (* x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * z);
	double tmp;
	if (y <= -1.65e-55) {
		tmp = t_0;
	} else if (y <= -4e-97) {
		tmp = x * (1.0 - z);
	} else if ((y <= -9.2e-132) || !(y <= 4e+42)) {
		tmp = t_0;
	} else {
		tmp = x - (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) :: t_0
    real(8) :: tmp
    t_0 = x + (y * z)
    if (y <= (-1.65d-55)) then
        tmp = t_0
    else if (y <= (-4d-97)) then
        tmp = x * (1.0d0 - z)
    else if ((y <= (-9.2d-132)) .or. (.not. (y <= 4d+42))) then
        tmp = t_0
    else
        tmp = x - (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * z);
	double tmp;
	if (y <= -1.65e-55) {
		tmp = t_0;
	} else if (y <= -4e-97) {
		tmp = x * (1.0 - z);
	} else if ((y <= -9.2e-132) || !(y <= 4e+42)) {
		tmp = t_0;
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * z)
	tmp = 0
	if y <= -1.65e-55:
		tmp = t_0
	elif y <= -4e-97:
		tmp = x * (1.0 - z)
	elif (y <= -9.2e-132) or not (y <= 4e+42):
		tmp = t_0
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * z))
	tmp = 0.0
	if (y <= -1.65e-55)
		tmp = t_0;
	elseif (y <= -4e-97)
		tmp = Float64(x * Float64(1.0 - z));
	elseif ((y <= -9.2e-132) || !(y <= 4e+42))
		tmp = t_0;
	else
		tmp = Float64(x - Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * z);
	tmp = 0.0;
	if (y <= -1.65e-55)
		tmp = t_0;
	elseif (y <= -4e-97)
		tmp = x * (1.0 - z);
	elseif ((y <= -9.2e-132) || ~((y <= 4e+42)))
		tmp = t_0;
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e-55], t$95$0, If[LessEqual[y, -4e-97], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -9.2e-132], N[Not[LessEqual[y, 4e+42]], $MachinePrecision]], t$95$0, N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65e-55 or -4.00000000000000014e-97 < y < -9.20000000000000012e-132 or 4.00000000000000018e42 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 91.4%

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

      1. *-commutative 91.4%

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

   5. Simplified 91.4%

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

   if -1.65e-55 < y < -4.00000000000000014e-97

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 90.4%

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

      1. mul-1-neg 90.4%

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

      2. unsub-neg 90.4%

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

   5. Simplified 90.4%

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

   if -9.20000000000000012e-132 < y < 4.00000000000000018e42

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 90.0%

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

      1. mul-1-neg 90.0%

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

      2. unsub-neg 90.0%

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

   5. Simplified 90.0%

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

      1. sub-neg 90.0%

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

      2. distribute-rgt-in 90.0%

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

      3. *-un-lft-identity 90.0%

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

      4. distribute-lft-neg-in 90.0%

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

      5. unsub-neg 90.0%

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

   7. Applied egg-rr 90.0%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-55}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-132} \lor \neg \left(y \leq 4 \cdot 10^{+42}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 z)))

C

double code(double x, double y, double z) {
	return x * (1.0 - 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 * (1.0d0 - z)
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - z);
}

Python

def code(x, y, z):
	return x * (1.0 - z)

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - z);
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf 62.8%

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

   1. mul-1-neg 62.8%

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

   2. unsub-neg 62.8%

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

5. Simplified 62.8%

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

Alternative 5: 36.8% 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 z around 0 36.5%

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

Reproduce

herbie shell --seed 2024111 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))