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

Percentage Accurate: 100.0% → 100.0%

Time: 4.8s

Alternatives: 6

Speedup: 1.0×

• 21.0% 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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 87.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+78} \lor \neg \left(x \leq 1550000\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.6e+78) (not (<= x 1550000.0)))
   (* x (- 1.0 z))
   (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.6e+78) || !(x <= 1550000.0)) {
		tmp = x * (1.0 - 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 <= (-1.6d+78)) .or. (.not. (x <= 1550000.0d0))) then
        tmp = x * (1.0d0 - 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 <= -1.6e+78) || !(x <= 1550000.0)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.6e+78) or not (x <= 1550000.0):
		tmp = x * (1.0 - z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.6e+78) || !(x <= 1550000.0))
		tmp = Float64(x * Float64(1.0 - 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 <= -1.6e+78) || ~((x <= 1550000.0)))
		tmp = x * (1.0 - z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.6e+78], N[Not[LessEqual[x, 1550000.0]], $MachinePrecision]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.59999999999999997e78 or 1.55e6 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.5%

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

      1. mul-1-neg 87.5%

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

      2. unsub-neg 87.5%

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

   5. Simplified 87.5%

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

   if -1.59999999999999997e78 < x < 1.55e6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.7%

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

      1. *-commutative 88.7%

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

   5. Simplified 88.7%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+78} \lor \neg \left(x \leq 1550000\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4600000000000 \lor \neg \left(x \leq 56\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4600000000000.0) (not (<= x 56.0))) (* x (- 1.0 z)) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4600000000000.0) || !(x <= 56.0)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = 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 <= (-4600000000000.0d0)) .or. (.not. (x <= 56.0d0))) then
        tmp = x * (1.0d0 - z)
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4600000000000.0) || !(x <= 56.0)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4600000000000.0) or not (x <= 56.0):
		tmp = x * (1.0 - z)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4600000000000.0) || !(x <= 56.0))
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4600000000000.0) || ~((x <= 56.0)))
		tmp = x * (1.0 - z);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4600000000000.0], N[Not[LessEqual[x, 56.0]], $MachinePrecision]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6e12 or 56 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.4%

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

      1. mul-1-neg 84.4%

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

      2. unsub-neg 84.4%

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

   5. Simplified 84.4%

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

   if -4.6e12 < x < 56

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 89.0%

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

      1. *-commutative 89.0%

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

   5. Simplified 89.0%

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

   6. Taylor expanded in y around inf 88.9%

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

   7. Taylor expanded in z around inf 69.4%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4600000000000 \lor \neg \left(x \leq 56\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;x \leq 4100000:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.75e+78)
   (* x (- 1.0 z))
   (if (<= x 4100000.0) (+ x (* y z)) (- x (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.75e+78) {
		tmp = x * (1.0 - z);
	} else if (x <= 4100000.0) {
		tmp = x + (y * z);
	} 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) :: tmp
    if (x <= (-1.75d+78)) then
        tmp = x * (1.0d0 - z)
    else if (x <= 4100000.0d0) then
        tmp = x + (y * z)
    else
        tmp = x - (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.75e+78) {
		tmp = x * (1.0 - z);
	} else if (x <= 4100000.0) {
		tmp = x + (y * z);
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.75e+78:
		tmp = x * (1.0 - z)
	elif x <= 4100000.0:
		tmp = x + (y * z)
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.75e+78)
		tmp = Float64(x * Float64(1.0 - z));
	elseif (x <= 4100000.0)
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x - Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.75e+78)
		tmp = x * (1.0 - z);
	elseif (x <= 4100000.0)
		tmp = x + (y * z);
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.75e+78], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4100000.0], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7500000000000001e78

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 93.0%

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

      1. mul-1-neg 93.0%

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

      2. unsub-neg 93.0%

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

   5. Simplified 93.0%

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

   if -1.7500000000000001e78 < x < 4.1e6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.7%

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

      1. *-commutative 88.7%

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

   5. Simplified 88.7%

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

   if 4.1e6 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.3%

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

      1. mul-1-neg 82.3%

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

      2. unsub-neg 82.3%

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

   5. Simplified 82.3%

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

      1. sub-neg 82.3%

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

      2. distribute-rgt-in 82.3%

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

      3. *-un-lft-identity 82.3%

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

      4. distribute-lft-neg-in 82.3%

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

      5. unsub-neg 82.3%

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

   7. Applied egg-rr 82.3%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;x \leq 4100000:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-26} \lor \neg \left(z \leq 7 \cdot 10^{-107}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.95e-26) (not (<= z 7e-107))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.95e-26) || !(z <= 7e-107)) {
		tmp = y * 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 <= (-1.95d-26)) .or. (.not. (z <= 7d-107))) then
        tmp = y * 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 <= -1.95e-26) || !(z <= 7e-107)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.95e-26) or not (z <= 7e-107):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.95e-26) || !(z <= 7e-107))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.95e-26) || ~((z <= 7e-107)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.95e-26], N[Not[LessEqual[z, 7e-107]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.94999999999999993e-26 or 6.99999999999999971e-107 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 64.6%

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

      1. *-commutative 64.6%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in y around inf 66.9%

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

   7. Taylor expanded in z around inf 59.5%

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

   if -1.94999999999999993e-26 < z < 6.99999999999999971e-107

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 79.0%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-26} \lor \neg \left(z \leq 7 \cdot 10^{-107}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 36.6% 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 32.5%

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

Reproduce

herbie shell --seed 2024157 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))