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

Percentage Accurate: 100.0% → 100.0%

Time: 7.2s

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: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot z\\ \mathbf{if}\;z \leq -13500000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.108:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) z)))
   (if (<= z -13500000.0) t_0 (if (<= z 0.108) (+ x (* y z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) * z;
	double tmp;
	if (z <= -13500000.0) {
		tmp = t_0;
	} else if (z <= 0.108) {
		tmp = x + (y * z);
	} else {
		tmp = t_0;
	}
	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 = (y - x) * z
    if (z <= (-13500000.0d0)) then
        tmp = t_0
    else if (z <= 0.108d0) then
        tmp = x + (y * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - x) * z;
	double tmp;
	if (z <= -13500000.0) {
		tmp = t_0;
	} else if (z <= 0.108) {
		tmp = x + (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) * z
	tmp = 0
	if z <= -13500000.0:
		tmp = t_0
	elif z <= 0.108:
		tmp = x + (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) * z)
	tmp = 0.0
	if (z <= -13500000.0)
		tmp = t_0;
	elseif (z <= 0.108)
		tmp = Float64(x + Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) * z;
	tmp = 0.0;
	if (z <= -13500000.0)
		tmp = t_0;
	elseif (z <= 0.108)
		tmp = x + (y * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -13500000.0], t$95$0, If[LessEqual[z, 0.108], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e7 or 0.107999999999999999 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right) \]

      2. --lowering--.f64 98.8%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right) \]

   5. Simplified 98.8%

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

   if -1.35e7 < z < 0.107999999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 99.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 99.0%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13500000:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{elif}\;z \leq 0.108:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - x\right) \cdot z\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{-153}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.0065:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- y x) z)))
   (if (<= z -7.8e-153) t_0 (if (<= z 0.0065) (* x (- 1.0 z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y - x) * z;
	double tmp;
	if (z <= -7.8e-153) {
		tmp = t_0;
	} else if (z <= 0.0065) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	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 = (y - x) * z
    if (z <= (-7.8d-153)) then
        tmp = t_0
    else if (z <= 0.0065d0) then
        tmp = x * (1.0d0 - z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - x) * z;
	double tmp;
	if (z <= -7.8e-153) {
		tmp = t_0;
	} else if (z <= 0.0065) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - x) * z
	tmp = 0
	if z <= -7.8e-153:
		tmp = t_0
	elif z <= 0.0065:
		tmp = x * (1.0 - z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - x) * z)
	tmp = 0.0
	if (z <= -7.8e-153)
		tmp = t_0;
	elseif (z <= 0.0065)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - x) * z;
	tmp = 0.0;
	if (z <= -7.8e-153)
		tmp = t_0;
	elseif (z <= 0.0065)
		tmp = x * (1.0 - z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -7.8e-153], t$95$0, If[LessEqual[z, 0.0065], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8000000000000004e-153 or 0.0064999999999999997 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(y - x\right)}\right) \]

      2. --lowering--.f64 94.4%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right) \]

   5. Simplified 94.4%

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

   if -7.8000000000000004e-153 < z < 0.0064999999999999997

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot z\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{z}\right)\right) \]

      4. --lowering--.f64 75.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]

   5. Simplified 75.9%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-153}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{elif}\;z \leq 0.0065:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+92}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.9e+92) (* y z) (if (<= y 3.1e+35) (* x (- 1.0 z)) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.9e+92) {
		tmp = y * z;
	} else if (y <= 3.1e+35) {
		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 (y <= (-4.9d+92)) then
        tmp = y * z
    else if (y <= 3.1d+35) 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 (y <= -4.9e+92) {
		tmp = y * z;
	} else if (y <= 3.1e+35) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.9e+92:
		tmp = y * z
	elif y <= 3.1e+35:
		tmp = x * (1.0 - z)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.9e+92)
		tmp = Float64(y * z);
	elseif (y <= 3.1e+35)
		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 (y <= -4.9e+92)
		tmp = y * z;
	elseif (y <= 3.1e+35)
		tmp = x * (1.0 - z);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.9e+92], N[(y * z), $MachinePrecision], If[LessEqual[y, 3.1e+35], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9000000000000002e92 or 3.09999999999999987e35 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 76.4%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{z}\right) \]

   5. Simplified 76.4%

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

   if -4.9000000000000002e92 < y < 3.09999999999999987e35

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot z\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{z}\right)\right) \]

      4. --lowering--.f64 82.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]

   5. Simplified 82.7%

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

Alternative 5: 58.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-153}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.8e-153) (* y z) (if (<= z 5.7e-8) x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.8e-153) {
		tmp = y * z;
	} else if (z <= 5.7e-8) {
		tmp = x;
	} 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 (z <= (-7.8d-153)) then
        tmp = y * z
    else if (z <= 5.7d-8) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.8e-153) {
		tmp = y * z;
	} else if (z <= 5.7e-8) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.8e-153:
		tmp = y * z
	elif z <= 5.7e-8:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.8e-153)
		tmp = Float64(y * z);
	elseif (z <= 5.7e-8)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.8e-153)
		tmp = y * z;
	elseif (z <= 5.7e-8)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.8e-153], N[(y * z), $MachinePrecision], If[LessEqual[z, 5.7e-8], x, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8000000000000004e-153 or 5.70000000000000009e-8 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 49.7%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{z}\right) \]

   5. Simplified 49.7%

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

   if -7.8000000000000004e-153 < z < 5.70000000000000009e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 74.6%

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

Alternative 6: 37.2% 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

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

5. Simplified 31.9%

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

Reproduce

herbie shell --seed 2024163 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))