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

Percentage Accurate: 100.0% → 100.0%

Time: 3.9s

Alternatives: 7

Speedup: 1.0×

• 21.1% 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, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, z, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- y x) z x))

C

double code(double x, double y, double z) {
	return fma((y - x), z, x);
}

Julia

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 60.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+183}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-111}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+19} \lor \neg \left(z \leq 1.6 \cdot 10^{+74} \lor \neg \left(z \leq 1.65 \cdot 10^{+214}\right) \land z \leq 1.12 \cdot 10^{+253}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -8e+183)
     (* y z)
     (if (<= z -4.4e+17)
       t_0
       (if (<= z -3.2e-111)
         (* y z)
         (if (<= z 2.4e-14)
           x
           (if (or (<= z 7.2e+19)
                   (not
                    (or (<= z 1.6e+74)
                        (and (not (<= z 1.65e+214)) (<= z 1.12e+253)))))
             (* y z)
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -8e+183) {
		tmp = y * z;
	} else if (z <= -4.4e+17) {
		tmp = t_0;
	} else if (z <= -3.2e-111) {
		tmp = y * z;
	} else if (z <= 2.4e-14) {
		tmp = x;
	} else if ((z <= 7.2e+19) || !((z <= 1.6e+74) || (!(z <= 1.65e+214) && (z <= 1.12e+253)))) {
		tmp = 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 = x * -z
    if (z <= (-8d+183)) then
        tmp = y * z
    else if (z <= (-4.4d+17)) then
        tmp = t_0
    else if (z <= (-3.2d-111)) then
        tmp = y * z
    else if (z <= 2.4d-14) then
        tmp = x
    else if ((z <= 7.2d+19) .or. (.not. (z <= 1.6d+74) .or. (.not. (z <= 1.65d+214)) .and. (z <= 1.12d+253))) then
        tmp = 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 = x * -z;
	double tmp;
	if (z <= -8e+183) {
		tmp = y * z;
	} else if (z <= -4.4e+17) {
		tmp = t_0;
	} else if (z <= -3.2e-111) {
		tmp = y * z;
	} else if (z <= 2.4e-14) {
		tmp = x;
	} else if ((z <= 7.2e+19) || !((z <= 1.6e+74) || (!(z <= 1.65e+214) && (z <= 1.12e+253)))) {
		tmp = y * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -8e+183:
		tmp = y * z
	elif z <= -4.4e+17:
		tmp = t_0
	elif z <= -3.2e-111:
		tmp = y * z
	elif z <= 2.4e-14:
		tmp = x
	elif (z <= 7.2e+19) or not ((z <= 1.6e+74) or (not (z <= 1.65e+214) and (z <= 1.12e+253))):
		tmp = y * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -8e+183)
		tmp = Float64(y * z);
	elseif (z <= -4.4e+17)
		tmp = t_0;
	elseif (z <= -3.2e-111)
		tmp = Float64(y * z);
	elseif (z <= 2.4e-14)
		tmp = x;
	elseif ((z <= 7.2e+19) || !((z <= 1.6e+74) || (!(z <= 1.65e+214) && (z <= 1.12e+253))))
		tmp = Float64(y * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (z <= -8e+183)
		tmp = y * z;
	elseif (z <= -4.4e+17)
		tmp = t_0;
	elseif (z <= -3.2e-111)
		tmp = y * z;
	elseif (z <= 2.4e-14)
		tmp = x;
	elseif ((z <= 7.2e+19) || ~(((z <= 1.6e+74) || (~((z <= 1.65e+214)) && (z <= 1.12e+253)))))
		tmp = y * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -8e+183], N[(y * z), $MachinePrecision], If[LessEqual[z, -4.4e+17], t$95$0, If[LessEqual[z, -3.2e-111], N[(y * z), $MachinePrecision], If[LessEqual[z, 2.4e-14], x, If[Or[LessEqual[z, 7.2e+19], N[Not[Or[LessEqual[z, 1.6e+74], And[N[Not[LessEqual[z, 1.65e+214]], $MachinePrecision], LessEqual[z, 1.12e+253]]]], $MachinePrecision]], N[(y * z), $MachinePrecision], t$95$0]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+134} \lor \neg \left(y \leq -2.16 \cdot 10^{+52}\right) \land \left(y \leq -1.85 \cdot 10^{+14} \lor \neg \left(y \leq 2.5 \cdot 10^{+34}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.5e+134)
         (and (not (<= y -2.16e+52))
              (or (<= y -1.85e+14) (not (<= y 2.5e+34)))))
   (* y z)
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5e+134) || (!(y <= -2.16e+52) && ((y <= -1.85e+14) || !(y <= 2.5e+34)))) {
		tmp = 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 <= (-1.5d+134)) .or. (.not. (y <= (-2.16d+52))) .and. (y <= (-1.85d+14)) .or. (.not. (y <= 2.5d+34))) then
        tmp = 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 <= -1.5e+134) || (!(y <= -2.16e+52) && ((y <= -1.85e+14) || !(y <= 2.5e+34)))) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.5e+134) or (not (y <= -2.16e+52) and ((y <= -1.85e+14) or not (y <= 2.5e+34))):
		tmp = y * z
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.5e+134) || (!(y <= -2.16e+52) && ((y <= -1.85e+14) || !(y <= 2.5e+34))))
		tmp = 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 <= -1.5e+134) || (~((y <= -2.16e+52)) && ((y <= -1.85e+14) || ~((y <= 2.5e+34)))))
		tmp = y * z;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.5e+134], And[N[Not[LessEqual[y, -2.16e+52]], $MachinePrecision], Or[LessEqual[y, -1.85e+14], N[Not[LessEqual[y, 2.5e+34]], $MachinePrecision]]]], N[(y * z), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-29} \lor \neg \left(y \leq 1.25 \cdot 10^{+34}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.6e-29) (not (<= y 1.25e+34))) (+ x (* y z)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.6e-29) || !(y <= 1.25e+34)) {
		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 <= (-5.6d-29)) .or. (.not. (y <= 1.25d+34))) 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 <= -5.6e-29) || !(y <= 1.25e+34)) {
		tmp = x + (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.6e-29) or not (y <= 1.25e+34):
		tmp = x + (y * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.6e-29) || !(y <= 1.25e+34))
		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 <= -5.6e-29) || ~((y <= 1.25e+34)))
		tmp = x + (y * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.6e-29], N[Not[LessEqual[y, 1.25e+34]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 59.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-111} \lor \neg \left(z \leq 6.4 \cdot 10^{-15}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.2e-111) (not (<= z 6.4e-15))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.2e-111) || !(z <= 6.4e-15)) {
		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 <= (-3.2d-111)) .or. (.not. (z <= 6.4d-15))) 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 <= -3.2e-111) || !(z <= 6.4e-15)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.2e-111) or not (z <= 6.4e-15):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.2e-111) || !(z <= 6.4e-15))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.2e-111) || ~((z <= 6.4e-15)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.2e-111], N[Not[LessEqual[z, 6.4e-15]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 36.3% 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2023350 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))