Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, B

Percentage Accurate: 100.0% → 100.0%

Time: 1.5s

Alternatives: 6

Speedup: N/A×

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

\[\begin{array}{l} \\ \left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))

C

double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

Python

def code(x, y, z, t):
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(1.0 / 8.0) * x) - Float64(Float64(y * z) / 2.0)) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))

C

double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

Python

def code(x, y, z, t):
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(1.0 / 8.0) * x) - Float64(Float64(y * z) / 2.0)) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\frac{1}{8} \cdot x + t\right) - \frac{y \cdot z}{2} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (+ (* (/ 1.0 8.0) x) t) (/ (* y z) 2.0)))

C

double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) + t) - ((y * z) / 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((1.0d0 / 8.0d0) * x) + t) - ((y * z) / 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) + t) - ((y * z) / 2.0);
}

Python

def code(x, y, z, t):
	return (((1.0 / 8.0) * x) + t) - ((y * z) / 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(1.0 / 8.0) * x) + t) - Float64(Float64(y * z) / 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((1.0 / 8.0) * x) + t) - ((y * z) / 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] + t), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(t + \frac{1}{8} \cdot x\right) - \frac{1}{2} \cdot \left(y \cdot z\right)} \]

5. Applied rewrites 68.7%

   \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \frac{y \cdot z}{2}} \]

6. Taylor expanded in x around 0

   \[\leadsto \frac{1}{8} \cdot x - \frac{\color{blue}{y \cdot z}}{2} \]

8. Applied rewrites 100.0%

   \[\leadsto \left(\frac{1}{8} \cdot x + t\right) - \frac{\color{blue}{y \cdot z}}{2} \]
9. Add Preprocessing

Alternative 2: 87.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{8} \cdot x\\ t_2 := t\_1 - \frac{y \cdot z}{2}\\ \mathbf{if}\;y \cdot z \leq -2.7 \cdot 10^{+98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \cdot z \leq 8.5 \cdot 10^{+110}:\\ \;\;\;\;t\_1 + t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ 1.0 8.0) x)) (t_2 (- t_1 (/ (* y z) 2.0))))
   (if (<= (* y z) -2.7e+98) t_2 (if (<= (* y z) 8.5e+110) (+ t_1 t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (1.0 / 8.0) * x;
	double t_2 = t_1 - ((y * z) / 2.0);
	double tmp;
	if ((y * z) <= -2.7e+98) {
		tmp = t_2;
	} else if ((y * z) <= 8.5e+110) {
		tmp = t_1 + t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (1.0d0 / 8.0d0) * x
    t_2 = t_1 - ((y * z) / 2.0d0)
    if ((y * z) <= (-2.7d+98)) then
        tmp = t_2
    else if ((y * z) <= 8.5d+110) then
        tmp = t_1 + t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (1.0 / 8.0) * x;
	double t_2 = t_1 - ((y * z) / 2.0);
	double tmp;
	if ((y * z) <= -2.7e+98) {
		tmp = t_2;
	} else if ((y * z) <= 8.5e+110) {
		tmp = t_1 + t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (1.0 / 8.0) * x
	t_2 = t_1 - ((y * z) / 2.0)
	tmp = 0
	if (y * z) <= -2.7e+98:
		tmp = t_2
	elif (y * z) <= 8.5e+110:
		tmp = t_1 + t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(1.0 / 8.0) * x)
	t_2 = Float64(t_1 - Float64(Float64(y * z) / 2.0))
	tmp = 0.0
	if (Float64(y * z) <= -2.7e+98)
		tmp = t_2;
	elseif (Float64(y * z) <= 8.5e+110)
		tmp = Float64(t_1 + t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (1.0 / 8.0) * x;
	t_2 = t_1 - ((y * z) / 2.0);
	tmp = 0.0;
	if ((y * z) <= -2.7e+98)
		tmp = t_2;
	elseif ((y * z) <= 8.5e+110)
		tmp = t_1 + t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -2.7e+98], t$95$2, If[LessEqual[N[(y * z), $MachinePrecision], 8.5e+110], N[(t$95$1 + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2.7e98 or 8.5000000000000004e110 < (*.f64 y z)

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(t + \frac{1}{8} \cdot x\right) - \frac{1}{2} \cdot \left(y \cdot z\right)} \]

   5. Applied rewrites 89.6%

      \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \frac{y \cdot z}{2}} \]

   if -2.7e98 < (*.f64 y z) < 8.5000000000000004e110

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \left(y \cdot z\right)} + t \]

   5. Applied rewrites 89.0%

      \[\leadsto \color{blue}{\frac{1}{8} \cdot x} + t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 50.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{8} + t\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+79}:\\ \;\;\;\;\frac{1}{8} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ 1.0 8.0) t)))
   (if (<= t -5.5e+117) t_1 (if (<= t 9e+79) (* (/ 1.0 8.0) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (1.0 / 8.0) + t;
	double tmp;
	if (t <= -5.5e+117) {
		tmp = t_1;
	} else if (t <= 9e+79) {
		tmp = (1.0 / 8.0) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 / 8.0d0) + t
    if (t <= (-5.5d+117)) then
        tmp = t_1
    else if (t <= 9d+79) then
        tmp = (1.0d0 / 8.0d0) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (1.0 / 8.0) + t;
	double tmp;
	if (t <= -5.5e+117) {
		tmp = t_1;
	} else if (t <= 9e+79) {
		tmp = (1.0 / 8.0) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (1.0 / 8.0) + t
	tmp = 0
	if t <= -5.5e+117:
		tmp = t_1
	elif t <= 9e+79:
		tmp = (1.0 / 8.0) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(1.0 / 8.0) + t)
	tmp = 0.0
	if (t <= -5.5e+117)
		tmp = t_1;
	elseif (t <= 9e+79)
		tmp = Float64(Float64(1.0 / 8.0) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (1.0 / 8.0) + t;
	tmp = 0.0;
	if (t <= -5.5e+117)
		tmp = t_1;
	elseif (t <= 9e+79)
		tmp = (1.0 / 8.0) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(1.0 / 8.0), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[t, -5.5e+117], t$95$1, If[LessEqual[t, 9e+79], N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.49999999999999965e117 or 8.99999999999999987e79 < t

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{1}{2} \cdot \left(y \cdot z\right)\right)} + t \]

   5. Applied rewrites 69.9%

      \[\leadsto \color{blue}{\frac{1}{8}} + t \]

   if -5.49999999999999965e117 < t < 8.99999999999999987e79

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(t + \frac{1}{8} \cdot x\right) - \frac{1}{2} \cdot \left(y \cdot z\right)} \]

   5. Applied rewrites 87.1%

      \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \frac{y \cdot z}{2}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{-1}{2} \cdot \color{blue}{\left(y \cdot z\right)} \]

   8. Applied rewrites 44.5%

      \[\leadsto \frac{1}{8} \cdot \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 64.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{8} \cdot x + t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ (* (/ 1.0 8.0) x) t))

C

double code(double x, double y, double z, double t) {
	return ((1.0 / 8.0) * x) + t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((1.0d0 / 8.0d0) * x) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((1.0 / 8.0) * x) + t;
}

Python

def code(x, y, z, t):
	return ((1.0 / 8.0) * x) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(1.0 / 8.0) * x) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((1.0 / 8.0) * x) + t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] + t), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-1}{2} \cdot \left(y \cdot z\right)} + t \]

5. Applied rewrites 65.5%

   \[\leadsto \color{blue}{\frac{1}{8} \cdot x} + t \]
6. Add Preprocessing

Alternative 5: 32.7% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ y \cdot z + t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ (* y z) t))

C

double code(double x, double y, double z, double t) {
	return (y * z) + t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (y * z) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (y * z) + t;
}

Python

def code(x, y, z, t):
	return (y * z) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(y * z) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (y * z) + t;
end

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-1}{2} \cdot \left(y \cdot z\right)} + t \]

5. Applied rewrites 65.5%

   \[\leadsto \color{blue}{\frac{1}{8} \cdot x} + t \]

6. Taylor expanded in x around 0

   \[\leadsto \frac{1}{8} \cdot \color{blue}{x} + t \]

8. Applied rewrites 39.9%

   \[\leadsto \left(\frac{1}{8} \cdot x + \color{blue}{t}\right) + t \]

9. Taylor expanded in x around 0

   \[\leadsto \frac{1}{8} \cdot \color{blue}{x} + t \]

11. Applied rewrites 32.2%

    \[\leadsto y \cdot \color{blue}{z} + t \]
12. Add Preprocessing

Alternative 6: 2.1% accurate, 6.5× speedup

Math

\[\begin{array}{l} \\ y \cdot z \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* y z))

C

double code(double x, double y, double z, double t) {
	return y * z;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = y * z
end function

Java

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

Python

def code(x, y, z, t):
	return y * z

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(t + \frac{1}{8} \cdot x\right) - \frac{1}{2} \cdot \left(y \cdot z\right)} \]

5. Applied rewrites 68.7%

   \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \frac{y \cdot z}{2}} \]

6. Taylor expanded in x around -inf

   \[\leadsto -1 \cdot \color{blue}{\left(x \cdot \left(\frac{1}{2} \cdot \frac{y \cdot z}{x} - \frac{1}{8}\right)\right)} \]

8. Applied rewrites 2.1%

   \[\leadsto y \cdot \color{blue}{z} \]
9. Add Preprocessing

Developer Target 1: 100.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left(\frac{x}{8} + t\right) - \frac{z}{2} \cdot y \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (+ (/ x 8.0) t) (* (/ z 2.0) y)))

C

double code(double x, double y, double z, double t) {
	return ((x / 8.0) + t) - ((z / 2.0) * y);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x / 8.0d0) + t) - ((z / 2.0d0) * y)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x / 8.0) + t) - ((z / 2.0) * y);
}

Python

def code(x, y, z, t):
	return ((x / 8.0) + t) - ((z / 2.0) * y)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x / 8.0) + t) - Float64(Float64(z / 2.0) * y))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x / 8.0) + t) - ((z / 2.0) * y);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x / 8.0), $MachinePrecision] + t), $MachinePrecision] - N[(N[(z / 2.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64
  :pre (TRUE)

  :alt
  (! :herbie-platform default (- (+ (/ x 8) t) (* (/ z 2) y)))

  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))