Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4

Percentage Accurate: 97.7% → 97.7%

Time: 1.3s

Alternatives: 7

Speedup: 1.0×

• 25.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((y - x) * (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 = x + ((y - x) * (z / t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((y - x) * (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 = x + ((y - x) * (z / t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((y - x) * (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 = x + ((y - x) * (z / t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

Alternative 2: 82.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -1.9 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq 3.4 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))))
   (if (<= (/ z t) -1.9e-17) t_1 (if (<= (/ z t) 3.4e-18) (+ x (/ z t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double tmp;
	if ((z / t) <= -1.9e-17) {
		tmp = t_1;
	} else if ((z / t) <= 3.4e-18) {
		tmp = x + (z / t);
	} 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 = (y - x) * (z / t)
    if ((z / t) <= (-1.9d-17)) then
        tmp = t_1
    else if ((z / t) <= 3.4d-18) then
        tmp = x + (z / t)
    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 = (y - x) * (z / t);
	double tmp;
	if ((z / t) <= -1.9e-17) {
		tmp = t_1;
	} else if ((z / t) <= 3.4e-18) {
		tmp = x + (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	tmp = 0
	if (z / t) <= -1.9e-17:
		tmp = t_1
	elif (z / t) <= 3.4e-18:
		tmp = x + (z / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -1.9e-17)
		tmp = t_1;
	elseif (Float64(z / t) <= 3.4e-18)
		tmp = Float64(x + Float64(z / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	tmp = 0.0;
	if ((z / t) <= -1.9e-17)
		tmp = t_1;
	elseif ((z / t) <= 3.4e-18)
		tmp = x + (z / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -1.9e-17], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 3.4e-18], N[(x + N[(z / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1.9000000000000001e-17 or 3.40000000000000001e-18 < (/.f64 z t)

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 92.3%

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

   if -1.9000000000000001e-17 < (/.f64 z t) < 3.40000000000000001e-18

   1. Initial program 98.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 3.2%

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

   6. Taylor expanded in x around 0

      \[\leadsto x + y \]

   8. Applied rewrites 76.6%

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

Alternative 3: 29.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4.6 \cdot 10^{+182}:\\ \;\;\;\;\frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(x + \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -4.6e+182) (/ z t) (+ x (+ x (- y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -4.6e+182) {
		tmp = z / t;
	} else {
		tmp = x + (x + (y - x));
	}
	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) :: tmp
    if ((z / t) <= (-4.6d+182)) then
        tmp = z / t
    else
        tmp = x + (x + (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -4.6e+182) {
		tmp = z / t;
	} else {
		tmp = x + (x + (y - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -4.6e+182:
		tmp = z / t
	else:
		tmp = x + (x + (y - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -4.6e+182)
		tmp = Float64(z / t);
	else
		tmp = Float64(x + Float64(x + Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -4.6e+182)
		tmp = z / t;
	else
		tmp = x + (x + (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -4.6e+182], N[(z / t), $MachinePrecision], N[(x + N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4.6000000000000001e182

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in x around 0

      \[\leadsto -1 \cdot \frac{x \cdot z}{t} + \color{blue}{\frac{y \cdot z}{t}} \]

   8. Applied rewrites 0.7%

      \[\leadsto y - \color{blue}{x} \]

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 20.9%

       \[\leadsto \frac{z}{t} \]

   if -4.6000000000000001e182 < (/.f64 z t)

   1. Initial program 98.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 3.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 34.6%

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

Alternative 4: 40.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ x + \frac{z}{t} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + (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 = x + (z / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 3.0%

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

6. Taylor expanded in x around 0

   \[\leadsto x + y \]

8. Applied rewrites 44.8%

   \[\leadsto x + \frac{z}{\color{blue}{t}} \]
9. Add Preprocessing

Alternative 5: 26.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ x + \left(x + \left(y - x\right)\right) \end{array} \]

FPCore

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

C

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

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 + (x + (y - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 3.0%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 30.5%

   \[\leadsto x + \left(x + \color{blue}{\left(y - x\right)}\right) \]
9. Add Preprocessing

Alternative 6: 3.1% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \end{array} \]

FPCore

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

C

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

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 + (y - x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 3.0%

   \[\leadsto x + \color{blue}{\left(y - x\right)} \]
6. Add Preprocessing

Alternative 7: 3.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ y - x \end{array} \]

FPCore

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

C

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

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 - x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 55.6%

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

6. Taylor expanded in x around 0

   \[\leadsto -1 \cdot \frac{x \cdot z}{t} + \color{blue}{\frac{y \cdot z}{t}} \]

8. Applied rewrites 2.6%

   \[\leadsto y - \color{blue}{x} \]
9. Add Preprocessing

Developer Target 1: 97.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ t_2 := x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{if}\;t\_1 < -1013646692435.8867:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))) (t_2 (+ x (/ (- y x) (/ t z)))))
   (if (< t_1 -1013646692435.8867)
     t_2
     (if (< t_1 0.0) (+ x (/ (* (- y x) z) t)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / 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 = (y - x) * (z / t)
    t_2 = x + ((y - x) / (t / z))
    if (t_1 < (-1013646692435.8867d0)) then
        tmp = t_2
    else if (t_1 < 0.0d0) then
        tmp = x + (((y - x) * z) / 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 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	t_2 = x + ((y - x) / (t / z))
	tmp = 0
	if t_1 < -1013646692435.8867:
		tmp = t_2
	elif t_1 < 0.0:
		tmp = x + (((y - x) * z) / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(t / z)))
	tmp = 0.0
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	t_2 = x + ((y - x) / (t / z));
	tmp = 0.0;
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = x + (((y - x) * z) / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$1, -1013646692435.8867], t$95$2, If[Less[t$95$1, 0.0], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64
  :pre (TRUE)

  :alt
  (! :herbie-platform default (if (< (* (- y x) (/ z t)) -10136466924358867/10000) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z))))))

  (+ x (* (- y x) (/ z t))))