Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B

Percentage Accurate: 81.3% → 91.9%

Time: 4.2s

Alternatives: 3

Speedup: 1.8×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 81.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} t = |t|\\ [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.85 \cdot 10^{-64}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: t should be positive before calling this function
NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.85e-64) (/ y (/ z x)) (* x (/ y z))))

C

t = abs(t);
assert(x < y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.85e-64) {
		tmp = y / (z / x);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

NOTE: t should be positive before calling this function
NOTE: x and y should be sorted in increasing order before calling this function.
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 (t <= 1.85d-64) then
        tmp = y / (z / x)
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

t = Math.abs(t);
assert x < y;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.85e-64) {
		tmp = y / (z / x);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

t = abs(t)
[x, y] = sort([x, y])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.85e-64:
		tmp = y / (z / x)
	else:
		tmp = x * (y / z)
	return tmp

Julia

t = abs(t)
x, y = sort([x, y])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.85e-64)
		tmp = Float64(y / Float64(z / x));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

t = abs(t)
x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.85e-64)
		tmp = y / (z / x);
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t should be positive before calling this function
NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1.85e-64], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.84999999999999999e-64

   1. Initial program 84.6%

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
   2. Step-by-step derivation

      1. associate-/l* 94.7%

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

      2. *-inverses 94.7%

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

      3. clear-num 94.4%

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

      4. clear-num 94.4%

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

      5. associate-/r/ 94.5%

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

   3. Applied egg-rr 94.5%

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

      1. associate-*l/ 94.7%

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

      2. *-un-lft-identity 94.7%

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

      3. associate-*r/ 92.5%

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

      4. *-commutative 92.5%

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

      5. associate-/l* 93.1%

         \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}} \]

   5. Applied egg-rr 93.1%

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}} \]

   if 1.84999999999999999e-64 < t

   1. Initial program 88.0%

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
   2. Step-by-step derivation

      1. associate-/l* 93.9%

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

      2. associate-*r/ 93.9%

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

      3. *-commutative 93.9%

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

      4. *-inverses 93.9%

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

      5. /-rgt-identity 93.9%

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

      6. *-commutative 93.9%

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

   3. Simplified 93.9%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.85 \cdot 10^{-64}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 2: 91.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} t = |t|\\ [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.2 \cdot 10^{-64}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: t should be positive before calling this function
NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.2e-64) (* y (/ x z)) (* x (/ y z))))

C

t = abs(t);
assert(x < y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.2e-64) {
		tmp = y * (x / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

NOTE: t should be positive before calling this function
NOTE: x and y should be sorted in increasing order before calling this function.
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 (t <= 1.2d-64) then
        tmp = y * (x / z)
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

t = Math.abs(t);
assert x < y;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.2e-64) {
		tmp = y * (x / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

t = abs(t)
[x, y] = sort([x, y])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.2e-64:
		tmp = y * (x / z)
	else:
		tmp = x * (y / z)
	return tmp

Julia

t = abs(t)
x, y = sort([x, y])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.2e-64)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

t = abs(t)
x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.2e-64)
		tmp = y * (x / z);
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t should be positive before calling this function
NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1.2e-64], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.19999999999999999e-64

   1. Initial program 84.6%

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
   2. Step-by-step derivation

      1. associate-/l* 94.7%

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

      2. associate-*r/ 94.7%

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

      3. *-commutative 94.7%

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

      4. *-inverses 94.7%

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

      5. /-rgt-identity 94.7%

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

      6. *-commutative 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in x around 0 92.5%

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

      1. associate-/l* 94.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

   6. Simplified 94.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 93.5%

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

   8. Applied egg-rr 93.5%

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

   if 1.19999999999999999e-64 < t

   1. Initial program 88.0%

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
   2. Step-by-step derivation

      1. associate-/l* 93.9%

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

      2. associate-*r/ 93.9%

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

      3. *-commutative 93.9%

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

      4. *-inverses 93.9%

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

      5. /-rgt-identity 93.9%

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

      6. *-commutative 93.9%

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

   3. Simplified 93.9%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.2 \cdot 10^{-64}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 3: 91.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} t = |t|\\ [x, y] = \mathsf{sort}([x, y])\\ \\ x \cdot \frac{y}{z} \end{array} \]

FPCore

NOTE: t should be positive before calling this function
NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (* x (/ y z)))

C

t = abs(t);
assert(x < y);
double code(double x, double y, double z, double t) {
	return x * (y / z);
}

Fortran

NOTE: t should be positive before calling this function
NOTE: x and y should be sorted in increasing order before calling this function.
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 / z)
end function

Java

t = Math.abs(t);
assert x < y;
public static double code(double x, double y, double z, double t) {
	return x * (y / z);
}

Python

t = abs(t)
[x, y] = sort([x, y])
def code(x, y, z, t):
	return x * (y / z)

Julia

t = abs(t)
x, y = sort([x, y])
function code(x, y, z, t)
	return Float64(x * Float64(y / z))
end

MATLAB

t = abs(t)
x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z, t)
	tmp = x * (y / z);
end

Wolfram

NOTE: t should be positive before calling this function
NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.7%

   \[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
2. Step-by-step derivation

   1. associate-/l* 94.4%

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

   2. associate-*r/ 94.4%

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

   3. *-commutative 94.4%

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

   4. *-inverses 94.4%

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

   5. /-rgt-identity 94.4%

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

   6. *-commutative 94.4%

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

3. Simplified 94.4%

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

4. Final simplification 94.4%

   \[\leadsto x \cdot \frac{y}{z} \]

Developer target: 98.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ t_2 := \frac{\frac{y}{z} \cdot t}{t}\\ t_3 := \frac{y}{\frac{z}{x}}\\ \mathbf{if}\;t_2 < -1.20672205123045 \cdot 10^{+245}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 < -5.907522236933906 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 < 5.658954423153415 \cdot 10^{-65}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 < 2.0087180502407133 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y z))) (t_2 (/ (* (/ y z) t) t)) (t_3 (/ y (/ z x))))
   (if (< t_2 -1.20672205123045e+245)
     t_3
     (if (< t_2 -5.907522236933906e-275)
       t_1
       (if (< t_2 5.658954423153415e-65)
         t_3
         (if (< t_2 2.0087180502407133e+217) t_1 (/ (* y x) z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / z);
	double t_2 = ((y / z) * t) / t;
	double t_3 = y / (z / x);
	double tmp;
	if (t_2 < -1.20672205123045e+245) {
		tmp = t_3;
	} else if (t_2 < -5.907522236933906e-275) {
		tmp = t_1;
	} else if (t_2 < 5.658954423153415e-65) {
		tmp = t_3;
	} else if (t_2 < 2.0087180502407133e+217) {
		tmp = t_1;
	} else {
		tmp = (y * x) / z;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = x * (y / z)
    t_2 = ((y / z) * t) / t
    t_3 = y / (z / x)
    if (t_2 < (-1.20672205123045d+245)) then
        tmp = t_3
    else if (t_2 < (-5.907522236933906d-275)) then
        tmp = t_1
    else if (t_2 < 5.658954423153415d-65) then
        tmp = t_3
    else if (t_2 < 2.0087180502407133d+217) then
        tmp = t_1
    else
        tmp = (y * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / z);
	double t_2 = ((y / z) * t) / t;
	double t_3 = y / (z / x);
	double tmp;
	if (t_2 < -1.20672205123045e+245) {
		tmp = t_3;
	} else if (t_2 < -5.907522236933906e-275) {
		tmp = t_1;
	} else if (t_2 < 5.658954423153415e-65) {
		tmp = t_3;
	} else if (t_2 < 2.0087180502407133e+217) {
		tmp = t_1;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / z)
	t_2 = ((y / z) * t) / t
	t_3 = y / (z / x)
	tmp = 0
	if t_2 < -1.20672205123045e+245:
		tmp = t_3
	elif t_2 < -5.907522236933906e-275:
		tmp = t_1
	elif t_2 < 5.658954423153415e-65:
		tmp = t_3
	elif t_2 < 2.0087180502407133e+217:
		tmp = t_1
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / z))
	t_2 = Float64(Float64(Float64(y / z) * t) / t)
	t_3 = Float64(y / Float64(z / x))
	tmp = 0.0
	if (t_2 < -1.20672205123045e+245)
		tmp = t_3;
	elseif (t_2 < -5.907522236933906e-275)
		tmp = t_1;
	elseif (t_2 < 5.658954423153415e-65)
		tmp = t_3;
	elseif (t_2 < 2.0087180502407133e+217)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / z);
	t_2 = ((y / z) * t) / t;
	t_3 = y / (z / x);
	tmp = 0.0;
	if (t_2 < -1.20672205123045e+245)
		tmp = t_3;
	elseif (t_2 < -5.907522236933906e-275)
		tmp = t_1;
	elseif (t_2 < 5.658954423153415e-65)
		tmp = t_3;
	elseif (t_2 < 2.0087180502407133e+217)
		tmp = t_1;
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y / z), $MachinePrecision] * t), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$3 = N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.20672205123045e+245], t$95$3, If[Less[t$95$2, -5.907522236933906e-275], t$95$1, If[Less[t$95$2, 5.658954423153415e-65], t$95$3, If[Less[t$95$2, 2.0087180502407133e+217], t$95$1, N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]]]]]]

Reproduce

herbie shell --seed 2023320 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"
  :precision binary64

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045e+245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.907522236933906e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.658954423153415e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e+217) (* x (/ y z)) (/ (* y x) z)))))

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