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

Average Accuracy: 76.9% → 99.1%

Time: 4.4s

Precision: binary64

Cost: 1362

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -\infty \lor \neg \left(\frac{y}{z} \leq -2 \cdot 10^{-187} \lor \neg \left(\frac{y}{z} \leq 5 \cdot 10^{-158}\right) \land \frac{y}{z} \leq 5 \cdot 10^{+190}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ y z) (- INFINITY))
         (not
          (or (<= (/ y z) -2e-187)
              (and (not (<= (/ y z) 5e-158)) (<= (/ y z) 5e+190)))))
   (* y (/ x z))
   (* (/ y z) x)))

C

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

↓

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y / z) <= -((double) INFINITY)) || !(((y / z) <= -2e-187) || (!((y / z) <= 5e-158) && ((y / z) <= 5e+190)))) {
		tmp = y * (x / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Java

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

↓

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y / z) <= -Double.POSITIVE_INFINITY) || !(((y / z) <= -2e-187) || (!((y / z) <= 5e-158) && ((y / z) <= 5e+190)))) {
		tmp = y * (x / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	tmp = 0
	if ((y / z) <= -math.inf) or not (((y / z) <= -2e-187) or (not ((y / z) <= 5e-158) and ((y / z) <= 5e+190))):
		tmp = y * (x / z)
	else:
		tmp = (y / z) * x
	return tmp

Julia

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

↓

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y / z) <= Float64(-Inf)) || !((Float64(y / z) <= -2e-187) || (!(Float64(y / z) <= 5e-158) && (Float64(y / z) <= 5e+190))))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y / z) <= -Inf) || ~((((y / z) <= -2e-187) || (~(((y / z) <= 5e-158)) && ((y / z) <= 5e+190)))))
		tmp = y * (x / z);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y / z), $MachinePrecision], (-Infinity)], N[Not[Or[LessEqual[N[(y / z), $MachinePrecision], -2e-187], And[N[Not[LessEqual[N[(y / z), $MachinePrecision], 5e-158]], $MachinePrecision], LessEqual[N[(y / z), $MachinePrecision], 5e+190]]]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Target

Original	76.9%
Target	97.5%
Herbie	99.1%

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 y z) < -inf.0 or -2e-187 < (/.f64 y z) < 4.99999999999999972e-158 or 5.00000000000000036e190 < (/.f64 y z)

   1. Initial program 63.9%

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

   2. Simplified 98.2%

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

      [Start] 63.9	\[ x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
      associate-/l* [=>] 76.8	\[ x \cdot \color{blue}{\frac{\frac{y}{z}}{\frac{t}{t}}} \]
      *-inverses [=>] 76.8	\[ x \cdot \frac{\frac{y}{z}}{\color{blue}{1}} \]
      /-rgt-identity [=>] 76.8	\[ x \cdot \color{blue}{\frac{y}{z}} \]
      associate-*r/ [=>] 98.3	\[ \color{blue}{\frac{x \cdot y}{z}} \]
      associate-*l/ [<=] 98.2	\[ \color{blue}{\frac{x}{z} \cdot y} \]
      *-commutative [<=] 98.2	\[ \color{blue}{y \cdot \frac{x}{z}} \]

   if -inf.0 < (/.f64 y z) < -2e-187 or 4.99999999999999972e-158 < (/.f64 y z) < 5.00000000000000036e190

   1. Initial program 85.5%

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

   2. Simplified 99.6%

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

      [Start] 85.5	\[ x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
      associate-/l* [=>] 99.6	\[ x \cdot \color{blue}{\frac{\frac{y}{z}}{\frac{t}{t}}} \]
      *-inverses [=>] 99.6	\[ x \cdot \frac{\frac{y}{z}}{\color{blue}{1}} \]
      /-rgt-identity [=>] 99.6	\[ x \cdot \color{blue}{\frac{y}{z}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -\infty \lor \neg \left(\frac{y}{z} \leq -2 \cdot 10^{-187} \lor \neg \left(\frac{y}{z} \leq 5 \cdot 10^{-158}\right) \land \frac{y}{z} \leq 5 \cdot 10^{+190}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	90.5%
Cost	320

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

Reproduce

herbie shell --seed 2023125 
(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)))