Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D

Percentage Accurate: 92.3% → 97.4%

Time: 12.1s

Precision: binary64

Cost: 576

• 25.2% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

\[x + \frac{z - x}{\frac{t}{y}} \]

FPCore

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

↓

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

C

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	92.3%
Target	91.0%
Herbie	97.4%

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

Derivation

1. Initial program 93.7%

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

2. Simplified 97.0%

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

   [Start] 93.7%	\[ x + \frac{y \cdot \left(z - x\right)}{t} \]
   associate-*l/ [<=] 97.0%	\[ x + \color{blue}{\frac{y}{t} \cdot \left(z - x\right)} \]

3. Applied egg-rr 97.1%

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

   [Start] 97.0%	\[ x + \frac{y}{t} \cdot \left(z - x\right) \]
   *-commutative [=>] 97.0%	\[ x + \color{blue}{\left(z - x\right) \cdot \frac{y}{t}} \]
   clear-num [=>] 96.9%	\[ x + \left(z - x\right) \cdot \color{blue}{\frac{1}{\frac{t}{y}}} \]
   un-div-inv [=>] 97.1%	\[ x + \color{blue}{\frac{z - x}{\frac{t}{y}}} \]

4. Final simplification 97.1%

   \[\leadsto x + \frac{z - x}{\frac{t}{y}} \]

Alternatives

Alternative 1
Accuracy	97.4%
Cost	576

\[x + \frac{z - x}{\frac{t}{y}} \]

Alternative 2
Accuracy	84.3%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+40} \lor \neg \left(x \leq 5.1 \cdot 10^{-26}\right):\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 3
Accuracy	50.8%
Cost	649

\[\begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-55} \lor \neg \left(y \leq 1.45 \cdot 10^{-27}\right):\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Accuracy	77.0%
Cost	580

\[\begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+226}:\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 5
Accuracy	76.9%
Cost	580

\[\begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+231}:\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 6
Accuracy	97.4%
Cost	576

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

Alternative 7
Accuracy	38.6%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023263 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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