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

Average Error: 10.14% → 3.01%

Time: 8.9s

Precision: binary64

Cost: 576

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	10.14%
Target	3.12%
Herbie	3.01%

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

Derivation

1. Initial program 10.14

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

2. Simplified 3.13

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

   [Start] 10.14	\[ x + \frac{y \cdot \left(z - x\right)}{t} \]
   associate-*l/ [<=] 3.13	\[ x + \color{blue}{\frac{y}{t} \cdot \left(z - x\right)} \]

3. Applied egg-rr 3.01

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

4. Final simplification 3.01

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

Alternatives

Alternative 1
Error	38.52%
Cost	1242

\[\begin{array}{l} \mathbf{if}\;x \leq -0.04:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-247} \lor \neg \left(x \leq 1.8 \cdot 10^{-186}\right) \land \left(x \leq 5.5 \cdot 10^{-100} \lor \neg \left(x \leq 1.04 \cdot 10^{-63}\right) \land x \leq 4.4 \cdot 10^{-39}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	36.52%
Cost	977

\[\begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-96} \lor \neg \left(x \leq 2.9 \cdot 10^{-80}\right) \land x \leq 4.6 \cdot 10^{-40}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	41.57%
Cost	849

\[\begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-272} \lor \neg \left(x \leq 6.5 \cdot 10^{-239}\right) \land x \leq 4.1 \cdot 10^{-97}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	41.39%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-272}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-97}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	17.77%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+166} \lor \neg \left(y \leq 8.8 \cdot 10^{+175}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \]

Alternative 6
Error	16.98%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-16} \lor \neg \left(x \leq 1.4 \cdot 10^{-75}\right):\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \]

Alternative 7
Error	3.13%
Cost	576

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

Alternative 8
Error	49.06%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023121 
(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)))