Average Error: 0.4 → 0.2

Time: 2.7s

Precision: binary64

Cost: 448

\[\frac{x \cdot 100}{x + y} \]

↓

\[\frac{x}{\frac{x + y}{100}} \]

(FPCore (x y) :precision binary64 (/ (* x 100.0) (+ x y)))

↓

(FPCore (x y) :precision binary64 (/ x (/ (+ x y) 100.0)))

double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

↓

double code(double x, double y) {
	return x / ((x + y) / 100.0);
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 100.0d0) / (x + y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / ((x + y) / 100.0d0)
end function

public static double code(double x, double y) {
	return (x * 100.0) / (x + y);
}

↓

public static double code(double x, double y) {
	return x / ((x + y) / 100.0);
}

def code(x, y):
	return (x * 100.0) / (x + y)

↓

def code(x, y):
	return x / ((x + y) / 100.0)

function code(x, y)
	return Float64(Float64(x * 100.0) / Float64(x + y))
end

↓

function code(x, y)
	return Float64(x / Float64(Float64(x + y) / 100.0))
end

function tmp = code(x, y)
	tmp = (x * 100.0) / (x + y);
end

↓

function tmp = code(x, y)
	tmp = x / ((x + y) / 100.0);
end

code[x_, y_] := N[(N[(x * 100.0), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(x / N[(N[(x + y), $MachinePrecision] / 100.0), $MachinePrecision]), $MachinePrecision]

\frac{x \cdot 100}{x + y}

↓

\frac{x}{\frac{x + y}{100}}

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	0.4
Target	0.2
Herbie	0.2

\[\frac{x}{1} \cdot \frac{100}{x + y} \]

Derivation

Initial program 0.4
\[\frac{x \cdot 100}{x + y} \]
Simplified0.2
\[\leadsto \color{blue}{\frac{x}{\frac{x + y}{100}}} \]
Proof
(/.f64 x (/.f64 (+.f64 x y) 100)): 0 points increase in error, 0 points decrease in error
(Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 x 100) (+.f64 x y))): 1 points increase in error, 0 points decrease in error
Final simplification0.2
\[\leadsto \frac{x}{\frac{x + y}{100}} \]

Alternatives

Alternative 1
Error	16.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+27}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 2.16 \cdot 10^{-16}:\\ \;\;\;\;100 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 2
Error	15.9
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+26}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3
Error	15.9
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+26}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 4
Error	0.2
Cost	448

\[x \cdot \frac{100}{x + y} \]

Alternative 5
Error	31.3
Cost	64

\[100 \]

Reproduce

herbie shell --seed 2022343 
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :herbie-target
  (* (/ x 1.0) (/ 100.0 (+ x y)))

  (/ (* x 100.0) (+ x y)))