Average Error: 0.4 → 0.2

Time: 4.0s

Precision: binary64

Cost: 448

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

↓

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

(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(Float64(x / 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[(N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision] * 100.0), $MachinePrecision]

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

↓

\frac{x}{x + y} \cdot 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
\[\leadsto \color{blue}{\frac{x}{x + y} \cdot 100} \]
Proof
(*.f64 (/.f64 x (+.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))): 35 points increase in error, 21 points decrease in error
Final simplification0.2
\[\leadsto \frac{x}{x + y} \cdot 100 \]

Alternatives

Alternative 1
Error	16.9
Cost	584

\[\begin{array}{l} t_0 := x \cdot \frac{100}{y}\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-61}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	17.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-61}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \end{array} \]

Alternative 3
Error	16.9
Cost	584

\[\begin{array}{l} t_0 := \frac{x}{\frac{y}{100}}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-61}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

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 2022337 
(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)))