Development.Shake.Progress:message from shake-0.15.5

Average Error: 0.3 → 0.2

Time: 3.4s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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 * (100.0d0 / (x + y))
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.3
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 0.3

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

2. Simplified 0.2

   \[\leadsto \color{blue}{x \cdot \frac{100}{x + y}} \]
   Proof
   (*.f64 x (/.f64 100 (+.f64 x y))): 0 points increase in error, 0 points decrease in error
   (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 x 100) (+.f64 x y))): 32 points increase in error, 34 points decrease in error

3. Final simplification 0.2

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

Alternatives

Alternative 1
Error	17.2
Cost	584

\[\begin{array}{l} t_0 := \frac{x}{y \cdot 0.01}\\ \mathbf{if}\;y \leq -3.459274420507047 \cdot 10^{-74}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.594983488427287 \cdot 10^{+52}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	17.2
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -3.459274420507047 \cdot 10^{-74}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{elif}\;y \leq 6.594983488427287 \cdot 10^{+52}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \end{array} \]

Alternative 3
Error	17.2
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -3.459274420507047 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 6.594983488427287 \cdot 10^{+52}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \end{array} \]

Alternative 4
Error	31.6
Cost	64

\[100 \]

Reproduce

herbie shell --seed 2022310 
(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)))