Development.Shake.Progress:message from shake-0.15.5

Average Error: 0.4 → 0.2

Time: 3.8s

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	0.4
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 0.4

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

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))): 25 points increase in error, 30 points decrease in error

3. Final simplification 0.2

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

Alternatives

Alternative 1
Error	17.5
Cost	848

\[\begin{array}{l} t_0 := x \cdot \frac{100}{y}\\ \mathbf{if}\;x \leq -1.0946692789448324 \cdot 10^{+55}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 8.284860875722656 \cdot 10^{+91}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.572295006533607 \cdot 10^{+111}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 2.613042532516956 \cdot 10^{+170}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 2
Error	17.5
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -1.0946692789448324 \cdot 10^{+55}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 8.284860875722656 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;x \leq 3.572295006533607 \cdot 10^{+111}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 2.613042532516956 \cdot 10^{+170}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 3
Error	17.5
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -1.0946692789448324 \cdot 10^{+55}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 8.284860875722656 \cdot 10^{+91}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{elif}\;x \leq 3.572295006533607 \cdot 10^{+111}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 2.613042532516956 \cdot 10^{+170}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 4
Error	17.5
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -1.0946692789448324 \cdot 10^{+55}:\\ \;\;\;\;100\\ \mathbf{elif}\;x \leq 8.284860875722656 \cdot 10^{+91}:\\ \;\;\;\;\frac{x \cdot 100}{y}\\ \mathbf{elif}\;x \leq 3.572295006533607 \cdot 10^{+111}:\\ \;\;\;\;100 + -100 \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 2.613042532516956 \cdot 10^{+170}:\\ \;\;\;\;\frac{100}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;100\\ \end{array} \]

Alternative 5
Error	32.4
Cost	64

\[100 \]

Reproduce

herbie shell --seed 2022318 
(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)))