Development.Shake.Progress:message from shake-0.15.5

Average Error: 0.4 → 0.2

Time: 2.0s

Precision: binary64

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

double code(double x, double y) {
	return 100.0 * (x / (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 = 100.0d0 * (x / (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 100.0 * (x / (x + y));
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

code[x_, y_] := N[(100.0 * N[(x / 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

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

3. Applied egg-rr 0.2

   \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot 0.01}} \]

4. Applied egg-rr 0.2

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

5. Final simplification 0.2

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

Reproduce

herbie shell --seed 2022210 
(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)))