Development.Shake.Progress:message from shake-0.15.5

Average Error: 0.4 → 0.4

Time: 3.5s

Precision: binary64

Cost: 448

Math

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

↓

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

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

Target

Original	0.4
Target	0.2
Herbie	0.4

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

Derivation

1. Initial program 0.4

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

2. Final simplification 0.4

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

Alternatives

Alternative 1
Error	16.3
Cost	848

\[\begin{array}{l} t_0 := x \cdot \frac{100}{y}\\ \mathbf{if}\;y \leq -3 \cdot 10^{+48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-29}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-76}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+59}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	16.3
Cost	848

\[\begin{array}{l} t_0 := x \cdot \frac{100}{y}\\ \mathbf{if}\;y \leq -2.35 \cdot 10^{+48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-29}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-76}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+59}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot 0.01}\\ \end{array} \]

Alternative 3
Error	16.3
Cost	848

\[\begin{array}{l} t_0 := \frac{x \cdot 100}{y}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-29}:\\ \;\;\;\;100\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \frac{100}{y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+59}:\\ \;\;\;\;100\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	0.2
Cost	448

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

Alternative 5
Error	31.2
Cost	64

\[100 \]

Reproduce

herbie shell --seed 2022325 
(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)))