bug329 (missed optimization)

Average Accuracy: 100.0% → 100.0%

Time: 1.5s

Precision: binary64

Cost: 6592

\[x \geq 0\]

Math

\[\tan^{-1} \left(\frac{y}{x}\right) \]

↓

\[\tan^{-1} \left(\frac{y}{x}\right) \]

FPCore

(FPCore (x y) :precision binary64 (atan (/ y x)))

↓

(FPCore (x y) :precision binary64 (atan (/ y x)))

C

double code(double x, double y) {
	return atan((y / x));
}

↓

double code(double x, double y) {
	return atan((y / x));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = atan((y / x))
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = atan((y / x))
end function

Java

public static double code(double x, double y) {
	return Math.atan((y / x));
}

↓

public static double code(double x, double y) {
	return Math.atan((y / x));
}

Python

def code(x, y):
	return math.atan((y / x))

↓

def code(x, y):
	return math.atan((y / x))

Julia

function code(x, y)
	return atan(Float64(y / x))
end

↓

function code(x, y)
	return atan(Float64(y / x))
end

MATLAB

function tmp = code(x, y)
	tmp = atan((y / x));
end

↓

function tmp = code(x, y)
	tmp = atan((y / x));
end

Wolfram

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

↓

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

Target

Original	100.0%
Target	100.0%
Herbie	100.0%

\[\tan^{-1}_* \frac{y}{x} \]

Derivation

1. Initial program 100.0%

   \[\tan^{-1} \left(\frac{y}{x}\right) \]

2. Final simplification 100.0%

   \[\leadsto \tan^{-1} \left(\frac{y}{x}\right) \]

Reproduce

herbie shell --seed 2023137 
(FPCore (x y)
  :name "bug329 (missed optimization)"
  :precision binary64
  :pre (>= x 0.0)

  :herbie-target
  (atan2 y x)

  (atan (/ y x)))