ab-angle->ABCF D

Average Error: 16.4 → 0.3

Time: 2.1s

Precision: binary64

Math

\[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]

↓

\[-{\left(a \cdot b\right)}^{2} \]

FPCore

(FPCore (a b) :precision binary64 (- (* (* (* a a) b) b)))

↓

(FPCore (a b) :precision binary64 (- (pow (* a b) 2.0)))

C

double code(double a, double b) {
	return -(((a * a) * b) * b);
}

↓

double code(double a, double b) {
	return -pow((a * b), 2.0);
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = -(((a * a) * b) * b)
end function

↓

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = -((a * b) ** 2.0d0)
end function

Java

public static double code(double a, double b) {
	return -(((a * a) * b) * b);
}

↓

public static double code(double a, double b) {
	return -Math.pow((a * b), 2.0);
}

Python

def code(a, b):
	return -(((a * a) * b) * b)

↓

def code(a, b):
	return -math.pow((a * b), 2.0)

Julia

function code(a, b)
	return Float64(-Float64(Float64(Float64(a * a) * b) * b))
end

↓

function code(a, b)
	return Float64(-(Float64(a * b) ^ 2.0))
end

MATLAB

function tmp = code(a, b)
	tmp = -(((a * a) * b) * b);
end

↓

function tmp = code(a, b)
	tmp = -((a * b) ^ 2.0);
end

Wolfram

code[a_, b_] := (-N[(N[(N[(a * a), $MachinePrecision] * b), $MachinePrecision] * b), $MachinePrecision])

↓

code[a_, b_] := (-N[Power[N[(a * b), $MachinePrecision], 2.0], $MachinePrecision])

Error

Bits error versus a

Bits error versus b

Derivation

1. Initial program 16.4

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]

2. Applied egg-rr 0.3

   \[\leadsto -\color{blue}{{\left(a \cdot b\right)}^{2}} \]

3. Final simplification 0.3

   \[\leadsto -{\left(a \cdot b\right)}^{2} \]

Reproduce

herbie shell --seed 2022150 
(FPCore (a b)
  :name "ab-angle->ABCF D"
  :precision binary64
  (- (* (* (* a a) b) b)))