ab-angle->ABCF D

Average Error: 15.6 → 0.3

Time: 4.0s

Precision: binary64

Cost: 6976

Math

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

↓

\[\left(b \cdot a\right) \cdot \frac{-b}{{a}^{-1}} \]

FPCore

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

↓

(FPCore (a b) :precision binary64 (* (* b a) (/ (- b) (pow a -1.0))))

C

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

↓

double code(double a, double b) {
	return (b * a) * (-b / pow(a, -1.0));
}

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 = (b * a) * (-b / (a ** (-1.0d0)))
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 (b * a) * (-b / Math.pow(a, -1.0));
}

Python

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

↓

def code(a, b):
	return (b * a) * (-b / math.pow(a, -1.0))

Julia

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

↓

function code(a, b)
	return Float64(Float64(b * a) * Float64(Float64(-b) / (a ^ -1.0)))
end

MATLAB

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

↓

function tmp = code(a, b)
	tmp = (b * a) * (-b / (a ^ -1.0));
end

Wolfram

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

↓

code[a_, b_] := N[(N[(b * a), $MachinePrecision] * N[((-b) / N[Power[a, -1.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 15.6

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

2. Applied egg-rr 21.0

   \[\leadsto -\color{blue}{\left(\left(1 + a \cdot \left(a \cdot b\right)\right) - 1\right)} \cdot b \]

3. Applied egg-rr 5.6

   \[\leadsto -\color{blue}{\frac{b}{\frac{1}{a \cdot \left(a \cdot b\right)}}} \]

4. Applied egg-rr 0.3

   \[\leadsto -\color{blue}{\frac{b}{{a}^{-1}} \cdot \left(b \cdot a\right)} \]

5. Final simplification 0.3

   \[\leadsto \left(b \cdot a\right) \cdot \frac{-b}{{a}^{-1}} \]

Alternatives

Alternative 1
Error	0.3
Cost	512

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

Alternative 2
Error	38.0
Cost	448

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

Alternative 3
Error	38.0
Cost	448

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

Reproduce

herbie shell --seed 2023057 
(FPCore (a b)
  :name "ab-angle->ABCF D"
  :precision binary64
  (- (* (* (* a a) b) b)))