ab-angle->ABCF D

Average Error: 15.8 → 0.3

Time: 1.1s

Precision: binary64

Cost: 640

Math

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

↓

\[-\left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) + 0\right) \]

FPCore

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

↓

(FPCore (a b) :precision binary64 (- (+ (* (* a b) (* a b)) 0.0)))

C

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

↓

double code(double a, double b) {
	return -(((a * b) * (a * b)) + 0.0);
}

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) * (a * b)) + 0.0d0)
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 -(((a * b) * (a * b)) + 0.0);
}

Python

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

↓

def code(a, b):
	return -(((a * b) * (a * b)) + 0.0)

Julia

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

↓

function code(a, b)
	return Float64(-Float64(Float64(Float64(a * b) * Float64(a * b)) + 0.0))
end

MATLAB

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

↓

function tmp = code(a, b)
	tmp = -(((a * b) * (a * b)) + 0.0);
end

Wolfram

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

↓

code[a_, b_] := (-N[(N[(N[(a * b), $MachinePrecision] * N[(a * b), $MachinePrecision]), $MachinePrecision] + 0.0), $MachinePrecision])

Derivation

1. Initial program 15.8

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

2. Applied egg-rr 0.3

   \[\leadsto -\color{blue}{\left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) + 0\right)} \]

3. Final simplification 0.3

   \[\leadsto -\left(\left(a \cdot b\right) \cdot \left(a \cdot b\right) + 0\right) \]

Alternatives

Alternative 1
Error	2.8
Cost	1036

\[\begin{array}{l} t_0 := -a \cdot \left(b \cdot \left(a \cdot b\right)\right)\\ t_1 := -\left(b \cdot \left(a \cdot \left(a \cdot b\right)\right) + 0\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+162}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-227}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	3.0
Cost	1032

\[\begin{array}{l} t_0 := -a \cdot \left(b \cdot \left(a \cdot b\right)\right)\\ \mathbf{if}\;a \cdot a \leq 5 \cdot 10^{-293}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a \cdot a \leq 10^{+302}:\\ \;\;\;\;-\left(\left(a \cdot a\right) \cdot b\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	16.4
Cost	512

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

Alternative 4
Error	5.6
Cost	512

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

Reproduce

herbie shell --seed 2023053 
(FPCore (a b)
  :name "ab-angle->ABCF D"
  :precision binary64
  (- (* (* (* a a) b) b)))