Difference of squares

Average Error: 0.01% → 0.01%

Time: 1.4s

Precision: binary64

Cost: 448

Math

\[a \cdot a - b \cdot b \]

↓

\[a \cdot a - b \cdot b \]

FPCore

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

↓

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

C

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

↓

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

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 * a) - (b * b)
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 * a) - (b * b);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.01%
Target	0%
Herbie	0.01%

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

Derivation

1. Initial program 0.01

   \[a \cdot a - b \cdot b \]

2. Final simplification 0.01

   \[\leadsto a \cdot a - b \cdot b \]

Reproduce

herbie shell --seed 2023115 
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

  :herbie-target
  (* (+ a b) (- a b))

  (- (* a a) (* b b)))