Expression 4, p15

Percentage Accurate: 100.0% → 100.0%

Time: 2.7s

Precision: binary64

Cost: 704

• Unsound rule application detected in e-graph. Results may not be sound.

\[\left(5 \leq a \land a \leq 10\right) \land \left(0 \leq b \land b \leq 0.001\right)\]

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	100.0%
Target	100.0%
Herbie	100.0%

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

Derivation

1. Initial program 100.0%

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

2. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{b \cdot \left(a + b\right) + a \cdot \left(a + b\right)} \]
   Step-by-step derivation

   [Start] 100.0%	\[ \left(a + b\right) \cdot \left(a + b\right) \]
   +-commutative [=>] 100.0%	\[ \left(a + b\right) \cdot \color{blue}{\left(b + a\right)} \]
   distribute-rgt-in [=>] 100.0%	\[ \color{blue}{b \cdot \left(a + b\right) + a \cdot \left(a + b\right)} \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	100.0%
Cost	704

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

Alternative 2
Accuracy	5.3%
Cost	448

\[b \cdot \left(b + a \cdot 2\right) \]

Alternative 3
Accuracy	100.0%
Cost	448

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

Alternative 4
Accuracy	4.1%
Cost	192

\[b \cdot b \]

Reproduce

herbie shell --seed 2023178 
(FPCore (a b)
  :name "Expression 4, p15"
  :precision binary64
  :pre (and (and (<= 5.0 a) (<= a 10.0)) (and (<= 0.0 b) (<= b 0.001)))

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

  (* (+ a b) (+ a b)))