Expression 3, p15

Average Accuracy: 100.0% → 100.0%

Time: 2.0s

Precision: binary64

Cost: 448

\[0 \leq x \land x \leq 2\]

Math

\[x \cdot \left(x \cdot x\right) + x \cdot x \]

↓

\[\left(x + 1\right) \cdot \left(x \cdot x\right) \]

FPCore

(FPCore (x) :precision binary64 (+ (* x (* x x)) (* x x)))

↓

(FPCore (x) :precision binary64 (* (+ x 1.0) (* x x)))

C

double code(double x) {
	return (x * (x * x)) + (x * x);
}

↓

double code(double x) {
	return (x + 1.0) * (x * x);
}

Fortran

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

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x + 1.0d0) * (x * x)
end function

Java

public static double code(double x) {
	return (x * (x * x)) + (x * x);
}

↓

public static double code(double x) {
	return (x + 1.0) * (x * x);
}

Python

def code(x):
	return (x * (x * x)) + (x * x)

↓

def code(x):
	return (x + 1.0) * (x * x)

Julia

function code(x)
	return Float64(Float64(x * Float64(x * x)) + Float64(x * x))
end

↓

function code(x)
	return Float64(Float64(x + 1.0) * Float64(x * x))
end

MATLAB

function tmp = code(x)
	tmp = (x * (x * x)) + (x * x);
end

↓

function tmp = code(x)
	tmp = (x + 1.0) * (x * x);
end

Wolfram

code[x_] := N[(N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision]

↓

code[x_] := N[(N[(x + 1.0), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision]

Target

Original	100.0%
Target	100.0%
Herbie	100.0%

\[\left(\left(1 + x\right) \cdot x\right) \cdot x \]

Derivation

1. Initial program 100.0%

   \[x \cdot \left(x \cdot x\right) + x \cdot x \]

2. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\left(x + 1\right) \cdot \left(x \cdot x\right)} \]
   Proof

   [Start] 100.0	\[ x \cdot \left(x \cdot x\right) + x \cdot x \]
   distribute-lft1-in [=>] 100.0	\[ \color{blue}{\left(x + 1\right) \cdot \left(x \cdot x\right)} \]

3. Final simplification 100.0%

   \[\leadsto \left(x + 1\right) \cdot \left(x \cdot x\right) \]

Alternatives

Alternative 1
Accuracy	98.0%
Cost	192

\[x \cdot x \]

Reproduce

herbie shell --seed 2023146 
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (and (<= 0.0 x) (<= x 2.0))

  :herbie-target
  (* (* (+ 1.0 x) x) x)

  (+ (* x (* x x)) (* x x)))