Expression 3, p15

Average Error: 0.0 → 0.0

Time: 2.6s

Precision: binary64

Cost: 7040

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

Math

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

↓

\[\frac{x \cdot \left({x}^{3} - x\right)}{x + -1} \]

FPCore

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

↓

(FPCore (x) :precision binary64 (/ (* x (- (pow x 3.0) x)) (+ x -1.0)))

C

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

↓

double code(double x) {
	return (x * (pow(x, 3.0) - x)) / (x + -1.0);
}

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 * ((x ** 3.0d0) - x)) / (x + (-1.0d0))
end function

Java

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

↓

public static double code(double x) {
	return (x * (Math.pow(x, 3.0) - x)) / (x + -1.0);
}

Python

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

↓

def code(x):
	return (x * (math.pow(x, 3.0) - x)) / (x + -1.0)

Julia

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

↓

function code(x)
	return Float64(Float64(x * Float64((x ^ 3.0) - x)) / Float64(x + -1.0))
end

MATLAB

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

↓

function tmp = code(x)
	tmp = (x * ((x ^ 3.0) - x)) / (x + -1.0);
end

Wolfram

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

↓

code[x_] := N[(N[(x * N[(N[Power[x, 3.0], $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

3. Applied egg-rr 0.0

   \[\leadsto \color{blue}{\frac{\left(x \cdot x\right) \cdot \mathsf{fma}\left(x, x, -1\right)}{x + -1}} \]

4. Taylor expanded in x around 0 0.0

   \[\leadsto \frac{\color{blue}{-1 \cdot {x}^{2} + {x}^{4}}}{x + -1} \]

5. Simplified 0.0

   \[\leadsto \frac{\color{blue}{x \cdot \left({x}^{3} - x\right)}}{x + -1} \]

6. Final simplification 0.0

   \[\leadsto \frac{x \cdot \left({x}^{3} - x\right)}{x + -1} \]

Alternatives

Alternative 1
Error	0.0
Cost	576

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

Alternative 2
Error	0.0
Cost	448

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

Alternative 3
Error	1.4
Cost	192

\[x \cdot x \]

Alternative 4
Error	60.9
Cost	128

\[-x \]

Reproduce

herbie shell --seed 2022228 
(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)))