Average Error: 0.2 → 0.2
Time: 6.8s
Precision: binary64
Cost: 320
\[\left(x \cdot 3\right) \cdot x\]
↓
\[x \cdot \left(x \cdot 3\right)\]
\left(x \cdot 3\right) \cdot x
↓
x \cdot \left(x \cdot 3\right)
(FPCore (x) :precision binary64 (* (* x 3.0) x))
↓
(FPCore (x) :precision binary64 (* x (* x 3.0)))
double code(double x) {
	return (x * 3.0) * x;
}
↓
double code(double x) {
	return x * (x * 3.0);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error0.5
Cost52032
\[\left|\sqrt[3]{\sqrt{3}} \cdot \left(x \cdot \left(\sqrt[3]{\sqrt{3}} \cdot \sqrt[3]{\sqrt{3}}\right)\right)\right| \cdot \sqrt{x \cdot \left(x \cdot 3\right)}\]
Alternative 2
Error0.5
Cost45632
\[\sqrt{x \cdot \left(x \cdot 3\right)} \cdot \left(\sqrt{\left|x \cdot \sqrt{3}\right|} \cdot \sqrt{\left|x \cdot \sqrt{3}\right|}\right)\]
Alternative 3
Error0.5
Cost45568
\[\sqrt{x \cdot \left(x \cdot 3\right)} \cdot \left|\sqrt[3]{\sqrt{3}} \cdot \left(x \cdot {\left(\sqrt[3]{\sqrt{3}}\right)}^{2}\right)\right|\]
Alternative 4
Error1.3
Cost39040
\[{\left(\sqrt[3]{\left|x \cdot \sqrt{3}\right|}\right)}^{5} \cdot \sqrt[3]{\sqrt{x \cdot \left(x \cdot 3\right)}}\]
Alternative 5
Error0.6
Cost39040
\[\sqrt{\sqrt{x \cdot \left(x \cdot 3\right)}} \cdot {\left(\sqrt{\left|x \cdot \sqrt{3}\right|}\right)}^{3}\]
Alternative 6
Error0.6
Cost32960
\[\sqrt{x \cdot \left(x \cdot 3\right)} \cdot \sqrt{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\left(x \cdot 3\right) \cdot \sqrt[3]{x}\right)}\]
Alternative 7
Error0.6
Cost32960
\[\sqrt{x \cdot \left(x \cdot 3\right)} \cdot \left(\sqrt[3]{x \cdot \left(x \cdot 3\right)} \cdot \sqrt[3]{\left|x \cdot \sqrt{3}\right|}\right)\]
Alternative 8
Error1.2
Cost32640
\[\sqrt[3]{x \cdot \left(x \cdot 3\right)} \cdot {\left(\sqrt[3]{\left|x \cdot \sqrt{3}\right|}\right)}^{4}\]
Alternative 9
Error14.1
Cost32640
\[\sqrt{x \cdot \left(x \cdot 3\right)} \cdot \sqrt[3]{{\left(\left|x \cdot \sqrt{3}\right|\right)}^{3}}\]
Alternative 10
Error32.3
Cost26176
\[\left(\left|x \cdot \sqrt{3}\right| \cdot \sqrt{x}\right) \cdot \sqrt{x \cdot 3}\]
Alternative 11
Error0.9
Cost20288
\[\sqrt[3]{x \cdot \left(x \cdot 3\right)} \cdot \left(\sqrt[3]{x \cdot \left(x \cdot 3\right)} \cdot \sqrt[3]{x \cdot \left(x \cdot 3\right)}\right)\]
Alternative 12
Error0.3
Cost19776
\[\left|x \cdot \sqrt{3}\right| \cdot \sqrt{3 \cdot \left(x \cdot x\right)}\]
Alternative 13
Error0.9
Cost19776
\[\sqrt[3]{x} \cdot \left(\left(x \cdot 3\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right)\]
Alternative 14
Error0.3
Cost19776
\[\left|x \cdot \sqrt{3}\right| \cdot \sqrt{x \cdot \left(x \cdot 3\right)}\]
Alternative 15
Error21.3
Cost19712
\[\left|x \cdot \sqrt{3}\right| \cdot \left(-x \cdot \sqrt{3}\right)\]
Alternative 16
Error0.4
Cost13504
\[\sqrt{x \cdot \left(x \cdot 3\right)} \cdot \sqrt{x \cdot \left(x \cdot 3\right)}\]
Alternative 17
Error0.3
Cost13504
\[\sqrt{3 \cdot \left(x \cdot x\right)} \cdot \sqrt{x \cdot \left(x \cdot 3\right)}\]
Alternative 18
Error21.2
Cost13440
\[\left(-x \cdot \sqrt{3}\right) \cdot \sqrt{x \cdot \left(x \cdot 3\right)}\]
Alternative 19
Error21.3
Cost13376
\[\left(x \cdot \sqrt{3}\right) \cdot \sqrt{x \cdot \left(x \cdot 3\right)}\]
Alternative 20
Error0.5
Cost13248
\[\left(x \cdot \sqrt{3}\right) \cdot \left(x \cdot \sqrt{3}\right)\]
Alternative 21
Error32.3
Cost13184
\[\left(3 \cdot {x}^{1.5}\right) \cdot \sqrt{x}\]
Alternative 22
Error0.4
Cost13184
\[{\left(\sqrt{x \cdot \left(x \cdot 3\right)}\right)}^{2}\]
Alternative 23
Error3.8
Cost13120
\[e^{\log \left(x \cdot \left(x \cdot 3\right)\right)}\]
Alternative 24
Error20.8
Cost13120
\[{\left(9 \cdot {x}^{4}\right)}^{0.5}\]
Alternative 25
Error28.1
Cost13056
\[\sqrt[3]{27 \cdot {x}^{6}}\]
Alternative 26
Error20.8
Cost13056
\[\sqrt{9 \cdot {x}^{4}}\]
Alternative 27
Error61.0
Cost64
\[1\]
Alternative 28
Error41.5
Cost64
\[0\]
Alternative 29
Error62.6
Cost64
\[-1\]

Error

Derivation

  1. Initial program 0.2

    \[\left(x \cdot 3\right) \cdot x\]

  2. Simplified0.2

    \[\leadsto \color{blue}{x \cdot \left(x \cdot 3\right)}\]

  3. Final simplification0.2

    \[\leadsto x \cdot \left(x \cdot 3\right)\]

Reproduce

herbie shell --seed 2021042 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, F"
  :precision binary64
  (* (* x 3.0) x))