Average Error: 0.5 → 0.5
Time: 3.2s
Precision: binary64
Cost: 13120
\[\sqrt{x - 1} \cdot \sqrt{x}\]
↓
\[\sqrt{x - 1} \cdot \sqrt{x}\]
\sqrt{x - 1} \cdot \sqrt{x}
↓
\sqrt{x - 1} \cdot \sqrt{x}
(FPCore (x) :precision binary64 (* (sqrt (- x 1.0)) (sqrt x)))
↓
(FPCore (x) :precision binary64 (* (sqrt (- x 1.0)) (sqrt x)))
double code(double x) {
	return sqrt(x - 1.0) * sqrt(x);
}
↓
double code(double x) {
	return sqrt(x - 1.0) * sqrt(x);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error1.4
Cost58688
\[\sqrt[3]{\sqrt{x - 1} \cdot \sqrt{x}} \cdot \left(\sqrt[3]{\sqrt{x - 1} \cdot \sqrt{x}} \cdot \sqrt[3]{\sqrt{x - 1} \cdot \sqrt{x}}\right)\]
Alternative 2
Error1.3
Cost45632
\[\left(\sqrt[3]{\sqrt{x - 1}} \cdot \sqrt[3]{\sqrt{x - 1}}\right) \cdot \left(\sqrt{x} \cdot \sqrt[3]{\sqrt{x - 1}}\right)\]
Alternative 3
Error1.3
Cost45632
\[\sqrt{x} \cdot \left(\sqrt[3]{\sqrt{x - 1}} \cdot \left(\sqrt[3]{\sqrt{x - 1}} \cdot \sqrt[3]{\sqrt{x - 1}}\right)\right)\]
Alternative 4
Error1.3
Cost45376
\[\sqrt[3]{\sqrt{x}} \cdot \left(\sqrt{x - 1} \cdot \left(\sqrt[3]{\sqrt{x}} \cdot \sqrt[3]{\sqrt{x}}\right)\right)\]
Alternative 5
Error0.8
Cost39232
\[\sqrt{\sqrt[3]{x - 1} \cdot \sqrt[3]{x - 1}} \cdot \left(\sqrt{x} \cdot \sqrt{\sqrt[3]{x - 1}}\right)\]
Alternative 6
Error0.5
Cost39104
\[\sqrt{\sqrt{x - 1} \cdot \sqrt{x}} \cdot \sqrt{\sqrt{x - 1} \cdot \sqrt{x}}\]
Alternative 7
Error0.7
Cost32576
\[\sqrt{1 + \sqrt{x}} \cdot \left(\sqrt{x} \cdot \sqrt{\sqrt{x} - 1}\right)\]
Alternative 8
Error0.7
Cost32576
\[\sqrt{\sqrt{x - 1}} \cdot \left(\sqrt{x} \cdot \sqrt{\sqrt{x - 1}}\right)\]
Alternative 9
Error0.9
Cost32576
\[\sqrt{x} \cdot \left(\sqrt{\sqrt[3]{x - 1}} \cdot \left|\sqrt[3]{x - 1}\right|\right)\]
Alternative 10
Error0.8
Cost32448
\[\left(\sqrt{x - 1} \cdot \left|\sqrt[3]{x}\right|\right) \cdot \sqrt{\sqrt[3]{x}}\]
Alternative 11
Error0.7
Cost32448
\[\sqrt{\sqrt{x}} \cdot \left(\sqrt{x - 1} \cdot \sqrt{\sqrt{x}}\right)\]
Alternative 12
Error22.3
Cost25984
\[\sqrt{x} \cdot \sqrt[3]{{\left(\sqrt{x - 1}\right)}^{3}}\]
Alternative 13
Error4.9
Cost25920
\[\sqrt{x} \cdot e^{\log \left(\sqrt{x - 1}\right)}\]
Alternative 14
Error32.6
Cost6784
\[{\left(x \cdot \left(x - 1\right)\right)}^{0.5}\]
Alternative 15
Error32.6
Cost6720
\[\sqrt{x \cdot \left(x - 1\right)}\]
Alternative 16
Error0.4
Cost448
\[x - \left(0.5 + \frac{0.125}{x}\right)\]
Alternative 17
Error0.6
Cost192
\[x - 0.5\]
Alternative 18
Error1.3
Cost64
\[x\]
Alternative 19
Error60.6
Cost64
\[1\]
Alternative 20
Error62.6
Cost64
\[0\]
Alternative 21
Error63.3
Cost64
\[-1\]

Error

Derivation

  1. Initial program 0.5

    \[\sqrt{x - 1} \cdot \sqrt{x}\]

  2. Simplified0.5

    \[\leadsto \color{blue}{\sqrt{x - 1} \cdot \sqrt{x}}\]

  3. Final simplification0.5

    \[\leadsto \sqrt{x - 1} \cdot \sqrt{x}\]

Reproduce

herbie shell --seed 2021022 
(FPCore (x)
  :name "sqrt times"
  :precision binary64
  (* (sqrt (- x 1.0)) (sqrt x)))