Average Error: 0.1 → 0.1

Time: 3.2s

Precision: binary64

Cost: 6912

\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

↓

\[x \cdot 0.954929658551372 - 0.12900613773279798 \cdot {x}^{3}\]

0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)

↓

x \cdot 0.954929658551372 - 0.12900613773279798 \cdot {x}^{3}

(FPCore (x)
 :precision binary64
 (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))

↓

(FPCore (x)
 :precision binary64
 (- (* x 0.954929658551372) (* 0.12900613773279798 (pow x 3.0))))

double code(double x) {
	return (0.954929658551372 * x) - (0.12900613773279798 * ((x * x) * x));
}

↓

double code(double x) {
	return (x * 0.954929658551372) - (0.12900613773279798 * pow(x, 3.0));
}

Error

The X axis uses an exponential scale — Bits error versus `x`

Try it out

In
Out

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error	0.4
Cost	39552

\[x \cdot 0.954929658551372 - \sqrt[3]{0.12900613773279798 \cdot {x}^{3}} \cdot \left(\sqrt[3]{0.12900613773279798 \cdot {x}^{3}} \cdot \sqrt[3]{0.12900613773279798 \cdot {x}^{3}}\right)\]

Alternative 2
Error	32.1
Cost	26688

\[\sqrt{x \cdot 0.954929658551372 - 0.12900613773279798 \cdot {x}^{3}} \cdot \sqrt{x \cdot 0.954929658551372 - 0.12900613773279798 \cdot {x}^{3}}\]

Alternative 3
Error	32.0
Cost	26560

\[x \cdot 0.954929658551372 - \left(\sqrt{0.12900613773279798} \cdot \left(x \cdot \sqrt{x}\right)\right) \cdot \left(\sqrt{0.12900613773279798} \cdot \left(x \cdot \sqrt{x}\right)\right)\]

Alternative 4
Error	32.0
Cost	26432

\[x \cdot 0.954929658551372 - \left(\sqrt{0.12900613773279798} \cdot {x}^{1.5}\right) \cdot \left(\sqrt{0.12900613773279798} \cdot {x}^{1.5}\right)\]

Alternative 5
Error	16.3
Cost	26432

\[x \cdot 0.954929658551372 - \sqrt{0.12900613773279798 \cdot {x}^{3}} \cdot \sqrt{0.12900613773279798 \cdot {x}^{3}}\]

Alternative 6
Error	40.3
Cost	19776

\[\sqrt[3]{{\left(x \cdot 0.954929658551372 - 0.12900613773279798 \cdot {x}^{3}\right)}^{3}}\]

Alternative 7
Error	29.7
Cost	14016

\[\frac{x \cdot \left(x \cdot 0.91189065278104\right) + -0.016642583572733644 \cdot {x}^{6}}{x \cdot 0.954929658551372 + 0.12900613773279798 \cdot {x}^{3}}\]

Alternative 8
Error	32.1
Cost	14016

\[\sqrt{x \cdot \left(0.954929658551372 + \left(x \cdot x\right) \cdot -0.12900613773279798\right)} \cdot \sqrt{x \cdot \left(0.954929658551372 + \left(x \cdot x\right) \cdot -0.12900613773279798\right)}\]

Alternative 9
Error	0.3
Cost	13568

\[x \cdot 0.954929658551372 - \left(\left(x \cdot x\right) \cdot 0.12900613773279798\right) \cdot {\left(\sqrt[3]{x}\right)}^{3}\]

Alternative 10
Error	10.5
Cost	13312

\[x \cdot 0.954929658551372 - \sqrt[3]{0.0021469954286136776 \cdot {x}^{9}}\]

Alternative 11
Error	29.7
Cost	7680

\[\frac{x \cdot \left(x \cdot 0.91189065278104\right) + -0.016642583572733644 \cdot {x}^{6}}{x \cdot \left(0.954929658551372 - \left(x \cdot x\right) \cdot -0.12900613773279798\right)}\]

Alternative 12
Error	6.4
Cost	7424

\[\frac{x \cdot \left(0.91189065278104 + {x}^{4} \cdot -0.016642583572733644\right)}{0.954929658551372 - \left(x \cdot x\right) \cdot -0.12900613773279798}\]

Alternative 13
Error	46.6
Cost	6656

\[-0.12900613773279798 \cdot {x}^{3}\]

Alternative 14
Error	0.1
Cost	704

\[x \cdot 0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot \left(x \cdot x\right)\right)\]

Alternative 15
Error	0.1
Cost	704

\[x \cdot 0.954929658551372 - \left(x \cdot x\right) \cdot \left(x \cdot 0.12900613773279798\right)\]

Alternative 16
Error	0.1
Cost	704

\[x \cdot 0.954929658551372 - x \cdot \left(\left(x \cdot x\right) \cdot 0.12900613773279798\right)\]

Alternative 17
Error	0.1
Cost	576

\[x \cdot \left(0.954929658551372 + \left(x \cdot x\right) \cdot -0.12900613773279798\right)\]

Alternative 18
Error	16.0
Cost	192

\[x \cdot 0.954929658551372\]

Alternative 19
Error	61.6
Cost	64

\[1\]

Alternative 20
Error	61.1
Cost	64

\[0\]

Alternative 21
Error	61.7
Cost	64

\[-1\]

Error

Derivation

Initial program 0.1
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
Simplified0.1
\[\leadsto \color{blue}{0.954929658551372 \cdot x - 0.12900613773279798 \cdot {x}^{3}}\]
Simplified0.1
\[\leadsto \color{blue}{x \cdot 0.954929658551372 - 0.12900613773279798 \cdot {x}^{3}}\]
Final simplification0.1
\[\leadsto x \cdot 0.954929658551372 - 0.12900613773279798 \cdot {x}^{3}\]

Reproduce

herbie shell --seed 2021042 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))