Average Error: 0.1 → 0.1
Time: 2.4s
Precision: binary64
\[x \cdot \left(1 - x \cdot y\right) \]
↓
\[x - x \cdot \left(x \cdot y\right) \]
x \cdot \left(1 - x \cdot y\right)
↓
x - x \cdot \left(x \cdot y\right)

(FPCore (x y) :precision binary64 (* x (- 1.0 (* x y))))
↓
(FPCore (x y) :precision binary64 (- x (* x (* x y))))
double code(double x, double y) {
	return x * (1.0 - (x * y));
}
↓
double code(double x, double y) {
	return x - (x * (x * y));
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[x \cdot \left(1 - x \cdot y\right) \]

  2. Applied add-cube-cbrt_binary641.4

    \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(1 - x \cdot y\right)} \cdot \sqrt[3]{x \cdot \left(1 - x \cdot y\right)}\right) \cdot \sqrt[3]{x \cdot \left(1 - x \cdot y\right)}} \]

  3. Applied pow1_binary641.4

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

  4. Applied pow1_binary641.4

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

  5. Applied pow1_binary641.4

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

  6. Applied pow-prod-down_binary641.4

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

  7. Applied pow-prod-down_binary641.4

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

  8. Simplified0.1

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

  9. Final simplification0.1

    \[\leadsto x - x \cdot \left(x \cdot y\right) \]

Reproduce

herbie shell --seed 2021313 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1.0 (* x y))))