?

Average Error: 0.17% → 0.24%
Time: 31.3s
Precision: binary64

?

\[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]
↓
\[-\mathsf{fma}\left(0.12, {x}^{2}, \mathsf{fma}\left(x, 0.253, -1\right)\right) \]
(FPCore (x) :precision binary64 (- 1.0 (* x (+ 0.253 (* x 0.12)))))
↓
(FPCore (x) :precision binary64 (- (fma 0.12 (pow x 2.0) (fma x 0.253 -1.0))))
double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}
↓
double code(double x) {
	return -fma(0.12, pow(x, 2.0), fma(x, 0.253, -1.0));
}

function code(x)
	return Float64(1.0 - Float64(x * Float64(0.253 + Float64(x * 0.12))))
end
↓
function code(x)
	return Float64(-fma(0.12, (x ^ 2.0), fma(x, 0.253, -1.0)))
end

code[x_] := N[(1.0 - N[(x * N[(0.253 + N[(x * 0.12), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := (-N[(0.12 * N[Power[x, 2.0], $MachinePrecision] + N[(x * 0.253 + -1.0), $MachinePrecision]), $MachinePrecision])

1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
-\mathsf{fma}\left(0.12, {x}^{2}, \mathsf{fma}\left(x, 0.253, -1\right)\right)

Error?

Derivation?

  1. Initial program 0.17

    \[1 - x \cdot \left(0.253 + x \cdot 0.12\right) \]

  2. Simplified0.16

    \[\leadsto \color{blue}{-\mathsf{fma}\left(x, \mathsf{fma}\left(0.12, x, 0.253\right), -1\right)} \]
    Proof

  3. Applied egg-rr0.25

    \[\leadsto -\color{blue}{\left(0.12 \cdot {x}^{2} + \left(x \cdot 0.253 + -1\right)\right)} \]

  4. Simplified0.24

    \[\leadsto -\color{blue}{\mathsf{fma}\left(0.12, {x}^{2}, \mathsf{fma}\left(x, 0.253, -1\right)\right)} \]
    Proof

Reproduce?

herbie shell --seed 2023136 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))