?

Average Error: 0.1 → 0.1
Time: 12.6s
Precision: binary64
Cost: 19648

?

\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]
↓
\[\mathsf{fma}\left(\log y, x, \log t - \left(y + z\right)\right) \]
(FPCore (x y z t) :precision binary64 (+ (- (- (* x (log y)) y) z) (log t)))
↓
(FPCore (x y z t) :precision binary64 (fma (log y) x (- (log t) (+ y z))))
double code(double x, double y, double z, double t) {
	return (((x * log(y)) - y) - z) + log(t);
}
↓
double code(double x, double y, double z, double t) {
	return fma(log(y), x, (log(t) - (y + z)));
}

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x * log(y)) - y) - z) + log(t))
end
↓
function code(x, y, z, t)
	return fma(log(y), x, Float64(log(t) - Float64(y + z)))
end

code[x_, y_, z_, t_] := N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_] := N[(N[Log[y], $MachinePrecision] * x + N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\mathsf{fma}\left(\log y, x, \log t - \left(y + z\right)\right)

Error?

Derivation?

  1. Initial program 0.1

    \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

  2. Simplified0.1

    \[\leadsto \color{blue}{\left(x \cdot \log y - y\right) - \left(z - \log t\right)} \]
    Proof

    [Start]0.1

    \[ \left(\left(x \cdot \log y - y\right) - z\right) + \log t \]

    associate-+l- [=>]0.1

    \[ \color{blue}{\left(x \cdot \log y - y\right) - \left(z - \log t\right)} \]

  3. Applied egg-rr0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, -\left(\left(y + z\right) - \log t\right)\right)} \]

  4. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\log y, x, \log t - \left(y + z\right)\right) \]

Alternatives

Alternative 1
Error1.9
Cost27080
\[\begin{array}{l} t_1 := \log y \cdot x\\ t_2 := \left(t_1 - y\right) - z\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 10^{+14}:\\ \;\;\;\;\left(\log t + t_1\right) - y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -z\right)\\ \end{array} \]
Alternative 2
Error1.6
Cost27016
\[\begin{array}{l} t_1 := \left(\log y \cdot x - y\right) - z\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0.005:\\ \;\;\;\;\left(-y\right) - \log \left(\frac{e^{z}}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -z\right)\\ \end{array} \]
Alternative 3
Error1.6
Cost27016
\[\begin{array}{l} t_1 := \left(\log y \cdot x - y\right) - z\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0.005:\\ \;\;\;\;\log \left(t \cdot {y}^{x}\right) - y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -z\right)\\ \end{array} \]
Alternative 4
Error1.5
Cost26632
\[\begin{array}{l} t_1 := \log y \cdot x - y\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+26}:\\ \;\;\;\;t_1 - z\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-67}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -z\right)\\ \end{array} \]
Alternative 5
Error1.5
Cost20296
\[\begin{array}{l} t_1 := \log y \cdot x\\ t_2 := t_1 - y\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+26}:\\ \;\;\;\;t_2 - z\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-67}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - z\\ \end{array} \]
Alternative 6
Error0.1
Cost13376
\[\log t + \left(\left(\log y \cdot x - y\right) - z\right) \]
Alternative 7
Error10.0
Cost6985
\[\begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+90} \lor \neg \left(x \leq 1.2 \cdot 10^{+121}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
Alternative 8
Error6.6
Cost6985
\[\begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+89} \lor \neg \left(x \leq 5.3 \cdot 10^{+76}\right):\\ \;\;\;\;\log y \cdot x - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
Alternative 9
Error6.9
Cost6985
\[\begin{array}{l} \mathbf{if}\;x \leq -6400000000 \lor \neg \left(x \leq 1.3 \cdot 10^{+23}\right):\\ \;\;\;\;\log y \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
Alternative 10
Error18.3
Cost6857
\[\begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+75} \lor \neg \left(x \leq 1.7 \cdot 10^{+122}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
Alternative 11
Error26.9
Cost6729
\[\begin{array}{l} \mathbf{if}\;z \leq -0.0036 \lor \neg \left(z \leq -2.6 \cdot 10^{-90}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log t\\ \end{array} \]
Alternative 12
Error32.6
Cost392
\[\begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+75}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+76}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
Alternative 13
Error26.2
Cost256
\[\left(-z\right) - y \]
Alternative 14
Error43.9
Cost128
\[-y \]

Error

Reproduce?

herbie shell --seed 2023018 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))