Average Error: 10.4 → 2.2
Time: 8.2s
Precision: 64
Internal Precision: 576
$\frac{d}{a \cdot d - b \cdot c}$
$\begin{array}{l} \mathbf{if}\;d \le -4.674245232507722 \cdot 10^{-77} \lor \neg \left(d \le 5.351892082359565 \cdot 10^{-170}\right):\\ \;\;\;\;\frac{1}{a - \frac{b}{\frac{d}{c}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{a \cdot d - b \cdot c}\\ \end{array}$

# Try it out

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# Derivation

1. Split input into 2 regimes
2. ## if d < -4.674245232507722e-77 or 5.351892082359565e-170 < d

1. Initial program 13.7

$\frac{d}{a \cdot d - b \cdot c}$
2. Initial simplification13.7

$\leadsto \frac{d}{d \cdot a - b \cdot c}$
3. Using strategy rm
4. Applied clear-num13.8

$\leadsto \color{blue}{\frac{1}{\frac{d \cdot a - b \cdot c}{d}}}$
5. Using strategy rm
6. Applied *-un-lft-identity13.8

$\leadsto \frac{1}{\color{blue}{1 \cdot \frac{d \cdot a - b \cdot c}{d}}}$
7. Applied associate-/r*13.8

$\leadsto \color{blue}{\frac{\frac{1}{1}}{\frac{d \cdot a - b \cdot c}{d}}}$
8. Simplified2.0

$\leadsto \frac{\frac{1}{1}}{\color{blue}{a - \frac{b}{\frac{d}{c}}}}$

## if -4.674245232507722e-77 < d < 5.351892082359565e-170

1. Initial program 2.6

$\frac{d}{a \cdot d - b \cdot c}$
2. Initial simplification2.6

$\leadsto \frac{d}{d \cdot a - b \cdot c}$
3. Recombined 2 regimes into one program.
4. Final simplification2.2

$\leadsto \begin{array}{l} \mathbf{if}\;d \le -4.674245232507722 \cdot 10^{-77} \lor \neg \left(d \le 5.351892082359565 \cdot 10^{-170}\right):\\ \;\;\;\;\frac{1}{a - \frac{b}{\frac{d}{c}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{d}{a \cdot d - b \cdot c}\\ \end{array}$

# Runtime

Time bar (total: 8.2s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (d a b c)
:name "d / (a * d - b * c)"
(/ d (- (* a d) (* b c))))