Average Error: 25.9 → 25.8
Time: 14.2s
Precision: 64
Internal Precision: 320
$\frac{a \cdot c + b \cdot d}{{c}^{2} + {d}^{2}}$
$\frac{\frac{a \cdot c + b \cdot d}{\sqrt{c \cdot c + d \cdot d}}}{\sqrt{c \cdot c + d \cdot d}}$

# Try it out

Results

 In Out
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# Derivation

1. Initial program 25.9

$\frac{a \cdot c + b \cdot d}{{c}^{2} + {d}^{2}}$
2. Initial simplification25.9

$\leadsto \frac{a \cdot c + b \cdot d}{d \cdot d + c \cdot c}$
3. Using strategy rm

$\leadsto \frac{a \cdot c + b \cdot d}{\color{blue}{\sqrt{d \cdot d + c \cdot c} \cdot \sqrt{d \cdot d + c \cdot c}}}$
5. Applied associate-/r*25.8

$\leadsto \color{blue}{\frac{\frac{a \cdot c + b \cdot d}{\sqrt{d \cdot d + c \cdot c}}}{\sqrt{d \cdot d + c \cdot c}}}$
6. Final simplification25.8

$\leadsto \frac{\frac{a \cdot c + b \cdot d}{\sqrt{c \cdot c + d \cdot d}}}{\sqrt{c \cdot c + d \cdot d}}$

# Runtime

Time bar (total: 14.2s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (a c b d)
:name "(a*c + b*d)/(c^2 + d^2)"
(/ (+ (* a c) (* b d)) (+ (pow c 2) (pow d 2))))