Average Error: 10.0 → 0.4
Time: 36.3s
Precision: 64
Internal Precision: 1344
$\sin \left(3 \cdot x\right) + \left(21 \cdot 56\right) \cdot xy$
$3 \cdot \sin x - \left(4 \cdot \left(\left(\sin x \cdot \sin x\right) \cdot \sin x\right) - \left(21 \cdot 56\right) \cdot xy\right)$

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 10.0

$\sin \left(3 \cdot x\right) + \left(21 \cdot 56\right) \cdot xy$
2. Using strategy rm
3. Applied sin-30.4

$\leadsto \color{blue}{\left(3 \cdot \sin x - 4 \cdot {\left(\sin x\right)}^{3}\right)} + \left(21 \cdot 56\right) \cdot xy$
4. Applied associate-+l-0.4

$\leadsto \color{blue}{3 \cdot \sin x - \left(4 \cdot {\left(\sin x\right)}^{3} - \left(21 \cdot 56\right) \cdot xy\right)}$
5. Using strategy rm

$\leadsto 3 \cdot \sin x - \left(4 \cdot {\color{blue}{\left(\left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right) \cdot \sqrt[3]{\sin x}\right)}}^{3} - \left(21 \cdot 56\right) \cdot xy\right)$
7. Applied unpow-prod-down0.8

$\leadsto 3 \cdot \sin x - \left(4 \cdot \color{blue}{\left({\left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right)}^{3} \cdot {\left(\sqrt[3]{\sin x}\right)}^{3}\right)} - \left(21 \cdot 56\right) \cdot xy\right)$
8. Applied simplify0.6

$\leadsto 3 \cdot \sin x - \left(4 \cdot \left(\color{blue}{\left(\sin x \cdot \sin x\right)} \cdot {\left(\sqrt[3]{\sin x}\right)}^{3}\right) - \left(21 \cdot 56\right) \cdot xy\right)$
9. Applied simplify0.4

$\leadsto 3 \cdot \sin x - \left(4 \cdot \left(\left(\sin x \cdot \sin x\right) \cdot \color{blue}{\sin x}\right) - \left(21 \cdot 56\right) \cdot xy\right)$

# Runtime

Time bar (total: 36.3s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x xy)
:name "sin(3x) + 21 * 56xy"
(+ (sin (* 3 x)) (* (* 21 56) xy)))