Average Error: 0.4 → 0.5
Time: 13.3s
Precision: 64
Internal Precision: 576
$\sin x - 1$
$\frac{\left(\sin x \cdot \sin x\right) \cdot \sin x - 1}{\left(\sin x + 1\right) + \sin x \cdot \sin x}$

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.4

$\sin x - 1$
2. Using strategy rm
3. Applied flip3--0.5

$\leadsto \color{blue}{\frac{{\left(\sin x\right)}^{3} - {1}^{3}}{\sin x \cdot \sin x + \left(1 \cdot 1 + \sin x \cdot 1\right)}}$
4. Applied simplify0.5

$\leadsto \frac{\color{blue}{{\left(\sin x\right)}^{3} - 1}}{\sin x \cdot \sin x + \left(1 \cdot 1 + \sin x \cdot 1\right)}$
5. Applied simplify0.5

$\leadsto \frac{{\left(\sin x\right)}^{3} - 1}{\color{blue}{\left(\sin x + 1\right) + \sin x \cdot \sin x}}$
6. Using strategy rm

$\leadsto \frac{{\color{blue}{\left(\left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right) \cdot \sqrt[3]{\sin x}\right)}}^{3} - 1}{\left(\sin x + 1\right) + \sin x \cdot \sin x}$
8. Applied unpow-prod-down0.9

$\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right)}^{3} \cdot {\left(\sqrt[3]{\sin x}\right)}^{3}} - 1}{\left(\sin x + 1\right) + \sin x \cdot \sin x}$
9. Applied simplify0.6

$\leadsto \frac{\color{blue}{\left(\sin x \cdot \sin x\right)} \cdot {\left(\sqrt[3]{\sin x}\right)}^{3} - 1}{\left(\sin x + 1\right) + \sin x \cdot \sin x}$
10. Applied simplify0.5

$\leadsto \frac{\left(\sin x \cdot \sin x\right) \cdot \color{blue}{\sin x} - 1}{\left(\sin x + 1\right) + \sin x \cdot \sin x}$

# Runtime

Time bar (total: 13.3s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x)
:name "sin(x) -1"
(- (sin x) 1))