Average Error: 0.0 → 0.0
Time: 9.6s
Precision: 64
$\left(1 - t\right) \cdot a + t \cdot b$
$1 \cdot a + t \cdot \left(b - a\right)$
\left(1 - t\right) \cdot a + t \cdot b
1 \cdot a + t \cdot \left(b - a\right)
double f(double t, double a, double b) {
double r2093558 = 1.0;
double r2093559 = t;
double r2093560 = r2093558 - r2093559;
double r2093561 = a;
double r2093562 = r2093560 * r2093561;
double r2093563 = b;
double r2093564 = r2093559 * r2093563;
double r2093565 = r2093562 + r2093564;
return r2093565;
}


double f(double t, double a, double b) {
double r2093566 = 1.0;
double r2093567 = a;
double r2093568 = r2093566 * r2093567;
double r2093569 = t;
double r2093570 = b;
double r2093571 = r2093570 - r2093567;
double r2093572 = r2093569 * r2093571;
double r2093573 = r2093568 + r2093572;
return r2093573;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.0

$\left(1 - t\right) \cdot a + t \cdot b$
2. Using strategy rm
3. Applied flip-+29.7

$\leadsto \color{blue}{\frac{\left(\left(1 - t\right) \cdot a\right) \cdot \left(\left(1 - t\right) \cdot a\right) - \left(t \cdot b\right) \cdot \left(t \cdot b\right)}{\left(1 - t\right) \cdot a - t \cdot b}}$
4. Taylor expanded around inf 0.0

$\leadsto \color{blue}{\left(1 \cdot a + t \cdot b\right) - a \cdot t}$
5. Simplified0.0

$\leadsto \color{blue}{1 \cdot a + t \cdot \left(b - a\right)}$
6. Final simplification0.0

$\leadsto 1 \cdot a + t \cdot \left(b - a\right)$

# Reproduce

herbie shell --seed 1
(FPCore (t a b)
:name "(1-t)*a + t*b"
:precision binary64
(+ (* (- 1 t) a) (* t b)))