Average Error: 0.0 → 0.0
Time: 14.8s
Precision: binary64
\[x + \left(y - z\right) \cdot \left(t - x\right)\]
↓
\[t \cdot \left(y - z\right) + x \cdot \left(\left(z + 1\right) - y\right)\]
x + \left(y - z\right) \cdot \left(t - x\right)
↓
t \cdot \left(y - z\right) + x \cdot \left(\left(z + 1\right) - y\right)
(FPCore (x y z t) :precision binary64 (+ x (* (- y z) (- t x))))
↓
(FPCore (x y z t) :precision binary64 (+ (* t (- y z)) (* x (- (+ z 1.0) y))))
double code(double x, double y, double z, double t) {
	return x + ((y - z) * (t - x));
}
↓
double code(double x, double y, double z, double t) {
	return (t * (y - z)) + (x * ((z + 1.0) - y));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[x + \left(t \cdot \left(y - z\right) + \left(-x\right) \cdot \left(y - z\right)\right)\]

Derivation

  1. Initial program 0.0

    \[x + \left(y - z\right) \cdot \left(t - x\right)\]
  2. Using strategy rm

  3. Applied sub-neg_binary64_218950.0

    \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(t + \left(-x\right)\right)}\]

  4. Applied distribute-rgt-in_binary64_218520.0

    \[\leadsto x + \color{blue}{\left(t \cdot \left(y - z\right) + \left(-x\right) \cdot \left(y - z\right)\right)}\]

  5. Simplified0.0

    \[\leadsto x + \left(t \cdot \left(y - z\right) + \color{blue}{x \cdot \left(z - y\right)}\right)\]

  6. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(x + \left(x \cdot z + t \cdot y\right)\right) - \left(x \cdot y + t \cdot z\right)}\]

  7. Simplified0.0

    \[\leadsto \color{blue}{t \cdot \left(y - z\right) + x \cdot \left(\left(z + 1\right) - y\right)}\]

  8. Final simplification0.0

    \[\leadsto t \cdot \left(y - z\right) + x \cdot \left(\left(z + 1\right) - y\right)\]

Reproduce

herbie shell --seed 2021027 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

  (+ x (* (- y z) (- t x))))