Average Error: 0.0 → 0.0
Time: 48.3s
Precision: binary64
Cost: 576
\[x + \left(y - z\right) \cdot \left(t - x\right)\]
↓
\[x + \left(y - z\right) \cdot \left(t - x\right)\]
x + \left(y - z\right) \cdot \left(t - x\right)
↓
x + \left(y - z\right) \cdot \left(t - x\right)
(FPCore (x y z t) :precision binary64 (+ x (* (- y z) (- t x))))
↓
(FPCore (x y z t) :precision binary64 (+ x (* (- y z) (- t x))))
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 x + ((y - z) * (t - x));
}

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
\[x + \left(t \cdot \left(y - z\right) + \left(-x\right) \cdot \left(y - z\right)\right)\]
Alternative 1
Accuracy0.0
Cost832
\[x + \left(\left(y - z\right) \cdot t + x \cdot \left(z - y\right)\right)\]
Alternative 2
Accuracy0.4
Cost1280
\[\left(x + \left(y - z\right) \cdot t\right) + \left(\sqrt[3]{x} \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right) \cdot \left(z - y\right)\]
Alternative 3
Accuracy32.4
Cost1088
\[\left(x + \left(y - z\right) \cdot t\right) + \left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \left(z - y\right)\]

Derivation

  1. Initial program 0.0

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

  3. Applied *-un-lft-identity_binary64_232660.0

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

  5. Applied *-un-lft-identity_binary64_232660.0

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

  6. Applied associate-*l*_binary64_232070.0

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

  8. Applied *-un-lft-identity_binary64_232660.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020322 
(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))))