Data.Colour.Matrix:determinant from colour-2.3.3, A

Average Error: 12.0 → 9.0

Time: 24.0s

Precision: binary64

Math

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↓

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Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Bits error versus j

Target

Original	12.0
Target	19.4
Herbie	9.0

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Derivation

1. Split input into 2 regimes

2. if b < -4.2721703133289528e49 or 6122062468061031420 < b

   1. Initial program 6.8

      \[\]

   2. Simplified 6.8

      \[\leadsto \]
   3. Using strategy rm

   4. Applied sub-neg 6.8

      \[\leadsto \]

   5. Applied distribute-lft-in 6.8

      \[\leadsto \]

   6. Simplified 6.8

      \[\leadsto \]

   7. Simplified 6.9

      \[\leadsto \]

   if -4.2721703133289528e49 < b < 6122062468061031420

   1. Initial program 14.7

      \[\]

   2. Simplified 14.7

      \[\leadsto \]
   3. Using strategy rm

   4. Applied sub-neg 14.7

      \[\leadsto \]

   5. Applied distribute-lft-in 14.7

      \[\leadsto \]

   6. Simplified 12.4

      \[\leadsto \]

   7. Simplified 10.0

      \[\leadsto \]
3. Recombined 2 regimes into one program.

4. Final simplification 9.0

   \[\leadsto \]

Reproduce

herbie shell --seed 2020181 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))