Average Error: 12.1 → 11.9
Time: 29.3s
Precision: binary64
\[\]
↓
\[\]

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

Original12.1
Target15.8
Herbie11.9
\[\]

Derivation

  1. Split input into 4 regimes

  2. if x < -3.2724221881762381e24

    1. Initial program 7.9

      \[\]
    2. Using strategy rm

    3. Applied sub-neg7.9

      \[\leadsto \]

    4. Applied distribute-lft-in7.9

      \[\leadsto \]

    5. Simplified7.9

      \[\leadsto \]

    6. Simplified7.5

      \[\leadsto \]
    7. Using strategy rm

    8. Applied add-cube-cbrt7.6

      \[\leadsto \]

    if -3.2724221881762381e24 < x < -1.09827367754077949e-130 or -6.61603541794831684e-230 < x < 13889868.629110064

    1. Initial program 14.4

      \[\]
    2. Using strategy rm

    3. Applied sub-neg14.4

      \[\leadsto \]

    4. Applied distribute-lft-in14.4

      \[\leadsto \]

    5. Simplified12.1

      \[\leadsto \]

    6. Simplified9.9

      \[\leadsto \]

    if -1.09827367754077949e-130 < x < -6.61603541794831684e-230

    1. Initial program 16.2

      \[\]
    2. Using strategy rm

    3. Applied sub-neg16.2

      \[\leadsto \]

    4. Applied distribute-lft-in16.2

      \[\leadsto \]

    5. Simplified16.7

      \[\leadsto \]

    6. Simplified16.0

      \[\leadsto \]
    7. Using strategy rm

    8. Applied associate-*r*15.9

      \[\leadsto \]
    9. Using strategy rm

    10. Applied add-cube-cbrt16.1

      \[\leadsto \]

    11. Applied associate-*l*16.1

      \[\leadsto \]

    12. Simplified15.4

      \[\leadsto \]

    if 13889868.629110064 < x

    1. Initial program 7.4

      \[\]
    2. Using strategy rm

    3. Applied sub-neg7.4

      \[\leadsto \]

    4. Applied distribute-lft-in7.4

      \[\leadsto \]

    5. Simplified7.4

      \[\leadsto \]

    6. Simplified8.2

      \[\leadsto \]
    7. Using strategy rm

    8. Applied associate-*r*8.5

      \[\leadsto \]

    9. Taylor expanded around 0 19.7

      \[\leadsto \]
  3. Recombined 4 regimes into one program.

  4. Final simplification11.9

    \[\leadsto \]

Reproduce

herbie shell --seed 2020179 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

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