Average Error: 2.0 → 3.2
Time: 8.5s
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

Target

Original2.0
Target11.7
Herbie3.2
\[\]

Derivation

  1. Split input into 2 regimes

  2. if (* (- t 1.0) (log a)) < -2.1755041691382755e98 or -32.420870981728442 < (* (- t 1.0) (log a))

    1. Initial program 0.5

      \[\]
    2. Using strategy rm

    3. Applied *-un-lft-identity0.5

      \[\leadsto \]

    4. Applied exp-prod0.6

      \[\leadsto \]

    5. Simplified0.6

      \[\leadsto \]
    6. Using strategy rm

    7. Applied add-sqr-sqrt0.7

      \[\leadsto \]

    8. Applied unpow-prod-down0.6

      \[\leadsto \]

    9. Simplified0.6

      \[\leadsto \]

    10. Simplified0.6

      \[\leadsto \]

    if -2.1755041691382755e98 < (* (- t 1.0) (log a)) < -32.420870981728442

    1. Initial program 4.2

      \[\]
    2. Using strategy rm

    3. Applied *-un-lft-identity4.2

      \[\leadsto \]

    4. Applied exp-prod4.3

      \[\leadsto \]

    5. Simplified4.3

      \[\leadsto \]

    6. Taylor expanded around inf 4.3

      \[\leadsto \]

    7. Simplified7.3

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

  4. Final simplification3.2

    \[\leadsto \]

Reproduce

herbie shell --seed 2020192 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))