Average Error: 4.5 → 4.5
Time: 56.1s
Precision: 64
Internal precision: 128
\[x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)\]
⬇
\[\begin{array}{l} \mathbf{if}\;z \le -3.419654050674021 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)\\ \mathbf{if}\;z \le 5.012870678088807 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1.0 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original4.5
Comparison4.2
Herbie4.5
\[ \begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \lt -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1.0 - z}\right)\\ \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right) \lt 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1.0 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1.0 - z}\right)\\ \end{array} \]

Derivation

  1. Split input into 2 regimes.

  2. if z < -3.419654050674021e+32 or 5.012870678088807e-64 < z

    1. Initial program 2.3

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)\]

    if -3.419654050674021e+32 < z < 5.012870678088807e-64

    1. Initial program 8.0

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1.0 - z}\right)\]
    2. Using strategy rm

    3. Applied div-inv 8.0

      \[\leadsto x \cdot \left(\frac{y}{z} - \color{blue}{t \cdot \frac{1}{1.0 - z}}\right)\]
  3. Recombined 2 regimes into one program.
  4. Removed slow pow expressions

Runtime

Time bar (total: 56.1s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(2793257380 3094807930 3205236181 503322065 4225904532 3249456527)'
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"

  :target
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1 (- 1.0 z)))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))