Average Error: 36.4 → 36.4
Time: 19.0s
Precision: binary64
\[\left(\left(\left(\frac{-{b}^{2} \cdot \log \left(\left|\frac{\left(\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{a}\right) + 2 \cdot \sqrt{\left(a + b\right) + c}}{\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{c}}\right|\right)}{8 \cdot {a}^{\left(\frac{3}{2}\right)}} + \frac{c \cdot \log \left(\left|\frac{\left(\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{a}\right) + 2 \cdot \sqrt{\left(a + b\right) + c}}{\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{c}}\right|\right)}{2 \cdot \sqrt{a}}\right) - \frac{b \cdot \sqrt{c}}{4 \cdot a}\right) + \frac{b \cdot \sqrt{\left(a + b\right) + c}}{4 \cdot a}\right) + \frac{1}{2} \cdot \sqrt{\left(a + b\right) + c}\]
↓
\[\left(\left(\left(\frac{-{b}^{2} \cdot \log \left(\left|\frac{\left(\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{a}\right) + 2 \cdot \sqrt{\left(a + b\right) + c}}{\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{c}}\right|\right)}{8 \cdot {a}^{\left(\frac{3}{2}\right)}} + \frac{c \cdot \log \left(\left|\frac{\left(\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{a}\right) + 2 \cdot \sqrt{\left(a + b\right) + c}}{\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{c}}\right|\right)}{2 \cdot \sqrt{a}}\right) - \frac{b \cdot \sqrt{c}}{4 \cdot a}\right) + \frac{b \cdot \sqrt{\left(a + b\right) + c}}{4 \cdot a}\right) + \frac{1}{2} \cdot \sqrt{\left(a + b\right) + c}\]

Error

Bits error versus b

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 36.4

    \[\left(\left(\left(\frac{-{b}^{2} \cdot \log \left(\left|\frac{\left(\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{a}\right) + 2 \cdot \sqrt{\left(a + b\right) + c}}{\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{c}}\right|\right)}{8 \cdot {a}^{\left(\frac{3}{2}\right)}} + \frac{c \cdot \log \left(\left|\frac{\left(\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{a}\right) + 2 \cdot \sqrt{\left(a + b\right) + c}}{\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{c}}\right|\right)}{2 \cdot \sqrt{a}}\right) - \frac{b \cdot \sqrt{c}}{4 \cdot a}\right) + \frac{b \cdot \sqrt{\left(a + b\right) + c}}{4 \cdot a}\right) + \frac{1}{2} \cdot \sqrt{\left(a + b\right) + c}\]

  2. Final simplification36.4

    \[\leadsto \left(\left(\left(\frac{-{b}^{2} \cdot \log \left(\left|\frac{\left(\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{a}\right) + 2 \cdot \sqrt{\left(a + b\right) + c}}{\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{c}}\right|\right)}{8 \cdot {a}^{\left(\frac{3}{2}\right)}} + \frac{c \cdot \log \left(\left|\frac{\left(\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{a}\right) + 2 \cdot \sqrt{\left(a + b\right) + c}}{\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{c}}\right|\right)}{2 \cdot \sqrt{a}}\right) - \frac{b \cdot \sqrt{c}}{4 \cdot a}\right) + \frac{b \cdot \sqrt{\left(a + b\right) + c}}{4 \cdot a}\right) + \frac{1}{2} \cdot \sqrt{\left(a + b\right) + c}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (b a c)
  :name "(+ (+ (- (+ (/ (- (* (pow b 2) (log (fabs (/ (+ (+ (/ b (sqrt a)) (* 2 (sqrt a))) (* 2 (sqrt (+ (+ a b) c)))) (+ (/ b (sqrt a)) (* 2 (sqrt c)))))))) (* 8 (pow a (/ 3 2)))) (/ (* c (log (fabs (/ (+ (+ (/ b (sqrt a)) (* 2 (sqrt a))) (* 2 (sqrt (+ (+ a b) c)))) (+ (/ b (sqrt a)) (* 2 (sqrt c))))))) (* 2 (sqrt a)))) (/ (* b (sqrt c)) (* 4 a))) (/ (* b (sqrt (+ (+ a b) c))) (* 4 a))) (* (/ 1 2) (sqrt (+ (+ a b) c))))"
  :precision binary64
  (+ (+ (- (+ (/ (neg (* (pow b 2.0) (log (fabs (/ (+ (+ (/ b (sqrt a)) (* 2.0 (sqrt a))) (* 2.0 (sqrt (+ (+ a b) c)))) (+ (/ b (sqrt a)) (* 2.0 (sqrt c)))))))) (* 8.0 (pow a (/ 3.0 2.0)))) (/ (* c (log (fabs (/ (+ (+ (/ b (sqrt a)) (* 2.0 (sqrt a))) (* 2.0 (sqrt (+ (+ a b) c)))) (+ (/ b (sqrt a)) (* 2.0 (sqrt c))))))) (* 2.0 (sqrt a)))) (/ (* b (sqrt c)) (* 4.0 a))) (/ (* b (sqrt (+ (+ a b) c))) (* 4.0 a))) (* (/ 1.0 2.0) (sqrt (+ (+ a b) c)))))