Average Error: 50.7 → 50.7
Time: 17.3s
Precision: binary64
\[\frac{\left(\left(4 \cdot \left({a}^{\left(\frac{3}{2}\right)} \cdot \sqrt{\left(a + b\right) + c}\right) + \left(\left(2 \cdot \sqrt{a}\right) \cdot b\right) \cdot \left(\sqrt{\left(a + b\right) + c} - \sqrt{c}\right)\right) - \left({b}^{2} - 4 \cdot \left(a \cdot c\right)\right) \cdot \log \left(\frac{\left(2 \cdot \sqrt{a} + \frac{b}{\sqrt{a}}\right) + 2 \cdot \sqrt{\left(a + b\right) + c}}{\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{c}}\right)\right) \cdot 1}{8 \cdot {a}^{\left(\frac{3}{2}\right)}}\]
↓
\[\frac{\left(\left(4 \cdot \left({a}^{\left(\frac{3}{2}\right)} \cdot \sqrt{\left(a + b\right) + c}\right) + \left(\left(2 \cdot \sqrt{a}\right) \cdot b\right) \cdot \left(\sqrt{\left(a + b\right) + c} - \sqrt{c}\right)\right) - \left({b}^{2} - 4 \cdot \left(a \cdot c\right)\right) \cdot \log \left(\frac{\left(2 \cdot \sqrt{a} + \frac{b}{\sqrt{a}}\right) + 2 \cdot \sqrt{\left(a + b\right) + c}}{\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{c}}\right)\right) \cdot 1}{8 \cdot {a}^{\left(\frac{3}{2}\right)}}\]
\frac{\left(\left(4 \cdot \left({a}^{\left(\frac{3}{2}\right)} \cdot \sqrt{\left(a + b\right) + c}\right) + \left(\left(2 \cdot \sqrt{a}\right) \cdot b\right) \cdot \left(\sqrt{\left(a + b\right) + c} - \sqrt{c}\right)\right) - \left({b}^{2} - 4 \cdot \left(a \cdot c\right)\right) \cdot \log \left(\frac{\left(2 \cdot \sqrt{a} + \frac{b}{\sqrt{a}}\right) + 2 \cdot \sqrt{\left(a + b\right) + c}}{\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{c}}\right)\right) \cdot 1}{8 \cdot {a}^{\left(\frac{3}{2}\right)}}
↓
\frac{\left(\left(4 \cdot \left({a}^{\left(\frac{3}{2}\right)} \cdot \sqrt{\left(a + b\right) + c}\right) + \left(\left(2 \cdot \sqrt{a}\right) \cdot b\right) \cdot \left(\sqrt{\left(a + b\right) + c} - \sqrt{c}\right)\right) - \left({b}^{2} - 4 \cdot \left(a \cdot c\right)\right) \cdot \log \left(\frac{\left(2 \cdot \sqrt{a} + \frac{b}{\sqrt{a}}\right) + 2 \cdot \sqrt{\left(a + b\right) + c}}{\frac{b}{\sqrt{a}} + 2 \cdot \sqrt{c}}\right)\right) \cdot 1}{8 \cdot {a}^{\left(\frac{3}{2}\right)}}
double code(double a, double b, double c) {
	return ((double) (((double) (((double) (((double) (((double) (4.0 * ((double) (((double) pow(a, ((double) (3.0 / 2.0)))) * ((double) sqrt(((double) (((double) (a + b)) + c)))))))) + ((double) (((double) (((double) (2.0 * ((double) sqrt(a)))) * b)) * ((double) (((double) sqrt(((double) (((double) (a + b)) + c)))) - ((double) sqrt(c)))))))) - ((double) (((double) (((double) pow(b, 2.0)) - ((double) (4.0 * ((double) (a * c)))))) * ((double) log(((double) (((double) (((double) (((double) (2.0 * ((double) sqrt(a)))) + ((double) (b / ((double) sqrt(a)))))) + ((double) (2.0 * ((double) sqrt(((double) (((double) (a + b)) + c)))))))) / ((double) (((double) (b / ((double) sqrt(a)))) + ((double) (2.0 * ((double) sqrt(c)))))))))))))) * 1.0)) / ((double) (8.0 * ((double) pow(a, ((double) (3.0 / 2.0))))))));
}
↓
double code(double a, double b, double c) {
	return ((double) (((double) (((double) (((double) (((double) (4.0 * ((double) (((double) pow(a, ((double) (3.0 / 2.0)))) * ((double) sqrt(((double) (((double) (a + b)) + c)))))))) + ((double) (((double) (((double) (2.0 * ((double) sqrt(a)))) * b)) * ((double) (((double) sqrt(((double) (((double) (a + b)) + c)))) - ((double) sqrt(c)))))))) - ((double) (((double) (((double) pow(b, 2.0)) - ((double) (4.0 * ((double) (a * c)))))) * ((double) log(((double) (((double) (((double) (((double) (2.0 * ((double) sqrt(a)))) + ((double) (b / ((double) sqrt(a)))))) + ((double) (2.0 * ((double) sqrt(((double) (((double) (a + b)) + c)))))))) / ((double) (((double) (b / ((double) sqrt(a)))) + ((double) (2.0 * ((double) sqrt(c)))))))))))))) * 1.0)) / ((double) (8.0 * ((double) pow(a, ((double) (3.0 / 2.0))))))));
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 50.7

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

  2. Final simplification50.7

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

Reproduce

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