Average Error: 16.8 → 16.8
Time: 7.8s
Precision: binary64
\[\left(a \cdot \left(\left(\ell \cdot e + m \cdot f\right) + n \cdot g\right) + b \cdot \left(\left(o \cdot e + p \cdot f\right) + q \cdot g\right)\right) + c \cdot \left(\left(r \cdot e + s \cdot f\right) + t \cdot g\right)\]
↓
\[\left(a \cdot \left(\left(\ell \cdot e + m \cdot f\right) + n \cdot g\right) + b \cdot \left(\left(o \cdot e + p \cdot f\right) + q \cdot g\right)\right) + c \cdot \left(\left(r \cdot e + s \cdot f\right) + t \cdot g\right)\]
\left(a \cdot \left(\left(\ell \cdot e + m \cdot f\right) + n \cdot g\right) + b \cdot \left(\left(o \cdot e + p \cdot f\right) + q \cdot g\right)\right) + c \cdot \left(\left(r \cdot e + s \cdot f\right) + t \cdot g\right)
↓
\left(a \cdot \left(\left(\ell \cdot e + m \cdot f\right) + n \cdot g\right) + b \cdot \left(\left(o \cdot e + p \cdot f\right) + q \cdot g\right)\right) + c \cdot \left(\left(r \cdot e + s \cdot f\right) + t \cdot g\right)
double code(double a, double l, double e, double m, double f, double n, double g, double b, double o, double p, double q, double c, double r, double s, double t) {
	return ((double) (((double) (((double) (a * ((double) (((double) (((double) (l * e)) + ((double) (m * f)))) + ((double) (n * g)))))) + ((double) (b * ((double) (((double) (((double) (o * e)) + ((double) (p * f)))) + ((double) (q * g)))))))) + ((double) (c * ((double) (((double) (((double) (r * e)) + ((double) (s * f)))) + ((double) (t * g))))))));
}
↓
double code(double a, double l, double e, double m, double f, double n, double g, double b, double o, double p, double q, double c, double r, double s, double t) {
	return ((double) (((double) (((double) (a * ((double) (((double) (((double) (l * e)) + ((double) (m * f)))) + ((double) (n * g)))))) + ((double) (b * ((double) (((double) (((double) (o * e)) + ((double) (p * f)))) + ((double) (q * g)))))))) + ((double) (c * ((double) (((double) (((double) (r * e)) + ((double) (s * f)))) + ((double) (t * g))))))));
}

Error

Bits error versus a

Bits error versus l

Bits error versus e

Bits error versus m

Bits error versus f

Bits error versus n

Bits error versus g

Bits error versus b

Bits error versus o

Bits error versus p

Bits error versus q

Bits error versus c

Bits error versus r

Bits error versus s

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.8

    \[\left(a \cdot \left(\left(\ell \cdot e + m \cdot f\right) + n \cdot g\right) + b \cdot \left(\left(o \cdot e + p \cdot f\right) + q \cdot g\right)\right) + c \cdot \left(\left(r \cdot e + s \cdot f\right) + t \cdot g\right)\]

  2. Final simplification16.8

    \[\leadsto \left(a \cdot \left(\left(\ell \cdot e + m \cdot f\right) + n \cdot g\right) + b \cdot \left(\left(o \cdot e + p \cdot f\right) + q \cdot g\right)\right) + c \cdot \left(\left(r \cdot e + s \cdot f\right) + t \cdot g\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a l e m f n g b o p q c r s t)
  :name "(+ (+ (* a (+ (+ (* l e) (* m f)) (* n g))) (* b (+ (+ (* o e) (* p f)) (* q g)))) (* c (+ (+ (* r e) (* s f)) (* t g))))"
  :precision binary64
  (+ (+ (* a (+ (+ (* l e) (* m f)) (* n g))) (* b (+ (+ (* o e) (* p f)) (* q g)))) (* c (+ (+ (* r e) (* s f)) (* t g)))))