(+ 1 (* (tan x) (tan x)))

Average Error: 0.1 → 0.1

Time: 1.1s

Precision: binary64

Math

\[1 + \tan x \cdot \tan x\]

↓

\[1 + \tan x \cdot \tan x\]

C

double code(double x) {
	return ((double) (1.0 + ((double) (((double) tan(x)) * ((double) tan(x))))));
}

↓

double code(double x) {
	return ((double) (1.0 + ((double) (((double) tan(x)) * ((double) tan(x))))));
}

Error

Bits error versus x

Derivation

1. Initial program 0.1

   \[1 + \tan x \cdot \tan x\]

2. Final simplification 0.1

   \[\leadsto 1 + \tan x \cdot \tan x\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ 1 (* (tan x) (tan x)))"
  :precision binary64
  (+ 1.0 (* (tan x) (tan x))))