Average Error: 29.6 → 0.0
Time: 15.4s
Precision: 64
Internal Precision: 128
\[\frac{1 - \cos x}{\sin x}\]
↓
\[\tan \left(\frac{x}{2}\right)\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.6
Target0.0
Herbie0.0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 29.6

    \[\frac{1 - \cos x}{\sin x}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\tan \left(\frac{x}{2}\right)}\]

  3. Final simplification0.0

    \[\leadsto \tan \left(\frac{x}{2}\right)\]

Reproduce

herbie shell --seed 323378853 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

  :herbie-target
  (tan (/ x 2))

  (/ (- 1 (cos x)) (sin x)))

Details

Time bar (total: 14.9s)Debug log

sample411.0ms

Algorithm
intervals
Results
164.0ms49×body2560valid
137.0ms86×body1280valid
67.0ms66×body640valid
21.0ms28×body320valid
10.0ms20×body160valid
2.0ms7×body80valid

simplify19.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
18.0ms
(/ (- 1 (cos x)) (sin x))

prune56.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0
Calls
0 calls:
Slowest

series0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

simplify0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

prune6.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample14.4s

Algorithm
intervals
Results
5.7s1559×body2560valid
5.2s2767×body1280valid
2.2s1925×body640valid
877.0ms941×body320valid
245.0ms478×body160valid
92.0ms327×body80valid
27.0ms3×body5120valid