Average Error: 0.0 → 0.0
Time: 5.0s
Precision: 64
Internal Precision: 128
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\log \left(\frac{1}{x} - 1\right)\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[-\log \left(\frac{1}{x} - 1\right)\]

  2. Final simplification0.0

    \[\leadsto -\log \left(\frac{1}{x} - 1\right)\]

Reproduce

herbie shell --seed 2019016 +o rules:numerics
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))

Details

Time bar (total: 4.4s)Debug log

sample220.0ms

Algorithm
intervals
Results
1052×(pre true 80)
796×(body nan 80)
256×(body real 80)

simplify13.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
13.0ms
(- (log (- (/ 1 x) 1)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (/ 1 x) 1)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
4×fma-neg
3×add-sqr-sqrt
2×add-cube-cbrt
2×add-exp-log
2×*-un-lft-identity
1×add-log-exp
1×flip--
1×div-inv
1×log1p-expm1-u
1×difference-of-sqr-1
1×add-cbrt-cube
1×flip3--
1×sub-neg
1×expm1-def
1×pow1
1×expm1-log1p-u
Counts
1 → 19
Calls
1 calls:
Slowest
5.0ms
(- (/ 1 x) 1)

series66.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
66.0ms
(- (/ 1 x) 1)

simplify82.0ms

Counts
7 → 22
Calls
7 calls:
Slowest
42.0ms
(- (/ 1 x) 1)
10.0ms
(- (/ 1 x) 1)
8.0ms
(- (/ 1 x) 1)
6.0ms
(* (cbrt (/ 1 x)) (cbrt (/ 1 x)))
6.0ms
(log (/ 1 x))

prune408.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample3.6s

Algorithm
intervals
Results
32004×(pre true 80)
24004×(body nan 80)
8000×(body real 80)