Average Error: 0.0 → 0.0
Time: 9.4s
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 2018362 +o rules:numerics
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))

Details

Time bar (total: 3.9s)Debug log

start652.0ms

Algorithm
intervals

setup37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 1 expressions with local error:

0.0b
(log (- (/ 1 x) 1))

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

7.0ms
(log (- (/ 1 x) 1))

series57.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

56.0ms
(log (- (/ 1 x) 1))

simplify555.0ms

Counts
10 → 20
Calls

10 calls. Slowest were:

188.0ms
(- (+ x (+ (* 1/2 (pow x 2)) (log x))))
112.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))
108.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))

prune162.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (fma -1/2 x -1) x)
0.0b
(- (* (fma -1/2 x -1) x) (log x))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
2 → 31
Calls

2 calls. Slowest were:

5.0ms
(- (* (fma -1/2 x -1) x) (log x))
3.0ms
(* (fma -1/2 x -1) x)

series68.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

36.0ms
(- (* (fma -1/2 x -1) x) (log x))
32.0ms
(* (fma -1/2 x -1) x)

simplify1.7s

Counts
16 → 37
Calls

16 calls. Slowest were:

623.0ms
(- (log (/ 1 x)) (+ (* 1/2 (pow x 2)) x))
477.0ms
(- (log (/ -1 x)) (+ x (+ (* 1/2 (pow x 2)) (log -1))))
149.0ms
(- (+ x (+ (* 1/2 (pow x 2)) (log x))))

prune366.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes190.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch2.0ms