Average Error: 0.1 → 0.1
Time: 11.8s
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 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2019008 +o rules:numerics
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))

Details

Time bar (total: 11.4s)Debug log

sample197.0ms

Algorithm
intervals

simplify19.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

18.0ms
(- (log (- (/ 1 x) 1)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 1 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

29.0ms
(log (- (/ 1 x) 1))

series38.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

37.0ms
(log (- (/ 1 x) 1))

simplify527.0ms

Counts
10 → 20
Calls

10 calls. Slowest were:

173.0ms
(- (+ x (+ (* 1/2 (pow x 2)) (log x))))
106.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))
104.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))

prune182.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize24.0ms

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)

series57.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

33.0ms
(* (fma -1/2 x -1) x)
24.0ms
(- (* (fma -1/2 x -1) x) (log x))

simplify1.6s

Counts
16 → 37
Calls

16 calls. Slowest were:

528.0ms
(- (log (/ 1 x)) (+ (* 1/2 (pow x 2)) x))
451.0ms
(- (log (/ -1 x)) (+ x (+ (* 1/2 (pow x 2)) (log -1))))
180.0ms
(- (+ x (+ (* 1/2 (pow x 2)) (log x))))

prune324.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

30.8b
(log (fma (/ 1 x) (/ 1 x) -1))
0.3b
(fma (/ 1 x) (/ 1 x) -1)
0.0b
(- (log (fma (/ 1 x) (/ 1 x) -1)) (log (+ (/ 1 x) 1)))
0.0b
(log (+ (/ 1 x) 1))

rewrite27.0ms

Algorithm
rewrite-expression-head
Counts
4 → 87
Calls

4 calls. Slowest were:

19.0ms
(- (log (fma (/ 1 x) (/ 1 x) -1)) (log (+ (/ 1 x) 1)))
4.0ms
(log (+ (/ 1 x) 1))
2.0ms
(log (fma (/ 1 x) (/ 1 x) -1))

series184.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

67.0ms
(log (fma (/ 1 x) (/ 1 x) -1))
55.0ms
(- (log (fma (/ 1 x) (/ 1 x) -1)) (log (+ (/ 1 x) 1)))
31.0ms
(fma (/ 1 x) (/ 1 x) -1)
31.0ms
(log (+ (/ 1 x) 1))

simplify4.2s

Counts
71 → 99
Calls

71 calls. Slowest were:

216.0ms
(- (+ (* 1/3 (/ 1 (pow x 3))) (/ 1 x)) (* 1/2 (/ 1 (pow x 2))))
214.0ms
(- (+ (* 1/3 (/ 1 (pow x 3))) (/ 1 x)) (* 1/2 (/ 1 (pow x 2))))
169.0ms
(- (+ x (+ (* 1/2 (pow x 2)) (log x))))

prune894.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes138.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch1.0ms

end0.0ms

sample2.9s

Algorithm
intervals