Average Error: 0.0 → 0.0
Time: 11.4s
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 2019002 +o rules:numerics
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))

Details

Time bar (total: 11.1s)Debug log

sample229.0ms

Algorithm
intervals

simplify10.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

10.0ms
(- (log (- (/ 1 x) 1)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

27.0ms
(log (- (/ 1 x) 1))

series27.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

27.0ms
(log (- (/ 1 x) 1))

simplify617.0ms

Counts
10 → 20
Calls

10 calls. Slowest were:

212.0ms
(- (+ x (+ (* 1/2 (pow x 2)) (log x))))
138.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))
125.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))

prune118.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (log (- (/ 1 x) 1))) (cbrt (log (- (/ 1 x) 1))))
0.5b
(cbrt (log (- (/ 1 x) 1)))
0.5b
(cbrt (log (- (/ 1 x) 1)))
0.5b
(cbrt (log (- (/ 1 x) 1)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
4 → 74
Calls

4 calls. Slowest were:

11.0ms
(* (cbrt (log (- (/ 1 x) 1))) (cbrt (log (- (/ 1 x) 1))))
1.0ms
(cbrt (log (- (/ 1 x) 1)))
1.0ms
(cbrt (log (- (/ 1 x) 1)))

series405.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

139.0ms
(* (cbrt (log (- (/ 1 x) 1))) (cbrt (log (- (/ 1 x) 1))))
91.0ms
(cbrt (log (- (/ 1 x) 1)))
88.0ms
(cbrt (log (- (/ 1 x) 1)))
87.0ms
(cbrt (log (- (/ 1 x) 1)))

simplify5.3s

Counts
46 → 86
Calls

46 calls. Slowest were:

633.0ms
(- (pow (log -1) 1/3) (+ (* 1/3 (* (/ 1 x) (pow (/ 1 (pow (log -1) 2)) 1/3))) (+ (* 1/6 (* (/ 1 (pow x 2)) (pow (/ 1 (pow (log -1) 2)) 1/3))) (* 1/9 (* (/ 1 (pow x 2)) (pow (/ 1 (pow (log -1) 5)) 1/3))))))
616.0ms
(- (pow (log -1) 1/3) (+ (* 1/3 (* (/ 1 x) (pow (/ 1 (pow (log -1) 2)) 1/3))) (+ (* 1/6 (* (/ 1 (pow x 2)) (pow (/ 1 (pow (log -1) 2)) 1/3))) (* 1/9 (* (/ 1 (pow x 2)) (pow (/ 1 (pow (log -1) 5)) 1/3))))))
557.0ms
(- (pow (log -1) 1/3) (+ (* 1/3 (* (/ 1 x) (pow (/ 1 (pow (log -1) 2)) 1/3))) (+ (* 1/6 (* (/ 1 (pow x 2)) (pow (/ 1 (pow (log -1) 2)) 1/3))) (* 1/9 (* (/ 1 (pow x 2)) (pow (/ 1 (pow (log -1) 5)) 1/3))))))

prune869.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes125.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample3.3s

Algorithm
intervals