Average Error: 0.0 → 0.0
Time: 12.8s
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 0.0

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2018365 +o rules:numerics
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))

Details

Time bar (total: 7.0s)Debug log

start639.0ms

Algorithm
intervals

setup21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

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

series53.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

52.0ms
(log (- (/ 1 x) 1))

simplify540.0ms

Counts
10 → 20
Calls

10 calls. Slowest were:

183.0ms
(- (+ x (+ (* 1/2 (pow x 2)) (log x))))
109.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))
107.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))

prune149.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- (/ 1 x) 1))
0.6b
(cbrt (- (/ 1 x) 1))
0.6b
(cbrt (- (/ 1 x) 1))
0.5b
(* (cbrt (- (/ 1 x) 1)) (cbrt (- (/ 1 x) 1)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Counts
4 → 88
Calls

4 calls. Slowest were:

10.0ms
(* (cbrt (- (/ 1 x) 1)) (cbrt (- (/ 1 x) 1)))
2.0ms
(cbrt (- (/ 1 x) 1))
2.0ms
(cbrt (- (/ 1 x) 1))

series238.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

75.0ms
(* (cbrt (- (/ 1 x) 1)) (cbrt (- (/ 1 x) 1)))
68.0ms
(cbrt (- (/ 1 x) 1))
54.0ms
(cbrt (- (/ 1 x) 1))
41.0ms
(cbrt (- (/ 1 x) 1))

simplify4.0s

Counts
64 → 100
Calls

64 calls. Slowest were:

361.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (/ 1 x) (pow -1 1/3))) (* 1/9 (* (/ 1 (pow x 2)) (pow -1 1/3)))))
335.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (/ 1 x) (pow -1 1/3))) (* 1/9 (* (/ 1 (pow x 2)) (pow -1 1/3)))))
308.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (/ 1 x) (pow -1 1/3))) (* 1/9 (* (/ 1 (pow x 2)) (pow -1 1/3)))))

prune1.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes189.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms