Average Error: 0.0 → 0.0
Time: 6.2s
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 2019010 
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))

Details

Time bar (total: 5.9s)Debug log

sample210.0ms

Algorithm
intervals

simplify15.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
15.0ms
(- (log (- (/ 1 x) 1)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
4×log-prod
3×add-sqr-sqrt
2×add-cube-cbrt
2×add-exp-log
2×*-un-lft-identity
2×log-div
2×pow1
1×add-log-exp
1×flip--
1×log-pow
1×rem-log-exp
1×difference-of-sqr-1
1×add-cbrt-cube
1×flip3--
Counts
1 → 15
Calls
1 calls:
Slowest
4.0ms
(log (- (/ 1 x) 1))

series66.0ms

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

simplify313.0ms

Counts
10 → 18
Calls
10 calls:
Slowest
87.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))
77.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))
72.0ms
(- (+ x (+ (* 1/2 (pow x 2)) (log x))))
29.0ms
(log (- (* (/ 1 x) (/ 1 x)) (* 1 1)))
26.0ms
(log (- (pow (/ 1 x) 3) (pow 1 3)))

prune125.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ 1 x))
0.1b
(sqrt (/ 1 x))
0.0b
(+ (log (+ (sqrt (/ 1 x)) 1)) (log (- (sqrt (/ 1 x)) 1)))
0.0b
(+ (sqrt (/ 1 x)) 1)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
12×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt
8×log-prod
8×pow1
5×associate-+r+
4×add-log-exp
4×distribute-lft-out
4×log-pow
4×add-exp-log
4×add-cbrt-cube
4×log-div
3×flip-+
3×flip3-+
3×associate-+l+
2×div-inv
2×associate-+l-
2×difference-of-sqr-1
2×sqrt-div
2×pow1/2
2×associate-+r-
2×rem-sqrt-square
2×+-commutative
1×flip--
1×flip3--
1×sum-log
Counts
4 → 65
Calls
4 calls:
Slowest
9.0ms
(+ (log (+ (sqrt (/ 1 x)) 1)) (log (- (sqrt (/ 1 x)) 1)))
4.0ms
(+ (sqrt (/ 1 x)) 1)
1.0ms
(sqrt (/ 1 x))
0.0ms
(sqrt (/ 1 x))

series110.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
72.0ms
(+ (log (+ (sqrt (/ 1 x)) 1)) (log (- (sqrt (/ 1 x)) 1)))
18.0ms
(+ (sqrt (/ 1 x)) 1)
11.0ms
(sqrt (/ 1 x))
9.0ms
(sqrt (/ 1 x))

simplify812.0ms

Counts
41 → 77
Calls
41 calls:
Slowest
620.0ms
(* (+ (sqrt (/ 1 x)) 1) (- (sqrt (/ 1 x)) 1))
52.0ms
(log (+ (* (sqrt (/ 1 x)) (sqrt (/ 1 x))) (+ (* 1 1) (* (sqrt (/ 1 x)) 1))))
30.0ms
(log (- (* (sqrt (/ 1 x)) (sqrt (/ 1 x))) (* 1 1)))
8.0ms
(log (- (sqrt (/ 1 x)) 1))
8.0ms
(log (+ (pow (sqrt (/ 1 x)) 3) (pow 1 3)))

prune793.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes128.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample3.3s

Algorithm
intervals