Average Error: 0.0 → 0.0
Time: 9.1s
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 +o rules:numerics
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))

Details

Time bar (total: 8.8s)Debug log

sample230.0ms

Algorithm
intervals

simplify11.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
11.0ms
(- (log (- (/ 1 x) 1)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

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×log1p-expm1-u
1×log-pow
1×rem-log-exp
1×difference-of-sqr-1
1×add-cbrt-cube
1×flip3--
1×expm1-log1p-u
Counts
1 → 17
Calls
1 calls:
Slowest
7.0ms
(log (- (/ 1 x) 1))

series45.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
44.0ms
(log (- (/ 1 x) 1))

simplify459.0ms

Counts
10 → 20
Calls
10 calls:
Slowest
141.0ms
(- (+ x (+ (* 1/2 (pow x 2)) (log x))))
79.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))
78.0ms
(- (log -1) (+ (/ 1 x) (* 1/2 (/ 1 (pow x 2)))))
68.0ms
(log (- (* (/ 1 x) (/ 1 x)) (* 1 1)))
58.0ms
(log (- (pow (/ 1 x) 3) (pow 1 3)))

prune190.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (* (* (log (- (/ 1 x) 1)) (log (- (/ 1 x) 1))) (log (- (/ 1 x) 1))))
0.5b
(* (log (- (/ 1 x) 1)) (log (- (/ 1 x) 1)))
0.3b
(* (* (log (- (/ 1 x) 1)) (log (- (/ 1 x) 1))) (log (- (/ 1 x) 1)))
0.0b
(log (- (/ 1 x) 1))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
27×pow1
20×log-prod
17×add-sqr-sqrt
12×add-cube-cbrt
12×add-exp-log
12×*-un-lft-identity
11×add-cbrt-cube
8×associate-*r*
8×distribute-lft-in
8×distribute-rgt-in
6×pow-prod-up
6×pow-plus
5×associate-*l*
5×difference-of-sqr-1
4×add-log-exp
4×log1p-expm1-u
4×cbrt-unprod
4×log-pow
4×prod-exp
4×pow-prod-down
4×expm1-log1p-u
3×pow2
2×*-commutative
2×pow3
2×log-div
1×flip--
1×rem-cbrt-cube
1×rem-log-exp
1×pow1/3
1×flip3--
1×cbrt-prod
Counts
4 → 97
Calls
4 calls:
Slowest
15.0ms
(* (* (log (- (/ 1 x) 1)) (log (- (/ 1 x) 1))) (log (- (/ 1 x) 1)))
12.0ms
(cbrt (* (* (log (- (/ 1 x) 1)) (log (- (/ 1 x) 1))) (log (- (/ 1 x) 1))))
8.0ms
(* (log (- (/ 1 x) 1)) (log (- (/ 1 x) 1)))
3.0ms
(log (- (/ 1 x) 1))

series168.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
67.0ms
(* (* (log (- (/ 1 x) 1)) (log (- (/ 1 x) 1))) (log (- (/ 1 x) 1)))
48.0ms
(* (log (- (/ 1 x) 1)) (log (- (/ 1 x) 1)))
33.0ms
(cbrt (* (* (log (- (/ 1 x) 1)) (log (- (/ 1 x) 1))) (log (- (/ 1 x) 1))))
21.0ms
(log (- (/ 1 x) 1))

simplify3.2s

Counts
70 → 109
Calls
70 calls:
Slowest
512.0ms
(+ (* 2 (* x (log x))) (+ (pow (log x) 2) (+ (pow x 2) (* (pow x 2) (log x)))))
361.0ms
(- (+ (* 3/2 (* (pow x 2) (pow (log x) 2))) (+ (* 3 (* x (pow (log x) 2))) (+ (* 3 (* (pow x 2) (log x))) (pow (log x) 3)))))
332.0ms
(- (+ (/ 1 (pow x 2)) (pow (log -1) 2)) (+ (* 2 (/ (log -1) x)) (/ (log -1) (pow x 2))))
307.0ms
(- (+ (/ 1 (pow x 2)) (pow (log -1) 2)) (+ (* 2 (/ (log -1) x)) (/ (log -1) (pow x 2))))
238.0ms
(- (+ x (+ (* 1/2 (pow x 2)) (log x))))

prune1.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes136.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample3.2s

Algorithm
intervals