Average Error: 0.0 → 0.0
Time: 27.3s
Precision: 64
Internal Precision: 128
\[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]

Error

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]

  2. Final simplification0.0

    \[\leadsto \frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]

Reproduce

herbie shell --seed 2019007 
(FPCore (t)
  :name "Kahan p13 Example 2"
  (/ (+ 1 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))) (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))))))

Details

Time bar (total: 27.0s)Debug log

sample69.0ms

Algorithm
intervals

simplify122.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

122.0ms
(/ (+ 1 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))) (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

4.6b
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
4.6b
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
4.6b
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
4.6b
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
4 → 44
Calls

4 calls. Slowest were:

1.0ms
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
1.0ms
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
1.0ms
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))

series51.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

18.0ms
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
11.0ms
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
11.0ms
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
11.0ms
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))

simplify2.7s

Counts
12 → 56
Calls

12 calls. Slowest were:

445.0ms
(- (+ (* 2 t) (* 2 (pow t 3))) (* 2 (pow t 2)))
430.0ms
(- (+ (* 2 t) (* 2 (pow t 3))) (* 2 (pow t 2)))
421.0ms
(- (+ (* 2 t) (* 2 (pow t 3))) (* 2 (pow t 2)))

prune441.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

4.6b
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
4.6b
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
4.6b
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
0.1b
(/ (+ 1 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (* (- (* t t) (- t 1)) (* t 2)))) (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Counts
4 → 64
Calls

4 calls. Slowest were:

18.0ms
(/ (+ 1 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (* (- (* t t) (- t 1)) (* t 2)))) (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))
1.0ms
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
1.0ms
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))

series145.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

98.0ms
(/ (+ 1 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (* (- (* t t) (- t 1)) (* t 2)))) (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))
19.0ms
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
16.0ms
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
11.0ms
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))

simplify16.1s

Counts
41 → 76
Calls

41 calls. Slowest were:

888.0ms
(/ (cbrt (+ 1 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (* (- (* t t) (- t 1)) (* t 2))))) (sqrt (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))))))
622.0ms
(/ (sqrt (+ 1 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (* (- (* t t) (- t 1)) (* t 2))))) (cbrt (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))))))
601.0ms
(/ (sqrt (+ 1 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (* (- (* t t) (- t 1)) (* t 2))))) (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))

prune857.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

4.6b
(- 2 (/ 2 (+ t 1)))
4.6b
(- 2 (/ 2 (+ t 1)))
4.6b
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
4.6b
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
4 → 44
Calls

4 calls. Slowest were:

1.0ms
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
0.0ms
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
0.0ms
(- 2 (/ 2 (+ t 1)))

series58.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

19.0ms
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
18.0ms
(- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))
12.0ms
(- 2 (/ 2 (+ t 1)))
9.0ms
(- 2 (/ 2 (+ t 1)))

simplify3.0s

Counts
12 → 56
Calls

12 calls. Slowest were:

516.0ms
(- (+ (* 2 t) (* 2 (pow t 3))) (* 2 (pow t 2)))
509.0ms
(- (+ (* 2 t) (* 2 (pow t 3))) (* 2 (pow t 2)))
456.0ms
(- (+ (* 2 t) (* 2 (pow t 3))) (* 2 (pow t 2)))

prune879.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes197.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample2.2s

Algorithm
intervals