Average Error: 0.2 → 0.2
Time: 11.4s
Precision: 64
Internal Precision: 128
\[\frac{a}{-\cos^{-1} a}\]
↓
\[\frac{a}{-\cos^{-1} a}\]

Error

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{a}{-\cos^{-1} a}\]

  2. Final simplification0.2

    \[\leadsto \frac{a}{-\cos^{-1} a}\]

Reproduce

herbie shell --seed 2019005 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 001"
  (/ a (- (acos a))))

Details

Time bar (total: 11.0s)Debug log

sample59.0ms

Algorithm
intervals

simplify1.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

1.0ms
(/ a (- (acos a)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 1 expressions with local error:

0.2b
(/ a (- (acos a)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
1 → 22
Calls

1 calls. Slowest were:

1.0ms
(/ a (- (acos a)))

series23.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

23.0ms
(/ a (- (acos a)))

simplify52.0ms

Counts
13 → 25
Calls

13 calls. Slowest were:

14.0ms
(* -1 (/ a (acos a)))
13.0ms
(* -1 (/ a (acos a)))
13.0ms
(* -1 (/ a (acos a)))

prune191.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ 1 (/ (- (acos a)) a))
0.3b
(/ (- (acos a)) a)

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
2 → 44
Calls

2 calls. Slowest were:

6.0ms
(/ (- (acos a)) a)
2.0ms
(/ 1 (/ (- (acos a)) a))

series46.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

23.0ms
(/ (- (acos a)) a)
23.0ms
(/ 1 (/ (- (acos a)) a))

simplify110.0ms

Counts
20 → 50
Calls

20 calls. Slowest were:

15.0ms
(* -1 (/ a (acos a)))
13.0ms
(* -1 (/ (acos a) a))
13.0ms
(* -1 (/ (acos a) a))

prune254.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (/ 1 (- (acos a))) (/ 1 a))
0.0b
(/ 1 (- (acos a)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
2 → 66
Calls

2 calls. Slowest were:

4.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
1.0ms
(/ 1 (- (acos a)))

series20.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

15.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
6.0ms
(/ 1 (- (acos a)))

simplify1.4s

Counts
58 → 72
Calls

58 calls. Slowest were:

696.0ms
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
83.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
82.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

prune400.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
1.0b
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
1.0b
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))
0.4b
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))

rewrite35.0ms

Algorithm
rewrite-expression-head
Counts
4 → 164
Calls

4 calls. Slowest were:

15.0ms
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
9.0ms
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
5.0ms
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))

series151.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

72.0ms
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))
36.0ms
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
28.0ms
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
15.0ms
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))

simplify5.2s

Counts
167 → 176
Calls

167 calls. Slowest were:

829.0ms
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
397.0ms
(* (* (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
376.0ms
(* (* (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (* (/ 1 (- (acos a))) (/ 1 (- (acos a))))) (* (/ 1 (- (acos a))) (/ 1 (- (acos a))))) (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))

prune1.5s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes112.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch1.0ms

end0.0ms

sample1.4s

Algorithm
intervals