Average Error: 0.2 → 0.2
Time: 6.2s
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 2019004 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 001"
  (/ a (- (acos a))))

Details

Time bar (total: 5.5s)Debug log

sample72.0ms

Algorithm
intervals

simplify2.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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)))

series21.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

21.0ms
(/ a (- (acos a)))

simplify49.0ms

Counts
13 → 25
Calls

13 calls. Slowest were:

15.0ms
(* -1 (/ a (acos a)))
12.0ms
(* -1 (/ a (acos a)))
9.0ms
(* -1 (/ a (acos a)))

prune212.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ 1 (/ (- (acos a)) a))
0.2b
(/ (- (acos a)) a)

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
2 → 44
Calls

2 calls. Slowest were:

7.0ms
(/ (- (acos a)) a)
2.0ms
(/ 1 (/ (- (acos a)) a))

series56.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

28.0ms
(/ 1 (/ (- (acos a)) a))
28.0ms
(/ (- (acos a)) a)

simplify151.0ms

Counts
20 → 50
Calls

20 calls. Slowest were:

20.0ms
(* -1 (/ a (acos a)))
19.0ms
(* -1 (/ (acos a) a))
18.0ms
(* -1 (/ (acos a) a))

prune392.0ms

Pruning

9 alts after pruning (7 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)))

series22.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

16.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
6.0ms
(/ 1 (- (acos a)))

simplify1.6s

Counts
58 → 72
Calls

58 calls. Slowest were:

895.0ms
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
79.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
77.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

prune582.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Counts
2 → 48
Calls

2 calls. Slowest were:

10.0ms
(* (/ 1 a) (- (acos a)))
8.0ms
(/ 1 (* (/ 1 a) (- (acos a))))

series56.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

30.0ms
(/ 1 (* (/ 1 a) (- (acos a))))
26.0ms
(* (/ 1 a) (- (acos a)))

simplify561.0ms

Counts
25 → 54
Calls

25 calls. Slowest were:

405.0ms
(* (* (* (/ 1 a) (/ 1 a)) (/ 1 a)) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
36.0ms
(* (/ 1 a) (- (acos a)))
18.0ms
(+ (log (/ 1 a)) (log (- (acos a))))

prune352.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes110.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample1.2s

Algorithm
intervals