Average Error: 0.2 → 0.2
Time: 12.2s
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 2019005 
(FPCore (a)
  :name "Fuzzer 001"
  (/ a (- (acos a))))

Details

Time bar (total: 11.8s)Debug log

sample55.0ms

Algorithm
intervals

simplify2.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 1 expressions with local error:

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

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
1 → 20
Calls

1 calls. Slowest were:

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

series24.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

24.0ms
(/ a (- (acos a)))

simplify63.0ms

Counts
13 → 23
Calls

13 calls. Slowest were:

17.0ms
(* -1 (/ a (acos a)))
16.0ms
(* -1 (/ a (acos a)))
16.0ms
(* -1 (/ a (acos a)))

prune179.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
2 → 40
Calls

2 calls. Slowest were:

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

series52.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

30.0ms
(/ (- (acos a)) a)
22.0ms
(/ 1 (/ (- (acos a)) a))

simplify102.0ms

Counts
20 → 46
Calls

20 calls. Slowest were:

16.0ms
(* -1 (/ (acos a) a))
15.0ms
(* -1 (/ a (acos a)))
12.0ms
(* -1 (/ (acos a) a))

prune271.0ms

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)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
2 → 62
Calls

2 calls. Slowest were:

5.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
2.0ms
(/ 1 (- (acos a)))

series35.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

25.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
10.0ms
(/ 1 (- (acos a)))

simplify1.6s

Counts
58 → 68
Calls

58 calls. Slowest were:

936.0ms
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
88.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
86.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

prune373.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

localize23.0ms

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))

rewrite73.0ms

Algorithm
rewrite-expression-head
Counts
4 → 156
Calls

4 calls. Slowest were:

26.0ms
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
19.0ms
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
10.0ms
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))

series160.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

62.0ms
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))
46.0ms
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
37.0ms
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
14.0ms
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))

simplify6.0s

Counts
167 → 168
Calls

167 calls. Slowest were:

828.0ms
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
573.0ms
(* (* (* (* (/ 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)))))
484.0ms
(* (* (* (* (/ 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)))))

prune1.3s

Pruning

5 alts after pruning (2 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

sample1.3s

Algorithm
intervals