Average Error: 0.2 → 0.2
Time: 12.7s
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 2019008 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 001"
  (/ a (- (acos a))))

Details

Time bar (total: 12.1s)Debug log

sample56.0ms

Algorithm
intervals

simplify2.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

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:

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

series24.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify75.0ms

Counts
13 → 25
Calls

13 calls. Slowest were:

26.0ms
(* -1 (/ a (acos a)))
17.0ms
(* -1 (/ a (acos a)))
16.0ms
(* -1 (/ a (acos a)))

prune223.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 2 expressions with local error:

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

simplify96.0ms

Counts
20 → 50
Calls

20 calls. Slowest were:

16.0ms
(* -1 (/ (acos a) a))
10.0ms
(* -1 (/ (acos a) a))
8.0ms
(* -1 (/ (acos a) a))

prune275.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
2 → 66
Calls

2 calls. Slowest were:

10.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
2.0ms
(/ 1 (- (acos a)))

series36.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

26.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
10.0ms
(/ 1 (- (acos a)))

simplify1.7s

Counts
58 → 72
Calls

58 calls. Slowest were:

996.0ms
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
85.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
75.0ms
(- (log (/ 1 (- (acos a)))) (log (/ 1 a)))

prune495.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))
1.0b
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
0.9b
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
0.4b
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))

rewrite38.0ms

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)))))
6.0ms
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))

series198.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

88.0ms
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))
57.0ms
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
38.0ms
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
16.0ms
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))

simplify6.1s

Counts
167 → 176
Calls

167 calls. Slowest were:

1.0s
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
537.0ms
(* (* (* (* (/ 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)))))
407.0ms
(* (* (* (* (/ 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)))))

prune1.4s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes80.0ms

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