Details

sample32.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
10.0ms	283×	body	80	nan

simplify4.0ms

Calls

1 calls:

Slowest

4.0ms

(/ a (- (acos a)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

10×	`associate-/r*`
4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
1×	`expm1-log1p-u` `pow1` `clear-num` `neg-mul-1` `frac-2neg` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Calls

1 calls:

Slowest

1.0ms

(/ a (- (acos a)))

series23.0ms

Calls

1 calls:

Slowest

23.0ms

(/ a (- (acos a)))

simplify145.0ms

Calls

13 calls:

Slowest

38.0ms	(* -1 (/ a (acos a)))
30.0ms	(* -1 (/ a (acos a)))
29.0ms	(* -1 (/ a (acos a)))
13.0ms	(sqrt (acos a))
6.0ms	(cbrt (- (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:

0.4b	(/ 1 (/ (- (acos a)) a))
0.3b	(/ (- (acos a)) a)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`associate-/l*`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`associate-/r*`
3×	`distribute-lft-neg-in` `pow1` `distribute-rgt-neg-in` `add-exp-log` `div-inv`
2×	`expm1-log1p-u` `clear-num` `frac-2neg` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`neg-sub0` `rec-exp` `neg-mul-1` `div-sub` `distribute-frac-neg` `associate-/r/` `pow-flip` `inv-pow`

Calls

2 calls:

Slowest

9.0ms	(/ (- (acos a)) a)
7.0ms	(/ 1 (/ (- (acos a)) a))

series41.0ms

Calls

2 calls:

Slowest

25.0ms	(/ 1 (/ (- (acos a)) a))
16.0ms	(/ (- (acos a)) a)

simplify294.0ms

Calls

20 calls:

Slowest

38.0ms	(* -1 (/ (acos a) a))
38.0ms	(* -1 (/ a (acos a)))
37.0ms	(* -1 (/ a (acos a)))
36.0ms	(* -1 (/ (acos a) a))
36.0ms	(* -1 (/ a (acos a)))

prune386.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (/ 1 (- (acos a))) (/ 1 a))
0.0b	(/ 1 (- (acos a)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

16×	`times-frac`
15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
14×	`associate-/r*`
12×	`div-inv`
7×	`add-exp-log`
4×	`add-cbrt-cube` `associate-/l*`
3×	`distribute-lft-neg-in` `pow1` `distribute-rgt-neg-in`
2×	`expm1-log1p-u` `rec-exp` `clear-num` `frac-2neg` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `neg-mul-1` `associate-/r/` `pow-flip` `inv-pow` `associate-/l/`

Calls

2 calls:

Slowest

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

series26.0ms

Calls

2 calls:

Slowest

19.0ms	(/ (/ 1 (- (acos a))) (/ 1 a))
6.0ms	(/ 1 (- (acos a)))

simplify2.8s

Calls

58 calls:

Slowest

1.2s	(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
121.0ms	(/ (/ 1 (- (acos a))) (/ 1 a))
103.0ms	(- (log (/ 1 (- (acos a)))) (log (/ 1 a)))
100.0ms	(/ (/ 1 (- (acos a))) (/ 1 a))
86.0ms	(/ (/ 1 (- (acos a))) (/ 1 a))

prune612.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ (/ -1 (acos a)) (/ 1 a))
0.0b	(/ -1 (acos a))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

16×	`times-frac`
13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`div-inv`
7×	`associate-/r*`
4×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
2×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `div-exp` `associate-/r/` `associate-/l/`

Calls

2 calls:

Slowest

5.0ms	(/ (/ -1 (acos a)) (/ 1 a))
1.0ms	(/ -1 (acos a))

series33.0ms

Calls

2 calls:

Slowest

21.0ms	(/ (/ -1 (acos a)) (/ 1 a))
11.0ms	(/ -1 (acos a))

simplify2.1s

Calls

49 calls:

Slowest

875.0ms	(/ (* (* (/ -1 (acos a)) (/ -1 (acos a))) (/ -1 (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
120.0ms	(- (log (/ -1 (acos a))) (log (/ 1 a)))
69.0ms	(/ (/ -1 (acos a)) (/ 1 a))
64.0ms	(/ (sqrt (/ -1 (acos a))) (/ 1 a))
61.0ms	(/ (sqrt (/ -1 (acos a))) (/ 1 a))

prune426.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes116.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.1s	8000×	body	80	valid
388.0ms	8022×	body	80	nan