Details

sample43.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
12.0ms	257×	body	80	nan

simplify3.0ms

Calls

1 calls:

Slowest

3.0ms

(/ a (- (acos a)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 1 expressions with local error:

0.2b	(/ 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)))

series53.0ms

Calls

1 calls:

Slowest

53.0ms

(/ a (- (acos a)))

simplify119.0ms

Calls

13 calls:

Slowest

29.0ms	(* -1 (/ a (acos a)))
20.0ms	(* -1 (/ a (acos a)))
20.0ms	(* -1 (/ a (acos a)))
7.0ms	(- (sqrt (acos a)))
6.0ms	(- (cbrt (acos a)))

prune189.0ms

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)

rewrite7.0ms

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

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

series120.0ms

Calls

2 calls:

Slowest

64.0ms	(/ 1 (/ (- (acos a)) a))
56.0ms	(/ (- (acos a)) a)

simplify282.0ms

Calls

20 calls:

Slowest

38.0ms	(* -1 (/ a (acos a)))
35.0ms	(* -1 (/ a (acos a)))
30.0ms	(* -1 (/ (acos a) a))
25.0ms	(* -1 (/ a (acos a)))
23.0ms	(* -1 (/ (acos a) a))

prune430.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

2 calls:

Slowest

6.0ms	(* (- (acos a)) (/ 1 a))
5.0ms	(/ 1 (* (- (acos a)) (/ 1 a)))

series101.0ms

Calls

2 calls:

Slowest

54.0ms	(/ 1 (* (- (acos a)) (/ 1 a)))
47.0ms	(* (- (acos a)) (/ 1 a))

simplify769.0ms

Calls

24 calls:

Slowest

344.0ms	(* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
73.0ms	(* (- (acos a)) (/ 1 a))
48.0ms	(+ (log (- (acos a))) (log (/ 1 a)))
37.0ms	(* -1 (/ a (acos a)))
36.0ms	(* -1 (/ (acos a) a))

prune490.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

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

10.0ms	(/ (/ 1 (- (acos a))) (/ 1 a))
3.0ms	(/ 1 (- (acos a)))

series46.0ms

Calls

2 calls:

Slowest

35.0ms	(/ (/ 1 (- (acos a))) (/ 1 a))
11.0ms	(/ 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)))
119.0ms	(/ (/ 1 (- (acos a))) (/ 1 a))
102.0ms	(/ (/ 1 (- (acos a))) (/ 1 a))
97.0ms	(- (log (/ 1 (- (acos a)))) (log (/ 1 a)))
93.0ms	(/ (/ 1 (- (acos a))) (/ 1 a))

prune560.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes92.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch1.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

995.0ms	8000×	body	80	valid
429.0ms	8010×	body	80	nan