Details

Time bar (total: 13.5s)

sample22.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
5.0ms277×body80nan

simplify1.0ms

Counts
1 → 1
Iterations
IterNodes
done4
04

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
24×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/r*
4×neg-mul-1
3×add-cbrt-cube add-exp-log associate-/l*
1×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp log1p-expm1-u div-inv add-log-exp
Counts
1 → 57
Calls
1 calls:
6.0ms
(/ a (- (acos a)))

series32.0ms

Counts
1 → 3
Calls
1 calls:
32.0ms
(/ a (- (acos a)))

simplify1.5s

Counts
60 → 60
Iterations
IterNodes
done5000
32093
2466
1173
096

prune313.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
140×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
48×distribute-lft-neg-in distribute-rgt-neg-in
37×associate-/r*
16×neg-mul-1
15×add-exp-log
13×associate-/l*
9×add-cbrt-cube
8×div-exp
6×div-inv
4×cbrt-undiv
3×pow1
2×expm1-log1p-u rec-exp clear-num frac-2neg 1-exp log1p-expm1-u add-log-exp
1×neg-sub0 div-sub distribute-frac-neg associate-/r/ pow-flip inv-pow
Counts
2 → 221
Calls
2 calls:
20.0ms
(/ 1 (/ (- (acos a)) a))
6.0ms
(/ (- (acos a)) a)

series99.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(/ 1 (/ (- (acos a)) a))
45.0ms
(/ (- (acos a)) a)

simplify1.9s

Counts
227 → 227
Iterations
IterNodes
done5000
24007
1790
0292

prune833.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
1207×times-frac
550×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
138×distribute-lft-neg-in distribute-rgt-neg-in
51×div-inv
46×neg-mul-1 add-exp-log
37×associate-/l*
34×div-exp
23×associate-/r*
16×add-cbrt-cube
9×cbrt-undiv rec-exp 1-exp
3×pow1
2×expm1-log1p-u clear-num frac-2neg log1p-expm1-u add-log-exp
1×associate-/r/ pow-flip inv-pow associate-/l/
Counts
2 → 584
Calls
2 calls:
11.0ms
(/ 1 (- (acos a)))
34.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series62.0ms

Counts
2 → 6
Calls
2 calls:
11.0ms
(/ 1 (- (acos a)))
51.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify2.8s

Counts
590 → 590
Iterations
IterNodes
done5001
12950
0811

prune1.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (acos a) (acos a))
0.4b
(/ (cbrt (/ 1 (- (* (* (acos a) (acos a)) (acos a))))) (/ 1 a))
1.0b
(* (* (acos a) (acos a)) (acos a))
1.0b
(cbrt (/ 1 (- (* (* (acos a) (acos a)) (acos a)))))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
829×times-frac
358×add-sqr-sqrt
355×*-un-lft-identity add-cube-cbrt
330×cbrt-prod
45×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in
42×div-inv
30×pow1
25×associate-/l*
20×add-exp-log
14×add-cbrt-cube
13×associate-/r*
7×pow-plus pow-prod-up
6×div-exp associate-*r*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow2 cbrt-undiv swap-sqr pow-sqr
2×cbrt-div *-commutative unswap-sqr
1×rec-exp clear-num frac-2neg pow1/3 1-exp pow3 associate-/r/ associate-/l/
Counts
4 → 473
Calls
4 calls:
11.0ms
(* (acos a) (acos a))
53.0ms
(/ (cbrt (/ 1 (- (* (* (acos a) (acos a)) (acos a))))) (/ 1 a))
15.0ms
(* (* (acos a) (acos a)) (acos a))
5.0ms
(cbrt (/ 1 (- (* (* (acos a) (acos a)) (acos a)))))

series226.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (acos a) (acos a))
121.0ms
(/ (cbrt (/ 1 (- (* (* (acos a) (acos a)) (acos a))))) (/ 1 a))
31.0ms
(* (* (acos a) (acos a)) (acos a))
59.0ms
(cbrt (/ 1 (- (* (* (acos a) (acos a)) (acos a)))))

simplify1.5s

Counts
485 → 485
Iterations
IterNodes
done5000
11822
0732

prune1.7s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes120.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
done4
04

end0.0ms

sample840.0ms

Algorithm
intervals
Results
340.0ms8000×body80valid
251.0ms8007×body80nan