Details

Time bar (total: 10.9s)

sample17.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
3.0ms272×body80nan

simplify1.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
045
done45

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/r*
4×neg-mul-1
3×add-exp-log add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv frac-2neg div-exp clear-num div-inv add-log-exp
Counts
1 → 55
Calls
1 calls:
3.0ms
(/ a (- (acos a)))

series23.0ms

Counts
1 → 3
Calls
1 calls:
23.0ms
(/ a (- (acos a)))

simplify2.6s

Counts
58 → 58
Iterations

Useful iterations: 4 (870.0ms)

IterNodesCost
094601
1167571
2478549
31470545
43410544
done5000544

prune109.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
140×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
48×distribute-lft-neg-in distribute-rgt-neg-in
44×associate-/r*
16×neg-mul-1
15×add-exp-log
9×add-cbrt-cube
8×div-exp
6×div-inv associate-/l*
4×cbrt-undiv
3×pow1
2×rec-exp frac-2neg 1-exp clear-num add-log-exp
1×acos-asin pow-flip div-sub associate-/r/ inv-pow
Counts
2 → 216
Calls
2 calls:
10.0ms
(/ 1 (/ (acos a) (- a)))
4.0ms
(/ (acos a) (- a))

series59.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(/ 1 (/ (acos a) (- a)))
36.0ms
(/ (acos a) (- a))

simplify2.1s

Counts
222 → 222
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02933186
16352769
221582318
done50002255

prune255.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
1186×times-frac
535×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
126×distribute-lft-neg-in distribute-rgt-neg-in
51×div-inv
46×add-exp-log
42×neg-mul-1
37×associate-/r*
34×div-exp
16×add-cbrt-cube associate-/l*
9×cbrt-undiv rec-exp 1-exp
3×pow1
2×frac-2neg clear-num add-log-exp
1×pow-flip associate-/r/ associate-/l/ inv-pow
Counts
2 → 552
Calls
2 calls:
2.0ms
(/ 1 (acos a))
23.0ms
(/ (/ 1 (acos a)) (/ 1 (- a)))

series35.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(/ 1 (acos a))
30.0ms
(/ (/ 1 (acos a)) (/ 1 (- a)))

simplify917.0ms

Counts
558 → 558
Iterations

Useful iterations: done (898.0ms)

IterNodesCost
080512210
124329814
done50008208

prune290.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

localize9.0ms

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))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
778×times-frac
339×add-sqr-sqrt
336×add-cube-cbrt *-un-lft-identity
252×cbrt-prod
99×distribute-lft-neg-in distribute-rgt-neg-in
48×div-inv
34×associate-/r*
33×neg-mul-1
30×pow1
20×add-exp-log
14×add-cbrt-cube
10×associate-/l*
7×pow-plus pow-prod-up
6×div-exp associate-*r*
4×associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
3×cbrt-undiv pow2 swap-sqr pow-sqr
2×cbrt-div *-commutative unswap-sqr
1×rec-exp frac-2neg pow1/3 1-exp pow3 clear-num associate-/r/ associate-/l/
Counts
4 → 471
Calls
4 calls:
6.0ms
(* (acos a) (acos a))
18.0ms
(/ (cbrt (/ 1 (* (* (acos a) (acos a)) (acos a)))) (/ 1 (- a)))
7.0ms
(* (* (acos a) (acos a)) (acos a))
13.0ms
(cbrt (/ 1 (* (* (acos a) (acos a)) (acos a))))

series74.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(* (acos a) (acos a))
29.0ms
(/ (cbrt (/ 1 (* (* (acos a) (acos a)) (acos a)))) (/ 1 (- a)))
26.0ms
(* (* (acos a) (acos a)) (acos a))
5.0ms
(cbrt (/ 1 (* (* (acos a) (acos a)) (acos a))))

simplify3.2s

Counts
483 → 483
Iterations

Useful iterations: 2 (521.0ms)

IterNodesCost
063313406
113479647
241518111
done50008111

prune442.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

end0.0ms

sample429.0ms

Algorithm
intervals
Results
156.0ms8000×body80valid
105.0ms8067×body80nan