Details

Time bar (total: 19.7s)

sample20.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
5.0ms271×body80nan

simplify1.0ms

Counts
1 → 1
Iterations
IterNodes
done4
04

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite13.0ms

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×pow1 cbrt-undiv clear-num frac-2neg div-exp div-inv add-log-exp
Counts
1 → 55
Calls
1 calls:
6.0ms
(/ a (- (acos a)))

series45.0ms

Counts
1 → 3
Calls
1 calls:
45.0ms
(/ a (- (acos a)))

simplify1.4s

Counts
58 → 58
Iterations
IterNodes
done5000
31308
2448
1171
094

prune263.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite44.0ms

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×rec-exp clear-num frac-2neg 1-exp add-log-exp
1×neg-sub0 div-sub distribute-frac-neg associate-/r/ pow-flip inv-pow
Counts
2 → 217
Calls
2 calls:
6.0ms
(/ (- (acos a)) a)
18.0ms
(/ 1 (/ (- (acos a)) a))

series92.0ms

Counts
2 → 6
Calls
2 calls:
59.0ms
(/ (- (acos a)) a)
32.0ms
(/ 1 (/ (- (acos a)) a))

simplify2.5s

Counts
223 → 223
Iterations
IterNodes
done5027
33823
21548
1768
0288

prune626.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite108.0ms

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×clear-num frac-2neg add-log-exp
1×associate-/r/ pow-flip inv-pow associate-/l/
Counts
2 → 580
Calls
2 calls:
9.0ms
(/ 1 (- (acos a)))
36.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series59.0ms

Counts
2 → 6
Calls
2 calls:
7.0ms
(/ 1 (- (acos a)))
53.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify2.8s

Counts
586 → 586
Iterations
IterNodes
done5002
24850
12680
0807

prune962.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite296.0ms

Algorithm
rewrite-expression-head
Rules
3206×times-frac
1202×add-sqr-sqrt
1200×*-un-lft-identity add-cube-cbrt
1110×cbrt-prod
315×distribute-lft-neg-in distribute-rgt-neg-in
245×div-inv
105×neg-mul-1
80×associate-/l*
26×add-exp-log
19×pow1
14×associate-/r* add-cbrt-cube
10×div-exp
6×pow-flip
5×cbrt-undiv
4×prod-exp add-log-exp
3×rec-exp 1-exp swap-sqr associate-*r* associate-*l*
2×pow2 cbrt-div clear-num frac-2neg pow-plus pow-prod-down pow-sqr pow-prod-up cbrt-unprod
1×pow1/3 associate-/r/ *-commutative inv-pow unswap-sqr associate-/l/
Counts
4 → 1249
Calls
4 calls:
5.0ms
(* (acos a) (acos a))
9.0ms
(/ 1 (* (acos a) (acos a)))
82.0ms
(/ (cbrt (/ (/ 1 (* (acos a) (acos a))) (- (acos a)))) (/ 1 a))
22.0ms
(cbrt (/ (/ 1 (* (acos a) (acos a))) (- (acos a))))

series214.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (acos a) (acos a))
42.0ms
(/ 1 (* (acos a) (acos a)))
99.0ms
(/ (cbrt (/ (/ 1 (* (acos a) (acos a))) (- (acos a)))) (/ 1 a))
50.0ms
(cbrt (/ (/ 1 (* (acos a) (acos a))) (- (acos a))))

simplify5.1s

Counts
1261 → 1261
Iterations
IterNodes
done5002
14141
01654

prune4.2s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes126.0ms

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

sample804.0ms

Algorithm
intervals
Results
340.0ms8000×body80valid
198.0ms8157×body80nan