Details

Time bar (total: 13.2s)

sample23.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
4.0ms262×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

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

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:
5.0ms
(/ a (- (acos a)))

series31.0ms

Counts
1 → 3
Calls
1 calls:
31.0ms
(/ a (- (acos a)))

simplify1.5s

Counts
58 → 58
Iterations
IterNodes
done5001
32040
2462
1171
094

prune292.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- (acos a)) a)
0.3b
(/ 1 (/ (- (acos a)) a))

rewrite49.0ms

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:
11.0ms
(/ (- (acos a)) a)
22.0ms
(/ 1 (/ (- (acos a)) a))

series100.0ms

Counts
2 → 6
Calls
2 calls:
66.0ms
(/ (- (acos a)) a)
34.0ms
(/ 1 (/ (- (acos a)) a))

simplify1.7s

Counts
223 → 223
Iterations
IterNodes
done5000
23876
1785
0288

prune763.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite96.0ms

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:
8.0ms
(/ 1 (- (acos a)))
36.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series51.0ms

Counts
2 → 6
Calls
2 calls:
12.0ms
(/ 1 (- (acos a)))
39.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify2.3s

Counts
586 → 586
Iterations
IterNodes
done5001
12939
0807

prune1.0s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize39.0ms

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

rewrite144.0ms

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
25×pow1 associate-/l*
20×add-exp-log
14×add-cbrt-cube
13×associate-/r*
6×div-exp associate-*l* pow-prod-up
4×associate-*r* pow-prod-down prod-exp cbrt-unprod add-log-exp
3×cbrt-undiv swap-sqr
2×pow2 cbrt-div pow-plus pow-sqr *-commutative unswap-sqr
1×rec-exp clear-num frac-2neg pow1/3 1-exp cube-unmult associate-/r/ associate-/l/
Counts
4 → 461
Calls
4 calls:
11.0ms
(* (acos a) (acos a))
52.0ms
(/ (cbrt (/ 1 (- (* (acos a) (* (acos a) (acos a)))))) (/ 1 a))
16.0ms
(cbrt (/ 1 (- (* (acos a) (* (acos a) (acos a))))))
26.0ms
(* (acos a) (* (acos a) (acos a)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (acos a) (acos a))
116.0ms
(/ (cbrt (/ 1 (- (* (acos a) (* (acos a) (acos a)))))) (/ 1 a))
50.0ms
(cbrt (/ 1 (- (* (acos a) (* (acos a) (acos a))))))
41.0ms
(* (acos a) (* (acos a) (acos a)))

simplify1.6s

Counts
473 → 473
Iterations
IterNodes
done5000
11818
0726

prune1.9s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes144.0ms

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

sample1.1s

Algorithm
intervals
Results
402.0ms8000×body80valid
280.0ms8212×body80nan