Details

Time bar (total: 10.4s)

sample38.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
8.0ms250×body80nan

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite17.0ms

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:
13.0ms
(/ a (- (acos a)))

series46.0ms

Counts
1 → 3
Calls
1 calls:
46.0ms
(/ a (- (acos a)))

simplify1.5s

Counts
58 → 58
Iterations

Useful iterations: 3 (381.0ms)

IterNodesCost
094601
1171569
2459553
31923551
done5000551

prune143.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite45.0ms

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
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 frac-2neg 1-exp clear-num add-log-exp
1×neg-sub0 pow-flip div-sub distribute-frac-neg associate-/r/ inv-pow
Counts
2 → 217
Calls
2 calls:
8.0ms
(/ (- (acos a)) a)
26.0ms
(/ 1 (/ (- (acos a)) a))

series96.0ms

Counts
2 → 6
Calls
2 calls:
45.0ms
(/ (- (acos a)) a)
51.0ms
(/ 1 (/ (- (acos a)) a))

simplify2.0s

Counts
223 → 223
Iterations

Useful iterations: 2 (811.0ms)

IterNodesCost
02883166
17852618
239032550
done50012550

prune461.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
1207×times-frac
550×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
138×distribute-lft-neg-in distribute-rgt-neg-in
51×div-inv
46×add-exp-log neg-mul-1
37×associate-/l*
34×div-exp
23×associate-/r*
16×add-cbrt-cube
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 → 580
Calls
2 calls:
14.0ms
(/ 1 (- (acos a)))
54.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series35.0ms

Counts
2 → 6
Calls
2 calls:
7.0ms
(/ 1 (- (acos a)))
28.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify2.5s

Counts
586 → 586
Iterations

Useful iterations: done (2.4s)

IterNodesCost
080712511
129399204
done50008268

prune387.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
69×times-frac
46×add-exp-log
43×add-sqr-sqrt
37×*-un-lft-identity
36×add-cube-cbrt
28×add-cbrt-cube
22×associate-/l*
21×div-exp
18×sqrt-prod
13×associate-*l*
12×cbrt-undiv prod-exp
6×cbrt-unprod
4×pow1 div-inv
3×rec-exp 1-exp associate-*r* unswap-sqr
2×associate-*l/ add-log-exp
1×frac-2neg pow-prod-down clear-num associate-/r* associate-/r/ *-commutative associate-/l/
Counts
2 → 108
Calls
2 calls:
23.0ms
(/ (/ (sqrt 1) -1) (* (/ 1 a) (acos a)))
17.0ms
(* (/ 1 a) (acos a))

series71.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(/ (/ (sqrt 1) -1) (* (/ 1 a) (acos a)))
37.0ms
(* (/ 1 a) (acos a))

simplify1.6s

Counts
114 → 114
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02011561
15871142
23328797
done5000785

prune191.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0b

regimes56.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

end0.0ms

sample964.0ms

Algorithm
intervals
Results
353.0ms8000×body80valid
249.0ms7919×body80nan