Details

Time bar (total: 38.1s)

sample17.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
3.0ms234×body80nan

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
045
done45

prune2.0ms

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)))

rewrite6.0ms

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:
4.0ms
(/ a (- (acos a)))

series27.0ms

Counts
1 → 3
Calls
1 calls:
27.0ms
(/ a (- (acos a)))

simplify2.0s

Counts
58 → 58
Iterations

Useful iterations: done (2.0s)

IterNodesCost
094601
1164569
2388549
31184545
42583544
done5000542

prune105.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

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:
4.0ms
(/ (- (acos a)) a)
10.0ms
(/ 1 (/ (- (acos a)) a))

series59.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(/ (- (acos a)) a)
27.0ms
(/ 1 (/ (- (acos a)) a))

simplify1.2s

Counts
223 → 223
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02883166
16612616
215172301
done50002236

prune250.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
46×add-exp-log
21×add-sqr-sqrt
18×div-exp
16×prod-exp add-cbrt-cube
15×*-un-lft-identity
14×add-cube-cbrt times-frac
13×associate-*r*
10×associate-*l*
9×rec-exp 1-exp
7×pow1
5×cbrt-undiv
4×cbrt-unprod
3×distribute-lft-neg-in distribute-rgt-neg-in associate-/l* unswap-sqr
2×pow-flip associate-*r/ pow-prod-down associate-/r/ un-div-inv div-inv add-log-exp
1×distribute-lft-neg-out neg-mul-1 frac-2neg clear-num associate-/r* *-commutative inv-pow
Counts
2 → 84
Calls
2 calls:
10.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
12.0ms
(* (- (acos a)) (/ 1 a))

series60.0ms

Counts
2 → 6
Calls
2 calls:
26.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
33.0ms
(* (- (acos a)) (/ 1 a))

simplify2.0s

Counts
90 → 90
Iterations

Useful iterations: 3 (591.0ms)

IterNodesCost
0125932
1348683
2967535
32694529
done5000529

prune112.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ (/ 1 (cbrt (/ (- (acos a)) a))) (cbrt (/ (- (acos a)) a))) (/ 1 (cbrt (/ (- (acos a)) a))))
0.5b
(cbrt (/ (- (acos a)) a))
0.5b
(cbrt (/ (- (acos a)) a))
0.5b
(cbrt (/ (- (acos a)) a))

rewrite7.2s

Algorithm
rewrite-expression-head
Rules
16048×times-frac
8196×cbrt-prod
7070×add-sqr-sqrt
6471×*-un-lft-identity
6339×add-cube-cbrt
4297×associate-*l*
2097×distribute-lft-neg-in distribute-rgt-neg-in
699×neg-mul-1
280×div-inv
161×unswap-sqr
116×associate-*r*
69×add-exp-log
42×cbrt-div
39×associate-/r/
34×div-exp
20×prod-exp
16×add-cbrt-cube
14×pow1
9×cbrt-undiv rec-exp 1-exp
6×pow-flip pow1/3 cbrt-unprod
5×pow-prod-up pow-div
4×inv-pow add-log-exp
1×frac-times associate-*r/ pow3 pow-prod-down associate-*l/ un-div-inv *-commutative
Counts
4 → 4748
Calls
4 calls:
6.4s
(* (/ (/ 1 (cbrt (/ (- (acos a)) a))) (cbrt (/ (- (acos a)) a))) (/ 1 (cbrt (/ (- (acos a)) a))))
3.0ms
(cbrt (/ (- (acos a)) a))
3.0ms
(cbrt (/ (- (acos a)) a))
3.0ms
(cbrt (/ (- (acos a)) a))

series607.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(* (/ (/ 1 (cbrt (/ (- (acos a)) a))) (cbrt (/ (- (acos a)) a))) (/ 1 (cbrt (/ (- (acos a)) a))))
168.0ms
(cbrt (/ (- (acos a)) a))
171.0ms
(cbrt (/ (- (acos a)) a))
177.0ms
(cbrt (/ (- (acos a)) a))

simplify1.5s

Counts
4760 → 4760
Iterations

Useful iterations: 0 (355.0ms)

IterNodesCost
05533127492
done5533127492

prune22.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes100.0ms

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

sample447.0ms

Algorithm
intervals
Results
164.0ms8000×body80valid
109.0ms8035×body80nan