Details

Time bar (total: 12.4s)

sample17.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
3.0ms272×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)))

series26.0ms

Counts
1 → 3
Calls
1 calls:
26.0ms
(/ a (- (acos a)))

simplify3.1s

Counts
58 → 58
Iterations

Useful iterations: 5 (1.4s)

IterNodesCost
094601
1164569
2328551
3713551
41237551
52175546
done5001546

prune110.0ms

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
171×times-frac
101×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
52×distribute-lft-neg-in distribute-rgt-neg-in
33×associate-/r*
10×div-inv
8×add-exp-log
6×add-cbrt-cube associate-/l*
4×neg-mul-1
3×pow1 div-exp
2×cbrt-undiv frac-2neg clear-num add-log-exp
1×acos-asin rec-exp pow-flip 1-exp div-sub associate-/r/ distribute-neg-frac inv-pow
Counts
2 → 168
Calls
2 calls:
2.0ms
(/ (acos a) a)
10.0ms
(/ 1 (- (/ (acos a) a)))

series54.0ms

Counts
2 → 6
Calls
2 calls:
26.0ms
(/ (acos a) a)
27.0ms
(/ 1 (- (/ (acos a) a)))

simplify3.4s

Counts
174 → 174
Iterations

Useful iterations: 3 (557.0ms)

IterNodesCost
02612383
14831978
27851835
317081689
434541689
done50011689

prune208.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
930×times-frac
437×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
182×distribute-lft-neg-in distribute-rgt-neg-in
61×div-inv
33×associate-/r*
16×associate-/l*
15×add-exp-log
14×neg-mul-1
9×add-cbrt-cube
8×div-exp
4×cbrt-undiv
3×pow1
2×rec-exp frac-2neg 1-exp clear-num add-log-exp
1×pow-flip associate-/r/ associate-/l/ distribute-neg-frac inv-pow
Counts
2 → 482
Calls
2 calls:
2.0ms
(/ 1 (acos a))
18.0ms
(/ (/ 1 (acos a)) (- (/ 1 a)))

series28.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(/ 1 (acos a))
23.0ms
(/ (/ 1 (acos a)) (- (/ 1 a)))

simplify1.7s

Counts
488 → 488
Iterations

Useful iterations: done (1.7s)

IterNodesCost
070910289
118287575
229986656
done50016638

prune294.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (pow (acos a) 3))
0.4b
(/ (cbrt (/ 1 (pow (acos a) 3))) (- (/ 1 a)))
1.0b
(cbrt (/ 1 (pow (acos a) 3)))
1.0b
(pow (acos a) 3)

rewrite264.0ms

Algorithm
rewrite-expression-head
Rules
3270×times-frac
1427×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
1280×cbrt-prod
572×distribute-lft-neg-in distribute-rgt-neg-in
303×unpow-prod-down cube-prod
122×div-inv
101×cube-mult unpow3 sqr-pow
46×associate-/l*
44×neg-mul-1
42×associate-/r*
16×add-exp-log
8×add-cbrt-cube
7×div-exp
5×pow1
4×pow-to-exp pow-exp add-log-exp
3×rec-exp pow-unpow 1-exp
2×cbrt-undiv cbrt-div frac-2neg clear-num
1×pow-flip pow-pow pow1/3 associate-/r/ associate-/l/ distribute-neg-frac inv-pow rem-cube-cbrt
Counts
4 → 1522
Calls
4 calls:
4.0ms
(/ 1 (pow (acos a) 3))
46.0ms
(/ (cbrt (/ 1 (pow (acos a) 3))) (- (/ 1 a)))
4.0ms
(cbrt (/ 1 (pow (acos a) 3)))
1.0ms
(pow (acos a) 3)

series95.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ 1 (pow (acos a) 3))
22.0ms
(/ (cbrt (/ 1 (pow (acos a) 3))) (- (/ 1 a)))
5.0ms
(cbrt (/ 1 (pow (acos a) 3)))
34.0ms
(pow (acos a) 3)

simplify1.7s

Counts
1534 → 1534
Iterations

Useful iterations: 2 (1.3s)

IterNodesCost
0170941962
1272329233
2396628486
done500128486

prune794.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

end0.0ms

sample437.0ms

Algorithm
intervals
Results
163.0ms8000×body80valid
104.0ms8067×body80nan