Details

Time bar (total: 14.5s)

sample36.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
7.0ms247×body80nan

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite21.0ms

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 expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 57
Calls
1 calls:
17.0ms
(/ a (- (acos a)))

series70.0ms

Counts
1 → 3
Calls
1 calls:
69.0ms
(/ a (- (acos a)))

simplify1.4s

Counts
60 → 60
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
096613
1173581
2463563
32074563
done5000563

prune266.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite77.0ms

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×expm1-log1p-u rec-exp frac-2neg 1-exp clear-num log1p-expm1-u add-log-exp
1×neg-sub0 pow-flip div-sub distribute-frac-neg associate-/r/ inv-pow
Counts
2 → 221
Calls
2 calls:
34.0ms
(/ 1 (/ (- (acos a)) a))
19.0ms
(/ (- (acos a)) a)

series81.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(/ 1 (/ (- (acos a)) a))
54.0ms
(/ (- (acos a)) a)

simplify2.5s

Counts
227 → 227
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
02923194
17902650
239032578
done50002578

prune614.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite147.0ms

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×expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
1×pow-flip associate-/r/ associate-/l/ inv-pow
Counts
2 → 584
Calls
2 calls:
17.0ms
(/ 1 (- (acos a)))
54.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series51.0ms

Counts
2 → 6
Calls
2 calls:
8.0ms
(/ 1 (- (acos a)))
43.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify2.8s

Counts
590 → 590
Iterations

Useful iterations: done (2.8s)

IterNodesCost
081112543
129509132
done50018296

prune761.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite453.0ms

Algorithm
rewrite-expression-head
Rules
2693×times-frac
1243×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
1110×cbrt-prod
544×unpow-prod-down cube-prod
300×distribute-lft-neg-in distribute-rgt-neg-in
112×div-inv
100×neg-mul-1
80×associate-/l*
23×associate-/r*
22×add-exp-log
16×cube-mult unpow3 sqr-pow
12×add-cbrt-cube
10×div-exp
7×pow1
5×cbrt-undiv
4×expm1-log1p-u pow-exp log1p-expm1-u add-log-exp
3×cube-div rec-exp pow-unpow pow-pow 1-exp
2×cbrt-div pow-flip frac-2neg clear-num inv-pow rem-cube-cbrt
1×pow-to-exp pow1/3 associate-/r/ rem-cbrt-cube associate-/l/
Counts
4 → 1352
Calls
4 calls:
16.0ms
(/ 1 (- (acos a)))
160.0ms
(/ (cbrt (pow (/ 1 (- (acos a))) 3)) (/ 1 a))
26.0ms
(pow (/ 1 (- (acos a))) 3)
33.0ms
(cbrt (pow (/ 1 (- (acos a))) 3))

series253.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(/ 1 (- (acos a)))
104.0ms
(/ (cbrt (pow (/ 1 (- (acos a))) 3)) (/ 1 a))
54.0ms
(pow (/ 1 (- (acos a))) 3)
86.0ms
(cbrt (pow (/ 1 (- (acos a))) 3))

simplify2.4s

Counts
1364 → 1364
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0110335839
1319822635
done500219579

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes113.0ms

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

sample1.1s

Algorithm
intervals
Results
393.0ms8000×body80valid
210.0ms7890×body80nan