Details

Time bar (total: 3.5s)

sample18.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
3.0ms241×body80nan

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
043
143
done43

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite18.0ms

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:
14.0ms
(/ a (- (acos a)))

series27.0ms

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

simplify93.0ms

Counts
60 → 60
Iterations

Useful iterations: 3 (35.0ms)

IterNodesCost
0166384
1493372
21442367
33704366
45002366
done5002366

prune154.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite37.0ms

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:
18.0ms
(/ 1 (/ (- (acos a)) a))
8.0ms
(/ (- (acos a)) a)

series64.0ms

Counts
2 → 6
Calls
2 calls:
30.0ms
(/ 1 (/ (- (acos a)) a))
34.0ms
(/ (- (acos a)) a)

simplify69.0ms

Counts
227 → 227
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
06631934
130641717
250011525
done50011525

prune308.0ms

Pruning

13 alts after pruning (11 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))

rewrite91.0ms

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:
7.0ms
(/ 1 (- (acos a)))
32.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series33.0ms

Counts
2 → 6
Calls
2 calls:
7.0ms
(/ 1 (- (acos a)))
26.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify109.0ms

Counts
590 → 590
Iterations

Useful iterations: 1 (49.0ms)

IterNodesCost
025217412
150026293
done50026293

prune697.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

localize10.0ms

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

rewrite258.0ms

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:
8.0ms
(/ 1 (- (acos a)))
74.0ms
(/ (cbrt (pow (/ 1 (- (acos a))) 3)) (/ 1 a))
13.0ms
(cbrt (pow (/ 1 (- (acos a))) 3))
13.0ms
(pow (/ 1 (- (acos a))) 3)

series153.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(/ 1 (- (acos a)))
71.0ms
(/ (cbrt (pow (/ 1 (- (acos a))) 3)) (/ 1 a))
38.0ms
(cbrt (pow (/ 1 (- (acos a))) 3))
37.0ms
(pow (/ 1 (- (acos a))) 3)

simplify201.0ms

Counts
1364 → 1364
Iterations

Useful iterations: 1 (42.0ms)

IterNodesCost
0246615220
1500112601
done500112601

prune562.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes49.0ms

Accuracy

0% (0.3b 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
043
143
done43

end0.0ms

sample484.0ms

Algorithm
intervals
Results
159.0ms8000×body80valid
105.0ms7894×body80nan