Details

Time bar (total: 11.1s)

sample23.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
5.0ms230×body80nan

simplify1.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

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

series33.0ms

Counts
1 → 3
Calls
1 calls:
33.0ms
(/ a (- (acos a)))

simplify1.2s

Counts
58 → 58
Iterations

Useful iterations: 3 (232.0ms)

IterNodesCost
094601
1171569
2459553
31923551
done5000551

prune157.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite60.0ms

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:
24.0ms
(/ 1 (/ (- (acos a)) a))
17.0ms
(/ (- (acos a)) a)

series78.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(/ 1 (/ (- (acos a)) a))
43.0ms
(/ (- (acos a)) a)

simplify1.9s

Counts
223 → 223
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02883166
17852622
243592554
done50002550

prune416.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

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:
13.0ms
(/ 1 (- (acos a)))
61.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series49.0ms

Counts
2 → 6
Calls
2 calls:
9.0ms
(/ 1 (- (acos a)))
40.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify2.6s

Counts
586 → 586
Iterations

Useful iterations: done (2.6s)

IterNodesCost
080712511
129399204
done50008268

prune387.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize22.0ms

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))

rewrite351.0ms

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×pow-exp 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 → 1344
Calls
4 calls:
15.0ms
(/ 1 (- (acos a)))
117.0ms
(/ (cbrt (pow (/ 1 (- (acos a))) 3)) (/ 1 a))
13.0ms
(pow (/ 1 (- (acos a))) 3)
22.0ms
(cbrt (pow (/ 1 (- (acos a))) 3))

series192.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(/ 1 (- (acos a)))
81.0ms
(/ (cbrt (pow (/ 1 (- (acos a))) 3)) (/ 1 a))
49.0ms
(pow (/ 1 (- (acos a))) 3)
53.0ms
(cbrt (pow (/ 1 (- (acos a))) 3))

simplify1.9s

Counts
1356 → 1356
Iterations

Useful iterations: done (1.9s)

IterNodesCost
0109535767
1318922591
done500119523

prune767.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes23.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
199
done99

end0.0ms

sample812.0ms

Algorithm
intervals
Results
303.0ms8000×body80valid
182.0ms8027×body80nan