Details

Time bar (total: 21.2s)

sample44.0ms

Algorithm
intervals
Results
16.0ms262×body80nan
13.0ms256×body80valid

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 expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 57
Calls
1 calls:
8.0ms
(/ a (- (acos a)))

series29.0ms

Counts
1 → 3
Calls
1 calls:
28.0ms
(/ a (- (acos a)))

simplify4.7s

Counts
60 → 60
Iterations

Useful iterations: 5 (1.9s)

IterNodesCost
096613
1166581
2333563
3587563
41105563
52150558
done5001558

prune184.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite56.0ms

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 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
1×acos-asin rec-exp pow-flip 1-exp div-sub associate-/r/ distribute-neg-frac inv-pow
Counts
2 → 172
Calls
2 calls:
27.0ms
(/ 1 (- (/ (acos a) a)))
11.0ms
(/ (acos a) a)

series104.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(/ 1 (- (/ (acos a) a)))
51.0ms
(/ (acos a) a)

simplify6.6s

Counts
178 → 178
Iterations

Useful iterations: 3 (736.0ms)

IterNodesCost
02652409
14722004
27821861
315341711
427841711
done50001711

prune385.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite150.0ms

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:
16.0ms
(/ 1 (- (acos a)))
70.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series62.0ms

Counts
2 → 6
Calls
2 calls:
7.0ms
(/ 1 (- (acos a)))
55.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify2.7s

Counts
590 → 590
Iterations

Useful iterations: done (2.7s)

IterNodesCost
081112543
123508820
232627448
done50007226

prune521.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize32.0ms

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)

rewrite861.0ms

Algorithm
rewrite-expression-head
Rules
3127×times-frac
1402×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
1230×cbrt-prod
500×unpow-prod-down cube-prod
300×distribute-lft-neg-in distribute-rgt-neg-in
103×div-inv
100×neg-mul-1
88×associate-/l*
50×cube-mult unpow3 sqr-pow
39×associate-/r*
23×add-exp-log
12×div-exp
10×add-cbrt-cube
5×pow1
4×cbrt-undiv expm1-log1p-u pow-to-exp rec-exp 1-exp pow-exp log1p-expm1-u add-log-exp
3×pow-unpow
2×cbrt-div frac-2neg clear-num
1×pow-flip pow-pow pow1/3 cube-neg associate-/r/ associate-/l/ inv-pow rem-cube-cbrt
Counts
4 → 1487
Calls
4 calls:
33.0ms
(/ 1 (pow (- (acos a)) 3))
114.0ms
(/ (cbrt (/ 1 (pow (- (acos a)) 3))) (/ 1 a))
18.0ms
(cbrt (/ 1 (pow (- (acos a)) 3)))
8.0ms
(pow (- (acos a)) 3)

series340.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(/ 1 (pow (- (acos a)) 3))
113.0ms
(/ (cbrt (/ 1 (pow (- (acos a)) 3))) (/ 1 a))
41.0ms
(cbrt (/ 1 (pow (- (acos a)) 3)))
126.0ms
(pow (- (acos a)) 3)

simplify2.4s

Counts
1499 → 1499
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0135939916
1237926154
2356925164
done500025160

prune1.1s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes48.0ms

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

sample877.0ms

Algorithm
intervals
Results
327.0ms8000×body80valid
264.0ms7984×body80nan