Details

Time bar (total: 14.5s)

sample41.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
7.0ms281×body80nan

simplify2.0ms

Counts
1 → 1
Iterations
IterNodes
done4
04

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
24×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/r*
4×neg-mul-1
3×add-cbrt-cube add-exp-log associate-/l*
1×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp log1p-expm1-u div-inv add-log-exp
Counts
1 → 57
Calls
1 calls:
6.0ms
(/ a (- (acos a)))

series40.0ms

Counts
1 → 3
Calls
1 calls:
40.0ms
(/ a (- (acos a)))

simplify1.5s

Counts
60 → 60
Iterations
IterNodes
done5003
31263
2437
1173
096

prune332.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
140×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
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 clear-num frac-2neg 1-exp log1p-expm1-u add-log-exp
1×neg-sub0 div-sub distribute-frac-neg associate-/r/ pow-flip inv-pow
Counts
2 → 221
Calls
2 calls:
14.0ms
(/ (- (acos a)) a)
28.0ms
(/ 1 (/ (- (acos a)) a))

series109.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(/ (- (acos a)) a)
60.0ms
(/ 1 (/ (- (acos a)) a))

simplify2.9s

Counts
227 → 227
Iterations
IterNodes
done5001
33681
21516
1776
0292

prune852.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
1177×times-frac
526×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
126×distribute-lft-neg-in distribute-rgt-neg-in
50×div-inv
42×neg-mul-1
41×add-exp-log
34×associate-/l*
32×div-exp
13×associate-/r* add-cbrt-cube
8×cbrt-undiv rec-exp 1-exp
1×expm1-log1p-u pow1 clear-num frac-2neg associate-/r/ log1p-expm1-u add-log-exp associate-/l/
Counts
1 → 523
Calls
1 calls:
49.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series50.0ms

Counts
1 → 3
Calls
1 calls:
50.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify3.5s

Counts
526 → 526
Iterations
IterNodes
done5003
24553
12625
0803

prune858.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt (acos a))
1.0b
(sqrt (acos a))
1.0b
(/ 1 (- (sqrt (acos a))))
1.0b
(/ 1 (sqrt (acos a)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
60×add-sqr-sqrt
58×*-un-lft-identity add-cube-cbrt
42×sqrt-prod
24×distribute-lft-neg-in distribute-rgt-neg-in
22×associate-/r*
12×add-exp-log
9×pow1
8×add-cbrt-cube
6×associate-/l*
4×expm1-log1p-u neg-mul-1 div-exp log1p-expm1-u pow-flip add-log-exp
3×sqrt-pow1 pow1/2
2×cbrt-undiv rem-sqrt-square rec-exp clear-num frac-2neg 1-exp div-inv inv-pow
Counts
4 → 162
Calls
4 calls:
1.0ms
(sqrt (acos a))
1.0ms
(sqrt (acos a))
10.0ms
(/ 1 (- (sqrt (acos a))))
11.0ms
(/ 1 (sqrt (acos a)))

series100.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(sqrt (acos a))
13.0ms
(sqrt (acos a))
48.0ms
(/ 1 (- (sqrt (acos a))))
26.0ms
(/ 1 (sqrt (acos a)))

simplify2.4s

Counts
174 → 174
Iterations
IterNodes
done5001
61618
5996
4789
3585
2423
1235
0143

prune522.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes125.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
done4
04

end0.0ms

sample870.0ms

Algorithm
intervals
Results
347.0ms8000×body80valid
239.0ms7989×body80nan