Details

Time bar (total: 12.2s)

sample37.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
7.0ms245×body80nan

simplify1.0ms

Counts
1 → 1
Iterations
IterNodes
done4
04

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

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)))

series51.0ms

Counts
1 → 3
Calls
1 calls:
51.0ms
(/ a (- (acos a)))

simplify1.1s

Counts
60 → 60
Iterations
IterNodes
done5000
32093
2466
1173
096

prune252.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(log1p (expm1 (/ a (- (acos a)))))
0.0b
(expm1 (/ a (- (acos a))))
0.3b
(/ a (- (acos a)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
26×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/r*
5×add-cbrt-cube add-exp-log
4×neg-mul-1 log1p-expm1-u
3×expm1-log1p-u pow1 associate-/l* add-log-exp
1×cbrt-undiv log1p-udef expm1-log1p clear-num frac-2neg div-exp log1p-expm1 div-inv expm1-udef
Counts
3 → 79
Calls
3 calls:
0.0ms
(log1p (expm1 (/ a (- (acos a)))))
1.0ms
(expm1 (/ a (- (acos a))))
9.0ms
(/ a (- (acos a)))

series185.0ms

Counts
3 → 9
Calls
3 calls:
134.0ms
(log1p (expm1 (/ a (- (acos a)))))
22.0ms
(expm1 (/ a (- (acos a))))
29.0ms
(/ a (- (acos a)))

simplify498.0ms

Counts
88 → 88
Iterations
IterNodes
done5000
2910
1253
0131

prune362.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (expm1 (/ 1 (- (/ (acos a) a)))))
0.0b
(expm1 (/ 1 (- (/ (acos a) a))))
0.2b
(/ (acos a) a)
0.3b
(/ 1 (- (/ (acos a) a)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
171×times-frac
103×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
52×distribute-lft-neg-in distribute-rgt-neg-in
33×associate-/r*
10×add-exp-log div-inv
8×add-cbrt-cube
6×associate-/l*
5×pow1 log1p-expm1-u
4×expm1-log1p-u neg-mul-1 add-log-exp
3×div-exp
2×cbrt-undiv clear-num frac-2neg
1×acos-asin rec-exp log1p-udef expm1-log1p 1-exp div-sub log1p-expm1 associate-/r/ pow-flip distribute-neg-frac inv-pow expm1-udef
Counts
4 → 194
Calls
4 calls:
0.0ms
(log1p (expm1 (/ 1 (- (/ (acos a) a)))))
0.0ms
(expm1 (/ 1 (- (/ (acos a) a))))
4.0ms
(/ (acos a) a)
13.0ms
(/ 1 (- (/ (acos a) a)))

series276.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(log1p (expm1 (/ 1 (- (/ (acos a) a)))))
18.0ms
(expm1 (/ 1 (- (/ (acos a) a))))
39.0ms
(/ (acos a) a)
40.0ms
(/ 1 (- (/ (acos a) a)))

simplify1.1s

Counts
206 → 206
Iterations
IterNodes
done5000
22855
1623
0299

prune715.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (expm1 (/ 1 (- (* (acos a) (/ 1 a))))))
0.0b
(expm1 (/ 1 (- (* (acos a) (/ 1 a)))))
0.3b
(/ 1 (- (* (acos a) (/ 1 a))))
0.3b
(* (acos a) (/ 1 a))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
29×times-frac
24×*-un-lft-identity
23×add-cube-cbrt
17×add-exp-log
13×associate-*r*
11×add-cbrt-cube
7×pow1
6×associate-/r*
5×log1p-expm1-u
4×distribute-lft-neg-in expm1-log1p-u neg-mul-1 distribute-rgt-neg-in div-exp prod-exp add-log-exp
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp 1-exp associate-*r/ associate-/r/ un-div-inv cbrt-unprod div-inv distribute-neg-frac
1×log1p-udef expm1-log1p clear-num frac-2neg pow-prod-down log1p-expm1 *-commutative pow-flip inv-pow expm1-udef
Counts
4 → 107
Calls
4 calls:
0.0ms
(log1p (expm1 (/ 1 (- (* (acos a) (/ 1 a))))))
1.0ms
(expm1 (/ 1 (- (* (acos a) (/ 1 a)))))
7.0ms
(/ 1 (- (* (acos a) (/ 1 a))))
12.0ms
(* (acos a) (/ 1 a))

series259.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(log1p (expm1 (/ 1 (- (* (acos a) (/ 1 a))))))
25.0ms
(expm1 (/ 1 (- (* (acos a) (/ 1 a)))))
38.0ms
(/ 1 (- (* (acos a) (/ 1 a))))
43.0ms
(* (acos a) (/ 1 a))

simplify5.6s

Counts
119 → 119
Iterations
IterNodes
done5000
23602
1403
0173

prune486.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes173.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done21
221
116
09

end0.0ms

sample1.0s

Algorithm
intervals
Results
388.0ms8000×body80valid
241.0ms8043×body80nan