Details

Time bar (total: 16.7s)

sample38.0ms

Algorithm
intervals
Results
18.0ms256×body80valid

simplify26.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01114
11514
22214
32414
done2414

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.3b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
32.6b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1
3×associate-/r* associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num sum-log
Counts
3 → 65
Calls
3 calls:
17.0ms
(+ (* x x) (* y y))
137.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
59.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series336.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(+ (* x x) (* y y))
87.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
199.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.1s

Counts
74 → 74
Iterations

Useful iterations: 3 (950.0ms)

IterNodesCost
01281436
12911370
28551241
327631233
done50011233

prune389.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.7b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.4b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
32.7b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite226.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×sqrt-prod
16×*-un-lft-identity associate-*r*
14×add-cube-cbrt
13×times-frac
9×sqrt-div
8×pow1 unswap-sqr
6×associate-*l*
5×add-exp-log add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×sqrt-pow1 pow1/2 pow-prod-down
2×frac-times associate-*l/
1×+-commutative rem-sqrt-square sqrt-unprod associate-*r/ prod-exp sum-log *-commutative cbrt-unprod div-inv
Counts
3 → 75
Calls
3 calls:
11.0ms
(+ (* x x) (* y y))
154.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
55.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series436.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(+ (* x x) (* y y))
246.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
150.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.1s

Counts
84 → 84
Iterations

Useful iterations: 3 (738.0ms)

IterNodesCost
01401688
13151536
27941451
322391429
done50001429

prune349.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.7b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
32.7b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
33×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 sqrt-div
3×flip3-+ flip-+
2×associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 89
Calls
3 calls:
8.0ms
(+ (* x x) (* y y))
75.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
70.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series494.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(+ (* x x) (* y y))
297.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
151.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.6s

Counts
98 → 98
Iterations

Useful iterations: 3 (571.0ms)

IterNodesCost
01412253
12922035
27271965
317921945
done50001945

prune319.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 16.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
0.4b
(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
1.0b
(/ 1 (sqrt 3.0))
32.5b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

rewrite366.0ms

Algorithm
rewrite-expression-head
Rules
170×sqrt-prod
148×add-sqr-sqrt
120×times-frac
83×*-un-lft-identity
75×add-cube-cbrt
25×associate-*r* associate-*l*
24×unswap-sqr
12×add-exp-log associate-/r*
11×pow1
10×add-cbrt-cube
6×associate-/l*
5×sqrt-div div-inv
4×sqrt-pow1 pow1/2 add-log-exp
3×rem-sqrt-square pow-flip div-exp pow-prod-down
2×cbrt-undiv frac-2neg clear-num associate-/l/
1×frac-times rec-exp flip3-+ sqrt-unprod 1-exp associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod flip-+ inv-pow
Counts
4 → 212
Calls
4 calls:
167.0ms
(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
102.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
14.0ms
(/ 1 (sqrt 3.0))
71.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

series978.0ms

Counts
4 → 10
Calls
4 calls:
320.0ms
(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
156.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
0.0ms
(/ 1 (sqrt 3.0))
502.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

simplify3.7s

Counts
222 → 222
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
02465163
14484821
212204610
347594588
done50004588

prune781.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 16.6b

regimes589.0ms

Accuracy

61.6% (7.4b remaining)

Error of 25.7b against oracle of 18.3b and baseline of 37.5b

bsearch66.0ms

Steps
ItersRangePoint
8
8.450123646982779e+130
1.3503261361162568e+135
9.739776979507706e+134
5
-2.294626366488831e+97
-1.033466382081211e+97
-1.472200864118953e+97

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02634
13434
done3434

end0.0ms

sample1.3s

Algorithm
intervals
Results
985.0ms8000×body80valid