Details

Time bar (total: 12.1s)

sample18.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01114
11514
22214
32414
done2414

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
33.9b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×times-frac
17×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
4×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
2×rem-sqrt-square div-inv associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg sqrt-pow1 flip3-+ pow1/2 sqrt-div div-exp clear-num flip-+
Counts
2 → 54
Calls
2 calls:
75.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
30.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series228.0ms

Counts
2 → 6
Calls
2 calls:
55.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
173.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.0s

Counts
60 → 60
Iterations

Useful iterations: 3 (391.0ms)

IterNodesCost
01071270
12131209
26241110
322441102
done50001102

prune169.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
33.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.9b
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

rewrite237.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
24×sqrt-prod
22×times-frac associate-*r*
21×add-cube-cbrt *-un-lft-identity
17×sqrt-div
11×pow1
9×add-exp-log add-cbrt-cube
6×flip3-+ associate-*l* flip-+ unswap-sqr
4×frac-times sqrt-pow1 associate-*l/ add-log-exp
3×pow1/2
2×rem-sqrt-square associate-*r/ pow-prod-down prod-exp cbrt-unprod
1×cbrt-undiv div-exp *-commutative div-inv
Counts
4 → 98
Calls
4 calls:
135.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
29.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
31.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
39.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
104.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
104.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
168.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

simplify2.0s

Counts
110 → 110
Iterations

Useful iterations: 3 (924.0ms)

IterNodesCost
01423195
13252567
210342267
339792139
done50012139

prune292.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 15.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
33.9b
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×associate-*r*
11×add-exp-log *-un-lft-identity times-frac
10×add-cube-cbrt
7×pow1 add-cbrt-cube
6×sqrt-div
4×frac-times flip3-+ associate-*l/ prod-exp flip-+
3×associate-*l* unswap-sqr
2×sqrt-pow1 associate-*r/ div-exp pow-prod-down un-div-inv cbrt-unprod add-log-exp
1×cbrt-undiv rec-exp pow1/2 1-exp sqrt-prod *-commutative div-inv
Counts
2 → 57
Calls
2 calls:
86.0ms
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
27.0ms
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

series226.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
172.0ms
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

simplify2.4s

Counts
63 → 63
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
01281346
13081182
210611042
347801018
done50001018

prune164.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 15.6b

localize16.0ms

Local error

Found 4 expressions with local error:

33.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.9b
(sqrt (* (* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))) (* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))))

rewrite405.0ms

Algorithm
rewrite-expression-head
Rules
173×sqrt-div
63×pow1
49×frac-times
43×sqrt-pow1
35×pow-prod-down
29×associate-*l/
27×flip3-+ flip-+
20×pow1/2
17×associate-*r/
10×add-sqr-sqrt sqrt-prod
8×pow-prod-up
7×add-cube-cbrt *-un-lft-identity
6×pow-sqr
4×add-exp-log rem-sqrt-square add-cbrt-cube add-log-exp
2×pow-plus
1×pow2
Counts
4 → 114
Calls
4 calls:
29.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
30.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
30.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
306.0ms
(sqrt (* (* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))) (* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))))

series495.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
107.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
105.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
176.0ms
(sqrt (* (* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))) (* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))))

simplify2.4s

Counts
126 → 126
Iterations

Useful iterations: 3 (377.0ms)

IterNodesCost
02135483
14304294
27793755
316283369
445973369
done50003369

prune363.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 15.6b

regimes373.0ms

Accuracy

63.3% (7.2b remaining)

Error of 25.1b against oracle of 18.0b and baseline of 37.5b

bsearch73.0ms

Steps
ItersRangePoint
8
5.2211603344189125e+47
1.338752107099957e+51
1.3221493030139048e+51
10
-1.1996080839781489e+124
-1.8713537616617044e+109
-3.655717002048407e+123

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02345
13145
23345
done3345

end0.0ms

sample476.0ms

Algorithm
intervals
Results
254.0ms8000×body80valid