Details

Time bar (total: 19.1s)

sample172.0ms

Algorithm
intervals
Results
52.0ms38×body640valid
51.0ms50×body1280valid
30.0ms142×body80valid
8.0ms17×body320valid
3.0msbody160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
11111
done1111

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize21.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (sqrt (+ (* x x) (* z z))) (tan p))
30.2b
(sqrt (+ (* x x) (* z z)))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
sqrt-prod
*-un-lft-identity sqrt-div associate-*l* add-cube-cbrt
pow1
add-cbrt-cube add-exp-log
flip3-+ associate-*r* tan-quot flip-+
frac-times associate-*l/ add-log-exp unswap-sqr
rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
2 → 42
Calls
2 calls:
94.0ms
(* (sqrt (+ (* x x) (* z z))) (tan p))
17.0ms
(sqrt (+ (* x x) (* z z)))

series373.0ms

Counts
2 → 6
Calls
2 calls:
299.0ms
(* (sqrt (+ (* x x) (* z z))) (tan p))
74.0ms
(sqrt (+ (* x x) (* z z)))

simplify5.4s

Counts
48 → 48
Iterations

Useful iterations: 3 (799.0ms)

IterNodesCost
076688
1174643
2518577
33021559
done5001559

prune763.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.6b

localize34.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (sin p) (sqrt (+ (* x x) (* z z))))
0.2b
(/ (* (sin p) (sqrt (+ (* x x) (* z z)))) (cos p))
30.2b
(sqrt (+ (* x x) (* z z)))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×add-cbrt-cube add-exp-log
*-un-lft-identity add-cube-cbrt
sqrt-prod
pow1 sqrt-div associate-*r*
associate-*r/
associate-/r* flip3-+ times-frac associate-*l* flip-+ add-log-exp
cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr associate-/l/
rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down *-commutative div-inv associate-/l*
Counts
3 → 62
Calls
3 calls:
107.0ms
(* (sin p) (sqrt (+ (* x x) (* z z))))
67.0ms
(/ (* (sin p) (sqrt (+ (* x x) (* z z)))) (cos p))
17.0ms
(sqrt (+ (* x x) (* z z)))

series993.0ms

Counts
3 → 9
Calls
3 calls:
293.0ms
(* (sin p) (sqrt (+ (* x x) (* z z))))
522.0ms
(/ (* (sin p) (sqrt (+ (* x x) (* z z)))) (cos p))
178.0ms
(sqrt (+ (* x x) (* z z)))

simplify1.7s

Counts
71 → 71
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01061074
1252979
21069873
done5000865

prune442.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

regimes1.6s

Accuracy

58.7% (9.5b remaining)

Error of 16.8b against oracle of 7.3b and baseline of 30.3b

bsearch570.0ms

Steps
ItersRangePoint
10
6.901660072962573e+82
5.41439995524433e+96
6.007290885134199e+89
9
1.1033515222944426e-137
9.766628192739036e-129
4.105107772534907e-137
9
2.605861693651396e-197
2.6083185712883704e-192
7.787518790332474e-195
6
-5.01434520362583e+93
-1.015701924495698e+93
-4.353106847248221e+93

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02857
13457
23757
done3757

end0.0ms

sample6.7s

Algorithm
intervals
Results
2.5s1503×body1280valid
1.4s1264×body640valid
1.2s4290×body80valid
537.0ms597×body320valid
204.0ms350×body160valid