Details

Time bar (total: 10.5s)

sample87.0ms

Algorithm
intervals
Results
24.0ms419×body80nan
19.0ms324×body80valid

simplify3.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11410
22110
33610
46210
513310
628610
772710
8332910
done500010

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (sqrt (- (* y y) (* z z))))
1.6b
(- (* y y) (* z z))
23.5b
(sqrt (- (* y y) (* z z)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×sqrt-prod
7×add-cube-cbrt *-un-lft-identity associate-*r*
6×pow1
5×add-exp-log add-cbrt-cube add-log-exp
4×sqrt-div
3×flip3-- associate-*l* flip-- difference-of-squares
2×associate-*r/ unswap-sqr
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
3 → 54
Calls
3 calls:
40.0ms
(* x (sqrt (- (* y y) (* z z))))
12.0ms
(- (* y y) (* z z))
14.0ms
(sqrt (- (* y y) (* z z)))

series219.0ms

Counts
3 → 9
Calls
3 calls:
105.0ms
(* x (sqrt (- (* y y) (* z z))))
51.0ms
(- (* y y) (* z z))
63.0ms
(sqrt (- (* y y) (* z z)))

simplify732.0ms

Counts
63 → 63
Iterations

Useful iterations: done (729.0ms)

IterNodesCost
085765
1211697
2930615
done5001613

prune179.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune6.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(* x (* (sqrt (+ y z)) (sqrt (- y z))))
0.3b
(* (sqrt (+ y z)) (sqrt (- y z)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
24×sqrt-div
17×add-sqr-sqrt
13×sqrt-prod
12×associate-*r/
11×pow1 *-un-lft-identity
10×associate-*l*
9×add-exp-log associate-*r* add-cbrt-cube
8×frac-times
7×add-cube-cbrt
6×flip3-- flip3-+ pow-prod-down flip-- flip-+
4×associate-*l/ prod-exp cbrt-unprod unswap-sqr
2×sqrt-pow1 pow1/2 *-commutative add-log-exp
1×sqrt-unprod distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
2 → 67
Calls
2 calls:
56.0ms
(* x (* (sqrt (+ y z)) (sqrt (- y z))))
48.0ms
(* (sqrt (+ y z)) (sqrt (- y z)))

series251.0ms

Counts
2 → 6
Calls
2 calls:
158.0ms
(* x (* (sqrt (+ y z)) (sqrt (- y z))))
93.0ms
(* (sqrt (+ y z)) (sqrt (- y z)))

simplify778.0ms

Counts
73 → 73
Iterations

Useful iterations: done (775.0ms)

IterNodesCost
01371064
1320973
21277915
done5001905

prune243.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* x (sqrt (+ y z)))
0.2b
(* (* x (sqrt (+ y z))) (sqrt (- y z)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
15×associate-*r*
14×sqrt-div
13×add-sqr-sqrt
11×*-un-lft-identity
10×associate-*r/ sqrt-prod
9×pow1 add-exp-log add-cbrt-cube
7×add-cube-cbrt
4×frac-times flip3-+ associate-*l* pow-prod-down prod-exp cbrt-unprod flip-+
3×flip3-- flip--
2×associate-*l/ *-commutative add-log-exp unswap-sqr
1×distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
2 → 56
Calls
2 calls:
32.0ms
(* x (sqrt (+ y z)))
66.0ms
(* (* x (sqrt (+ y z))) (sqrt (- y z)))

series230.0ms

Counts
2 → 6
Calls
2 calls:
88.0ms
(* x (sqrt (+ y z)))
142.0ms
(* (* x (sqrt (+ y z))) (sqrt (- y z)))

simplify778.0ms

Counts
62 → 62
Iterations

Useful iterations: done (776.0ms)

IterNodesCost
0139870
1355782
21590720
done5000702

prune147.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.1b

regimes776.0ms

Accuracy

97.6% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 24.7b

bsearch178.0ms

Steps
ItersRangePoint
8
-4.487087750964639e-249
-7.152300718152866e-253
-7.287557259675908e-253

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11111
21411
done1411

end0.0ms

sample1.9s

Algorithm
intervals
Results
537.0ms9960×body80nan
451.0ms10033×body80valid