Details

Time bar (total: 13.3s)

sample71.0ms

Algorithm
intervals
Results
19.0ms419×body80nan
15.0ms324×body80valid

simplify4.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11510
22210
33910
47110
516410
636910
790810
8375310
done500010

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.0b

localize10.0ms

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)))

rewrite92.0ms

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×expm1-log1p-u flip3-- associate-*l* flip-- log1p-expm1-u difference-of-squares
2×associate-*r/ unswap-sqr
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
3 → 62
Calls
3 calls:
64.0ms
(* x (sqrt (- (* y y) (* z z))))
12.0ms
(- (* y y) (* z z))
12.0ms
(sqrt (- (* y y) (* z z)))

series268.0ms

Counts
3 → 9
Calls
3 calls:
135.0ms
(* x (sqrt (- (* y y) (* z z))))
64.0ms
(- (* y y) (* z z))
69.0ms
(sqrt (- (* y y) (* z z)))

simplify860.0ms

Counts
71 → 71
Iterations

Useful iterations: done (857.0ms)

IterNodesCost
094839
1222763
2948678
done5000676

prune313.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune13.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize25.0ms

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)))

rewrite144.0ms

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×expm1-log1p-u sqrt-pow1 pow1/2 *-commutative log1p-expm1-u add-log-exp
1×sqrt-unprod distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
2 → 71
Calls
2 calls:
75.0ms
(* x (* (sqrt (+ y z)) (sqrt (- y z))))
63.0ms
(* (sqrt (+ y z)) (sqrt (- y z)))

series274.0ms

Counts
2 → 6
Calls
2 calls:
174.0ms
(* x (* (sqrt (+ y z)) (sqrt (- y z))))
100.0ms
(* (sqrt (+ y z)) (sqrt (- y z)))

simplify1.3s

Counts
77 → 77
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01411108
13341013
21314949
done5000939

prune322.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 2 expressions with local error:

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

rewrite124.0ms

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×expm1-log1p-u associate-*l/ *-commutative log1p-expm1-u add-log-exp unswap-sqr
1×distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
2 → 60
Calls
2 calls:
25.0ms
(* x (sqrt (+ y z)))
97.0ms
(* (* x (sqrt (+ y z))) (sqrt (- y z)))

series340.0ms

Counts
2 → 6
Calls
2 calls:
126.0ms
(* x (sqrt (+ y z)))
214.0ms
(* (* x (sqrt (+ y z))) (sqrt (- y z)))

simplify1.3s

Counts
66 → 66
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0143908
1370816
21613754
done5000732

prune255.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.1b

regimes488.0ms

Accuracy

97.6% (0.6b remaining)

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

bsearch162.0ms

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

sample2.4s

Algorithm
intervals
Results
651.0ms10033×body80valid
568.0ms9960×body80nan