Details

Time bar (total: 12.8s)

sample35.0ms

Algorithm
intervals
Results
18.0ms256×body80valid

simplify23.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01114
11613
22612
33312
done3312

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (fma z z (fma x x (* y y))) 3.0)
35.5b
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

rewrite14.0ms

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×expm1-log1p-u rem-sqrt-square log1p-expm1-u div-inv add-log-exp
1×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
2 → 56
Calls
2 calls:
6.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
4.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

series402.0ms

Counts
2 → 6
Calls
2 calls:
95.0ms
(/ (fma z z (fma x x (* y y))) 3.0)
306.0ms
(sqrt (/ (fma z z (fma x x (* y y))) 3.0))

simplify1.6s

Counts
62 → 62
Iterations

Useful iterations: 3 (394.0ms)

IterNodesCost
01011118
11681062
2454977
32048974
done5002974

prune401.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.2b

localize17.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
35.7b
(sqrt (fma z z (fma x x (* y y))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
29×sqrt-prod
16×associate-*r*
15×*-un-lft-identity
13×add-cube-cbrt times-frac
8×unswap-sqr
7×pow1
6×associate-*l*
4×add-exp-log add-cbrt-cube
3×sqrt-pow1 pow1/2 pow-prod-down
2×expm1-log1p-u log1p-expm1-u add-log-exp
1×rem-sqrt-square sqrt-unprod sqrt-div associate-*r/ prod-exp *-commutative cbrt-unprod div-inv
Counts
2 → 62
Calls
2 calls:
35.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
2.0ms
(sqrt (fma z z (fma x x (* y y))))

series437.0ms

Counts
2 → 6
Calls
2 calls:
233.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
204.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify3.5s

Counts
68 → 68
Iterations

Useful iterations: 3 (822.0ms)

IterNodesCost
0991192
11761089
25191032
334711030
done50011030

prune446.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 19.2b

localize26.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (sqrt (fma z z (fma y y (* x x)))) (sqrt 3.0))
35.7b
(sqrt (fma z z (fma y y (* x x))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
32×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube
3×pow1
2×expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
2 → 78
Calls
2 calls:
11.0ms
(/ (sqrt (fma z z (fma y y (* x x)))) (sqrt 3.0))
4.0ms
(sqrt (fma z z (fma y y (* x x))))

series521.0ms

Counts
2 → 6
Calls
2 calls:
349.0ms
(/ (sqrt (fma z z (fma y y (* x x)))) (sqrt 3.0))
171.0ms
(sqrt (fma z z (fma y y (* x x))))

simplify1.7s

Counts
84 → 84
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01041761
11611588
24641546
320791546
done50011544

prune425.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.4b

localize16.0ms

Local error

Found 1 expressions with local error:

0.4b
(* (- z) (sqrt (/ 1 3.0)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
16×associate-*r* sqrt-prod
13×*-un-lft-identity
12×add-cube-cbrt
11×times-frac
10×associate-*l*
4×unswap-sqr
3×pow1 add-exp-log distribute-lft-neg-in distribute-rgt-neg-in add-cbrt-cube
1×distribute-lft-neg-out expm1-log1p-u neg-mul-1 sqrt-div associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod log1p-expm1-u div-inv add-log-exp
Counts
1 → 45
Calls
1 calls:
44.0ms
(* (- z) (sqrt (/ 1 3.0)))

series75.0ms

Counts
1 → 3
Calls
1 calls:
75.0ms
(* (- z) (sqrt (/ 1 3.0)))

simplify605.0ms

Counts
48 → 48
Iterations

Useful iterations: done (603.0ms)

IterNodesCost
089460
1198394
2870373
done5000371

prune206.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 12.4b

regimes894.0ms

Accuracy

48.6% (13.2b remaining)

Error of 25.5b against oracle of 12.3b and baseline of 38.0b

bsearch94.0ms

Steps
ItersRangePoint
10
3.045750668387966e+83
9.982081272343965e+98
2.7166609535198792e+98
5
-1.1259454966916272e+94
-2.918087972802078e+93
-1.1005165876387523e+94

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02232
12732
done2732

end0.0ms

sample1.2s

Algorithm
intervals
Results
741.0ms8000×body80valid