Details

Time bar (total: 19.9s)

sample31.0ms

Algorithm
intervals
Results
13.0ms413×body80valid

simplify57.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (13.0ms)

IterNodesCost
0815
11614
23311
3568
4748
5808
done808

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x y) (* z z))
0.0b
(+ (+ (* x y) (* z z)) (* z z))
0.1b
(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
19×add-log-exp
10×sum-log
7×fma-def
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
3×pow1 add-exp-log +-commutative expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u
2×associate-+l+
Counts
3 → 51
Calls
3 calls:
17.0ms
(+ (* x y) (* z z))
66.0ms
(+ (+ (* x y) (* z z)) (* z z))
239.0ms
(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

series215.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(+ (* x y) (* z z))
86.0ms
(+ (+ (* x y) (* z z)) (* z z))
78.0ms
(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

simplify3.4s

Counts
60 → 60
Iterations

Useful iterations: 3 (1.7s)

IterNodesCost
076863
1228666
2839590
33573521
done5000521

prune179.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b
(fma 3 (* z z) (* x y))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
0.0ms
(fma 3 (* z z) (* x y))

series46.0ms

Counts
1 → 3
Calls
1 calls:
46.0ms
(fma 3 (* z z) (* x y))

simplify4.0s

Counts
13 → 13
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
021140
133137
269121
3207121
4706121
53689121
done5000121

prune57.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x y) (* z z)) (* z z))
0.3b
(fma (sqrt (+ (+ (* x y) (* z z)) (* z z))) (sqrt (+ (+ (* x y) (* z z)) (* z z))) (* z z))
2.1b
(sqrt (+ (+ (* x y) (* z z)) (* z z)))
2.1b
(sqrt (+ (+ (* x y) (* z z)) (* z z)))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×add-log-exp
7×add-cube-cbrt *-un-lft-identity
6×pow1 sqrt-prod
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×fma-def flip3-+ sum-log flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×+-commutative associate-+l+ fma-udef
Counts
4 → 64
Calls
4 calls:
61.0ms
(+ (+ (* x y) (* z z)) (* z z))
0.0ms
(fma (sqrt (+ (+ (* x y) (* z z)) (* z z))) (sqrt (+ (+ (* x y) (* z z)) (* z z))) (* z z))
40.0ms
(sqrt (+ (+ (* x y) (* z z)) (* z z)))
56.0ms
(sqrt (+ (+ (* x y) (* z z)) (* z z)))

series717.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(+ (+ (* x y) (* z z)) (* z z))
306.0ms
(fma (sqrt (+ (+ (* x y) (* z z)) (* z z))) (sqrt (+ (+ (* x y) (* z z)) (* z z))) (* z z))
170.0ms
(sqrt (+ (+ (* x y) (* z z)) (* z z)))
172.0ms
(sqrt (+ (+ (* x y) (* z z)) (* z z)))

simplify2.8s

Counts
76 → 76
Iterations

Useful iterations: done (2.8s)

IterNodesCost
0851406
1205945
2656793
32755740
done5000737

prune335.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 3 (* z z))
0.3b
(* (sqrt (fma x y (* 3 (* z z)))) (sqrt (fma x y (* 3 (* z z)))))
2.0b
(sqrt (fma x y (* 3 (* z z))))
2.0b
(sqrt (fma x y (* 3 (* z z))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
26×pow1
24×sqrt-prod
15×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
10×sqrt-pow1 pow1/2
9×associate-*l*
8×swap-sqr
7×associate-*r*
6×pow-prod-down
5×pow-prod-up unswap-sqr
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow-sqr
2×rem-sqrt-square *-commutative
1×pow2 pow-plus sqrt-unprod rem-square-sqrt
Counts
4 → 102
Calls
4 calls:
34.0ms
(* 3 (* z z))
15.0ms
(* (sqrt (fma x y (* 3 (* z z)))) (sqrt (fma x y (* 3 (* z z)))))
2.0ms
(sqrt (fma x y (* 3 (* z z))))
2.0ms
(sqrt (fma x y (* 3 (* z z))))

series436.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* 3 (* z z))
71.0ms
(* (sqrt (fma x y (* 3 (* z z)))) (sqrt (fma x y (* 3 (* z z)))))
140.0ms
(sqrt (fma x y (* 3 (* z z))))
177.0ms
(sqrt (fma x y (* 3 (* z z))))

simplify5.1s

Counts
114 → 114
Iterations

Useful iterations: 4 (2.8s)

IterNodesCost
0951766
11711195
24341077
312891026
443401001
done50001001

prune326.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes277.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0815
11215
done1215

end0.0ms

sample1.4s

Algorithm
intervals
Results
807.0ms12223×body80valid