Details

Time bar (total: 16.4s)

sample45.0ms

Algorithm
intervals
Results
10.0ms335×body80nan
9.0ms256×body80valid

simplify57.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01114
12212
24411
36311
46711
56811
done6811

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (+ y z))
0.3b
(fma y z (* x (+ y z)))
17.8b
(sqrt (fma y z (* x (+ y z))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity
6×pow1 add-cube-cbrt
5×add-exp-log add-cbrt-cube
4×associate-*r*
3×expm1-log1p-u associate-*l* sqrt-prod log1p-expm1-u add-log-exp
2×associate-*r/
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 flip3-+ pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ fma-udef distribute-lft-out unswap-sqr
Counts
3 → 50
Calls
3 calls:
31.0ms
(* x (+ y z))
1.0ms
(fma y z (* x (+ y z)))
3.0ms
(sqrt (fma y z (* x (+ y z))))

series292.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(* x (+ y z))
42.0ms
(fma y z (* x (+ y z)))
209.0ms
(sqrt (fma y z (* x (+ y z))))

simplify1.6s

Counts
59 → 59
Iterations

Useful iterations: done (1.6s)

IterNodesCost
091581
1220532
2621483
32012479
done5000478

prune235.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ y z))
0.6b
(cbrt (+ y z))
0.6b
(cbrt (+ y z))
17.8b
(sqrt (fma y z (* (* x (* (cbrt (+ y z)) (cbrt (+ y z)))) (cbrt (+ y z)))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×cbrt-prod
9×add-sqr-sqrt
8×add-cube-cbrt
6×cbrt-div
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 sqrt-prod flip-+ distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 63
Calls
4 calls:
4.0ms
(cbrt (+ y z))
8.0ms
(cbrt (+ y z))
8.0ms
(cbrt (+ y z))
3.0ms
(sqrt (fma y z (* (* x (* (cbrt (+ y z)) (cbrt (+ y z)))) (cbrt (+ y z)))))

series867.0ms

Counts
4 → 12
Calls
4 calls:
268.0ms
(cbrt (+ y z))
200.0ms
(cbrt (+ y z))
213.0ms
(cbrt (+ y z))
185.0ms
(sqrt (fma y z (* (* x (* (cbrt (+ y z)) (cbrt (+ y z)))) (cbrt (+ y z)))))

simplify3.2s

Counts
75 → 75
Iterations

Useful iterations: done (3.2s)

IterNodesCost
095942
1213858
2467690
31091629
42732620
done5001618

prune445.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma y z (* x (+ y z)))
0.5b
(* (sqrt (sqrt (fma y z (* x (+ y z))))) (sqrt (sqrt (fma y z (* x (+ y z))))))
17.8b
(sqrt (fma y z (* x (+ y z))))
17.8b
(sqrt (fma y z (* x (+ y z))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×add-sqr-sqrt
34×sqrt-pow1
29×pow1
18×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
6×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod fma-udef
Counts
4 → 117
Calls
4 calls:
1.0ms
(fma y z (* x (+ y z)))
47.0ms
(* (sqrt (sqrt (fma y z (* x (+ y z))))) (sqrt (sqrt (fma y z (* x (+ y z))))))
3.0ms
(sqrt (fma y z (* x (+ y z))))
2.0ms
(sqrt (fma y z (* x (+ y z))))

series630.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(fma y z (* x (+ y z)))
196.0ms
(* (sqrt (sqrt (fma y z (* x (+ y z))))) (sqrt (sqrt (fma y z (* x (+ y z))))))
211.0ms
(sqrt (fma y z (* x (+ y z))))
181.0ms
(sqrt (fma y z (* x (+ y z))))

simplify1.9s

Counts
129 → 129
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01102711
12021644
24861506
315831452
done50001407

prune534.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma z y (* (+ y z) x))
0.3b
(* (fabs (cbrt (fma z y (* (+ y z) x)))) (sqrt (cbrt (fma z y (* (+ y z) x)))))
18.3b
(cbrt (fma z y (* (+ y z) x)))
18.3b
(cbrt (fma z y (* (+ y z) x)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×cbrt-prod add-cube-cbrt *-un-lft-identity
9×associate-*r*
8×sqrt-prod
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l* unswap-sqr
2×pow1/3
1×pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef
Counts
4 → 64
Calls
4 calls:
1.0ms
(fma z y (* (+ y z) x))
23.0ms
(* (fabs (cbrt (fma z y (* (+ y z) x)))) (sqrt (cbrt (fma z y (* (+ y z) x)))))
1.0ms
(cbrt (fma z y (* (+ y z) x)))
1.0ms
(cbrt (fma z y (* (+ y z) x)))

series1.3s

Counts
4 → 12
Calls
4 calls:
28.0ms
(fma z y (* (+ y z) x))
369.0ms
(* (fabs (cbrt (fma z y (* (+ y z) x)))) (sqrt (cbrt (fma z y (* (+ y z) x)))))
437.0ms
(cbrt (fma z y (* (+ y z) x)))
445.0ms
(cbrt (fma z y (* (+ y z) x)))

simplify2.9s

Counts
76 → 76
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01561561
13641485
210521332
333331278
done50001275

prune419.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.8b

regimes190.0ms

Accuracy

0% (0.2b remaining)

Error of 19.3b against oracle of 19.1b and baseline of 19.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
11211
done1211

end0.0ms

sample1.5s

Algorithm
intervals
Results
387.0ms8000×body80valid
363.0ms7862×body80nan