Details

Time bar (total: 21.7s)

sample101.0ms

Algorithm
intervals
Results
66.0ms659×body80valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
01931
15529
217928
358828
4219528
done500028

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
0.1b
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.3b
(pow (fma a a (* b b)) 2.0)
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt pow1 add-exp-log
9×*-un-lft-identity add-cbrt-cube add-cube-cbrt
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow unpow-prod-down associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg associate-*r/ fma-udef
1×pow-to-exp pow-pow flip3-- associate-*l* pow-exp *-commutative flip-- unswap-sqr sqr-pow
Counts
4 → 72
Calls
4 calls:
0.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
0.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
3.0ms
(pow (fma a a (* b b)) 2.0)
22.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series392.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
66.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
137.0ms
(pow (fma a a (* b b)) 2.0)
67.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify2.6s

Counts
84 → 84
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01581452
14241415
225451226
done50001215

prune549.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma a a (* b b))
0.0b
(fma 1.0 (fma a a (pow b 2)) (pow a 3))
0.0b
(fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0))
0.3b
(pow (fma a a (* b b)) 2.0)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-unpow unpow-prod-down fma-udef
1×pow-to-exp pow-pow pow-exp sqr-pow
Counts
4 → 49
Calls
4 calls:
0.0ms
(fma a a (* b b))
0.0ms
(fma 1.0 (fma a a (pow b 2)) (pow a 3))
1.0ms
(fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0))
4.0ms
(pow (fma a a (* b b)) 2.0)

series429.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(fma a a (* b b))
74.0ms
(fma 1.0 (fma a a (pow b 2)) (pow a 3))
146.0ms
(fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0))
144.0ms
(pow (fma a a (* b b)) 2.0)

simplify1.7s

Counts
61 → 61
Iterations

Useful iterations: 3 (881.0ms)

IterNodesCost
091889
1198858
2685744
33322741
done5001741

prune442.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (fma a a (* b b)) 2.0)
0.3b
(pow (fma a a (* b b)) 2.0)
8.1b
(sqrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))
8.1b
(sqrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
8×pow1
6×pow-unpow unpow-prod-down add-exp-log sqrt-prod
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 pow-exp sqr-pow
Counts
4 → 68
Calls
4 calls:
2.0ms
(pow (fma a a (* b b)) 2.0)
2.0ms
(pow (fma a a (* b b)) 2.0)
1.0ms
(sqrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))
1.0ms
(sqrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))

series928.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(pow (fma a a (* b b)) 2.0)
198.0ms
(pow (fma a a (* b b)) 2.0)
253.0ms
(sqrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))
294.0ms
(sqrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))

simplify2.8s

Counts
80 → 80
Iterations

Useful iterations: done (2.8s)

IterNodesCost
0971474
12281336
27361252
331201240
done50021238

prune794.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (fabs (cbrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))) (sqrt (cbrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))))
8.1b
(sqrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))
8.6b
(cbrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))
8.6b
(cbrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt sqrt-prod
10×cbrt-prod
9×associate-*r*
7×pow1
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l* unswap-sqr
2×pow1/3
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 69
Calls
4 calls:
10.0ms
(* (fabs (cbrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))) (sqrt (cbrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))))
2.0ms
(sqrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))
1.0ms
(cbrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))
1.0ms
(cbrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
331.0ms
(* (fabs (cbrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))) (sqrt (cbrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))))
247.0ms
(sqrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))
328.0ms
(cbrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))
307.0ms
(cbrt (fma 4.0 (fma 1.0 (fma a a (pow b 2)) (pow a 3)) (pow (fma a a (* b b)) 2.0)))

simplify931.0ms

Counts
81 → 81
Iterations

Useful iterations: done (925.0ms)

IterNodesCost
01963655
14533487
216803161
done50002930

prune971.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes285.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01623
done1623

end0.0ms

sample4.2s

Algorithm
intervals
Results
3.4s20551×body80valid