Details

Time bar (total: 19.1s)

sample100.0ms

Algorithm
intervals
Results
64.0ms669×body80valid

simplify4.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01217
12616
25015
38715
415415
547315
6370915
done500015

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma a a (* b b))
0.0b
(fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))
0.3b
(pow (fma a a (* b b)) 2.0)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log
3×expm1-log1p-u unpow-prod-down pow-unpow add-cbrt-cube log1p-expm1-u add-log-exp
2×fma-udef
1×pow-to-exp pow-pow pow-exp sqr-pow
Counts
3 → 39
Calls
3 calls:
0.0ms
(fma a a (* b b))
0.0ms
(fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))
3.0ms
(pow (fma a a (* b b)) 2.0)

series316.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(fma a a (* b b))
114.0ms
(fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))
149.0ms
(pow (fma a a (* b b)) 2.0)

simplify2.1s

Counts
48 → 48
Iterations

Useful iterations: 3 (555.0ms)

IterNodesCost
079580
1167561
2530493
32276492
done5000492

prune210.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

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)
12.6b
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
12.6b
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×add-exp-log unpow-prod-down pow-unpow 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:
3.0ms
(pow (fma a a (* b b)) 2.0)
3.0ms
(pow (fma a a (* b b)) 2.0)
2.0ms
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
3.0ms
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

series736.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(pow (fma a a (* b b)) 2.0)
146.0ms
(pow (fma a a (* b b)) 2.0)
200.0ms
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
242.0ms
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

simplify1.5s

Counts
80 → 80
Iterations

Useful iterations: 2 (162.0ms)

IterNodesCost
0861148
11891050
2564988
32230988
done5000988

prune433.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0))
0.3b
(pow (fma a a (* b b)) 2.0)
12.6b
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
12.6b
(sqrt (fma (* 4.0 b) b (* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
21×unpow-prod-down
17×add-exp-log
16×add-cube-cbrt *-un-lft-identity
11×sqr-pow
9×prod-exp unswap-sqr
7×pow1 pow-to-exp swap-sqr associate-*r* associate-*l* pow-exp
6×sqrt-prod add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×rem-sqrt-square sqrt-pow1 pow1/2
1×pow2 pow-pow pow-prod-down pow-sqr *-commutative pow-prod-up cbrt-unprod
Counts
4 → 103
Calls
4 calls:
39.0ms
(* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0))
3.0ms
(pow (fma a a (* b b)) 2.0)
2.0ms
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
2.0ms
(sqrt (fma (* 4.0 b) b (* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0))))

series1.0s

Counts
4 → 12
Calls
4 calls:
293.0ms
(* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0))
154.0ms
(pow (fma a a (* b b)) 2.0)
281.0ms
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
288.0ms
(sqrt (fma (* 4.0 b) b (* (pow (hypot a b) 2.0) (pow (hypot a b) 2.0))))

simplify1.6s

Counts
115 → 115
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01631890
13701525
215291412
done50011400

prune686.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))) (sqrt (fma (* 4.0 b) b (* 1 (pow (hypot a b) (* 2 2.0))))))
0.3b
(pow (fma a a (* b b)) 2.0)
12.6b
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
12.6b
(sqrt (fma (* 4.0 b) b (* 1 (pow (hypot a b) (* 2 2.0)))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
16×sqrt-prod
12×add-cube-cbrt *-un-lft-identity
11×pow1
7×add-exp-log
6×associate-*r* associate-*l* add-cbrt-cube
4×expm1-log1p-u sqrt-pow1 pow1/2 log1p-expm1-u add-log-exp unswap-sqr
3×unpow-prod-down pow-unpow pow-prod-down
2×rem-sqrt-square
1×pow-to-exp pow-pow sqrt-unprod pow-exp prod-exp *-commutative cbrt-unprod sqr-pow
Counts
4 → 81
Calls
4 calls:
15.0ms
(* (sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))) (sqrt (fma (* 4.0 b) b (* 1 (pow (hypot a b) (* 2 2.0))))))
5.0ms
(pow (fma a a (* b b)) 2.0)
3.0ms
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
4.0ms
(sqrt (fma (* 4.0 b) b (* 1 (pow (hypot a b) (* 2 2.0)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
404.0ms
(* (sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))) (sqrt (fma (* 4.0 b) b (* 1 (pow (hypot a b) (* 2 2.0))))))
168.0ms
(pow (fma a a (* b b)) 2.0)
256.0ms
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
316.0ms
(sqrt (fma (* 4.0 b) b (* 1 (pow (hypot a b) (* 2 2.0)))))

simplify757.0ms

Counts
93 → 93
Iterations

Useful iterations: done (752.0ms)

IterNodesCost
01402209
13051940
210691828
done50001824

prune706.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes107.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02147
12547
done2547

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.2s20565×body80valid