Details

Time bar (total: 22.7s)

sample111.0ms

Algorithm
intervals
Results
75.0ms606×body80valid

simplify3.8s

Counts
1 → 1
Iterations
IterNodes
done5000
54328
41635
3521
2171
153
018

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×pow1 add-exp-log
6×add-cbrt-cube
4×expm1-log1p-u fma-udef log1p-expm1-u add-log-exp
3×pow-unpow unpow-prod-down associate-*r* associate-*l*
1×distribute-rgt-in pow-to-exp pow-pow distribute-lft-in pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod unswap-sqr sqr-pow
Counts
4 → 61
Calls
4 calls:
0.0ms
(fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0))
1.0ms
(fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b))))
11.0ms
(* a (fma (- 1.0 a) a (* b b)))
4.0ms
(pow (fma b b (* a a)) 2.0)

series442.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0))
77.0ms
(fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b))))
72.0ms
(* a (fma (- 1.0 a) a (* b b)))
151.0ms
(pow (fma b b (* a a)) 2.0)

simplify2.0s

Counts
73 → 73
Iterations
IterNodes
done5004
32632
2759
1284
0127

prune657.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (fma b b (* a a)) 2.0)
0.3b
(pow (fma b b (* a a)) 2.0)
9.2b
(sqrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))
9.2b
(sqrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))

rewrite12.0ms

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:
5.0ms
(pow (fma b b (* a a)) 2.0)
2.0ms
(pow (fma b b (* a a)) 2.0)
1.0ms
(sqrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))
2.0ms
(sqrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))

series896.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(pow (fma b b (* a a)) 2.0)
174.0ms
(pow (fma b b (* a a)) 2.0)
258.0ms
(sqrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))
290.0ms
(sqrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))

simplify2.6s

Counts
80 → 80
Iterations
IterNodes
done5005
43721
31321
2489
1214
098

prune837.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize79.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (fma b b (* a a)) 2.0)
0.3b
(pow (fma b b (* a a)) 2.0)
9.2b
(sqrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))
9.2b
(sqrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))

rewrite8.0ms

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 b b (* a a)) 2.0)
2.0ms
(pow (fma b b (* a a)) 2.0)
1.0ms
(sqrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))
2.0ms
(sqrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))

series963.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(pow (fma b b (* a a)) 2.0)
185.0ms
(pow (fma b b (* a a)) 2.0)
320.0ms
(sqrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))
261.0ms
(sqrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))

simplify2.4s

Counts
80 → 80
Iterations
IterNodes
done5005
43721
31321
2489
1214
098

prune627.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize119.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))
9.8b
(cbrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))
9.8b
(cbrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))
9.8b
(cbrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
1.0ms
(sqrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))
1.0ms
(cbrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))
1.0ms
(cbrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))
1.0ms
(cbrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))

series1.8s

Counts
4 → 12
Calls
4 calls:
258.0ms
(sqrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))
429.0ms
(cbrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))
658.0ms
(cbrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))
416.0ms
(cbrt (fma (fma 3.0 (* b b) (* a (fma (- 1.0 a) a (* b b)))) 4.0 (pow (fma b b (* a a)) 2.0)))

simplify2.1s

Counts
66 → 66
Iterations
IterNodes
done5000
32557
2800
1309
0134

prune548.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes216.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done21
121
019

end0.0ms

sample2.5s

Algorithm
intervals
Results
2.1s20397×body80valid