Details

Time bar (total: 5.0s)

sample63.0ms

Algorithm
intervals
Results
39.0ms709×body80valid

simplify80.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
05314
117313
253212
3168112
4427812
5500112
done500112

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
0.1b
(* (* a a) (- 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.5b
(* (* b b) (+ 3.0 a))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×*-un-lft-identity
22×add-cube-cbrt
18×associate-*r/ prod-diff
17×pow1 add-exp-log
16×add-cbrt-cube
13×distribute-rgt-in distribute-lft-in
12×associate-*r*
7×pow-prod-down prod-exp cbrt-unprod
5×associate-*l*
4×expm1-log1p-u flip3-+ frac-add flip-+ log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow flip3-- *-commutative flip-- unswap-sqr
2×sub-neg
1×pow-to-exp pow-pow pow-exp distribute-lft-out distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 120
Calls
4 calls:
83.0ms
(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
32.0ms
(* (* a a) (- 1.0 a))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
31.0ms
(* (* b b) (+ 3.0 a))

series251.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
53.0ms
(* (* a a) (- 1.0 a))
105.0ms
(pow (+ (* a a) (* b b)) 2.0)
34.0ms
(* (* b b) (+ 3.0 a))

simplify121.0ms

Counts
132 → 132
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
07881033
14587830
25001830
done5001830

prune326.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (fma (pow a 2) 4.0 (- (* 12.0 (pow b 2)) (* 4.0 (pow a 3)))))
0.0b
(fma (pow a 2) 4.0 (- (* 12.0 (pow b 2)) (* 4.0 (pow a 3))))
0.2b
(* 12.0 (pow b 2))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×*-un-lft-identity
11×add-cube-cbrt
10×add-exp-log unpow-prod-down
8×associate-*r*
7×fma-def
6×add-cbrt-cube add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u unswap-sqr sqr-pow
3×pow-unpow associate-*l* prod-exp
2×pow-to-exp pow-exp fma-udef unpow2
1×+-commutative associate-+r+ pow-pow flip3-+ sum-log *-commutative cbrt-unprod flip-+ distribute-lft-out
Counts
4 → 80
Calls
4 calls:
57.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (fma (pow a 2) 4.0 (- (* 12.0 (pow b 2)) (* 4.0 (pow a 3)))))
0.0ms
(fma (pow a 2) 4.0 (- (* 12.0 (pow b 2)) (* 4.0 (pow a 3))))
14.0ms
(* 12.0 (pow b 2))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)

series283.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (fma (pow a 2) 4.0 (- (* 12.0 (pow b 2)) (* 4.0 (pow a 3)))))
52.0ms
(fma (pow a 2) 4.0 (- (* 12.0 (pow b 2)) (* 4.0 (pow a 3))))
25.0ms
(* 12.0 (pow b 2))
105.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify39.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0301619
11203572
25002562
done5002562

prune365.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (fma 4.0 (pow a 2) (pow (+ (* a a) (* b b)) 2.0)) (- (* 12.0 (pow b 2)) (* 4.0 (pow a 3))))
0.0b
(fma 4.0 (pow a 2) (pow (+ (* a a) (* b b)) 2.0))
0.2b
(* 12.0 (pow b 2))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
12×*-un-lft-identity
10×add-exp-log add-cube-cbrt
9×add-log-exp
8×associate-*r*
7×unpow-prod-down
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u log1p-expm1-u unswap-sqr
3×pow-unpow associate-+r+ fma-def associate-*l* prod-exp sqr-pow
2×pow-to-exp pow-exp sum-log fma-udef unpow2
1×+-commutative associate-+r- sub-neg associate-+l+ pow-pow flip3-+ diff-log prod-diff *-commutative cbrt-unprod flip-+ distribute-lft-out
Counts
4 → 81
Calls
4 calls:
16.0ms
(+ (fma 4.0 (pow a 2) (pow (+ (* a a) (* b b)) 2.0)) (- (* 12.0 (pow b 2)) (* 4.0 (pow a 3))))
0.0ms
(fma 4.0 (pow a 2) (pow (+ (* a a) (* b b)) 2.0))
11.0ms
(* 12.0 (pow b 2))
13.0ms
(pow (+ (* a a) (* b b)) 2.0)

series273.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ (fma 4.0 (pow a 2) (pow (+ (* a a) (* b b)) 2.0)) (- (* 12.0 (pow b 2)) (* 4.0 (pow a 3))))
60.0ms
(fma 4.0 (pow a 2) (pow (+ (* a a) (* b b)) 2.0))
30.0ms
(* 12.0 (pow b 2))
103.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify44.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0334677
11193619
25001609
done5001609

prune376.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (fma (pow b 2) 12.0 (fma 4.0 (pow a 2) (pow (+ (* a a) (* b b)) 2.0))) (- (* 4.0 (pow a 3))))
0.0b
(fma 4.0 (pow a 2) (pow (+ (* a a) (* b b)) 2.0))
0.1b
(fma (pow b 2) 12.0 (fma 4.0 (pow a 2) (pow (+ (* a a) (* b b)) 2.0)))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
8×add-log-exp
7×add-sqr-sqrt add-cube-cbrt
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×unpow-prod-down pow-unpow fma-def fma-udef
2×sum-log
1×+-commutative neg-sub0 pow-to-exp associate-+r- associate-+l+ pow-pow flip3-+ unsub-neg neg-log pow-exp flip-+ distribute-lft-out sqr-pow
Counts
4 → 61
Calls
4 calls:
7.0ms
(+ (fma (pow b 2) 12.0 (fma 4.0 (pow a 2) (pow (+ (* a a) (* b b)) 2.0))) (- (* 4.0 (pow a 3))))
0.0ms
(fma 4.0 (pow a 2) (pow (+ (* a a) (* b b)) 2.0))
0.0ms
(fma (pow b 2) 12.0 (fma 4.0 (pow a 2) (pow (+ (* a a) (* b b)) 2.0)))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)

series367.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(+ (fma (pow b 2) 12.0 (fma 4.0 (pow a 2) (pow (+ (* a a) (* b b)) 2.0))) (- (* 4.0 (pow a 3))))
66.0ms
(fma 4.0 (pow a 2) (pow (+ (* a a) (* b b)) 2.0))
101.0ms
(fma (pow b 2) 12.0 (fma 4.0 (pow a 2) (pow (+ (* a a) (* b b)) 2.0)))
108.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify44.0ms

Counts
73 → 73
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0291670
11163612
25002603
done5002603

prune317.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

regimes51.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02412
12412
done2412

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.0s20533×body80valid