Details

Time bar (total: 5.5s)

sample65.0ms

Algorithm
intervals
Results
42.0ms709×body80valid

simplify52.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213
done500213

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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 (+ (* a a) (* b b)) 2.0) 1.0))
0.1b
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.4b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg associate-*r/ fma-udef
1×pow-to-exp flip3-- pow-pow 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 (+ (* a a) (* b b)) 2.0) 1.0))
0.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
31.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series325.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
58.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
107.0ms
(pow (+ (* a a) (* b b)) 2.0)
50.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify50.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0391706
11680606
25001592
done5001592

prune288.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* b b) (- 1.0 (* 3.0 a)))
10.3b
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
10.3b
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
10.3b
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-cbrt-cube
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 72
Calls
4 calls:
27.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
1.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
1.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))

series475.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
138.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
139.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
145.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))

simplify40.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0325916
11279815
25002777
done5002777

prune372.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

10.3b
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
10.3b
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
10.3b
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
10.3b
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 52
Calls
4 calls:
1.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
1.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
1.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
1.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))

series562.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
135.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
143.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))
141.0ms
(cbrt (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))))

simplify42.0ms

Counts
64 → 64
Iterations

Useful iterations: 3 (35.0ms)

IterNodesCost
0130876
1331796
21174724
35002700
done5002700

prune372.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (cbrt (+ (* a a) (* b b))) 2.0)
10.3b
(cbrt (+ (* a a) (* b b)))
10.3b
(cbrt (+ (* a a) (* b b)))
10.3b
(cbrt (+ (* a a) (* b b)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cbrt-div
5×pow1 add-exp-log
4×expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-unpow flip3-+ flip-+
2×pow-pow
1×pow-to-exp pow-exp sqr-pow
Counts
4 → 68
Calls
4 calls:
10.0ms
(pow (cbrt (+ (* a a) (* b b))) 2.0)
5.0ms
(cbrt (+ (* a a) (* b b)))
5.0ms
(cbrt (+ (* a a) (* b b)))
9.0ms
(cbrt (+ (* a a) (* b b)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(pow (cbrt (+ (* a a) (* b b))) 2.0)
93.0ms
(cbrt (+ (* a a) (* b b)))
93.0ms
(cbrt (+ (* a a) (* b b)))
94.0ms
(cbrt (+ (* a a) (* b b)))

simplify85.0ms

Counts
80 → 80
Iterations

Useful iterations: 3 (78.0ms)

IterNodesCost
0224589
1806555
23031546
35002541
done5002541

prune385.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes151.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03053
13053
done3053

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s20533×body80valid