Details

Time bar (total: 6.8s)

sample58.0ms

Algorithm
intervals
Results
36.0ms646×body80valid

simplify60.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213
done500213

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.4b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-sqr-sqrt *-un-lft-identity add-cbrt-cube
12×add-cube-cbrt
7×distribute-rgt-in fma-def distribute-lft-in associate-*r*
6×unpow-prod-down prod-diff pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr sqr-pow
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out
Counts
4 → 100
Calls
4 calls:
64.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
34.0ms
(* (* a a) (+ 1.0 a))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
30.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series315.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
47.0ms
(* (* a a) (+ 1.0 a))
104.0ms
(pow (+ (* a a) (* b b)) 2.0)
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify72.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
0564828
12826724
25001715
done5001715

prune355.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* b b) (- 1.0 (* 3.0 a)))
25.0b
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
25.0b
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
25.0b
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log add-cbrt-cube
8×add-sqr-sqrt associate-*r/
7×add-cube-cbrt *-un-lft-identity
6×cbrt-div prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg
1×associate-*l* *-commutative unswap-sqr
Counts
4 → 72
Calls
4 calls:
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
16.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
19.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
16.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))

series552.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
169.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
168.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
165.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))

simplify50.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04181003
11679925
25001798
done5001798

prune407.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* b b) (- 1.0 (* 3.0 a)))
0.4b
(* (* b b) (- 1.0 (* 3.0 a)))
10.8b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.8b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 add-sqr-sqrt
14×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity prod-diff
10×distribute-rgt-in distribute-lft-in
6×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×expm1-log1p-u sub-neg sqrt-div associate-*r/ log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 associate-*l* *-commutative flip-- flip-+ unswap-sqr
Counts
4 → 100
Calls
4 calls:
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
30.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
69.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
70.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series467.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
58.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
180.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
178.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify54.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
03881304
116741186
250021176
done50021176

prune410.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.8b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.8b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.8b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite268.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
Counts
4 → 68
Calls
4 calls:
66.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
67.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
65.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
69.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series721.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
181.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
173.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
181.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify117.0ms

Counts
80 → 80
Iterations

Useful iterations: 3 (104.0ms)

IterNodesCost
01951572
17461500
238811500
350011496
done50011496

prune423.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes232.0ms

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
03128
13128
done3128

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.2s20589×body80valid