Details

Time bar (total: 6.3s)

sample58.0ms

Algorithm
intervals
Results
36.0ms646×body80valid

simplify90.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05315
116115
245915
3132315
4299215
5500115
done500115

prune3.0ms

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
(+ (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)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×distribute-rgt-in distribute-lft-in associate-*r/
3×unpow-prod-down pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out sqr-pow
Counts
4 → 79
Calls
4 calls:
58.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
32.0ms
(* (* a a) (+ 1.0 a))
13.0ms
(pow (+ (* a a) (* b b)) 2.0)
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(+ (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))
108.0ms
(pow (+ (* a a) (* b b)) 2.0)
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify75.0ms

Counts
91 → 91
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0504702
12520622
25002622
done5002622

prune245.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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×associate-*r/
6×add-sqr-sqrt cbrt-div
5×add-cube-cbrt *-un-lft-identity
4×flip3-- flip-- add-log-exp
3×cbrt-prod pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod
2×distribute-rgt-in sub-neg distribute-lft-in
1×associate-*l* *-commutative unswap-sqr
Counts
4 → 58
Calls
4 calls:
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
16.0ms
(cbrt (* (* 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))))

series529.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
161.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
155.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
161.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))

simplify40.0ms

Counts
70 → 70
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0365894
11439828
25002693
done5002693

prune340.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

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)))))))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-div associate-*r/ add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 associate-*l* *-commutative flip-- flip-+ unswap-sqr
Counts
4 → 80
Calls
4 calls:
30.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
61.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
63.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series454.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
54.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
175.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
176.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify45.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03331080
11424980
25002978
done5002978

prune326.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize26.0ms

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)))))))

rewrite450.0ms

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 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
262.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
61.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
61.0ms
(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)))))))

series701.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
174.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
175.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
176.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify110.0ms

Counts
72 → 72
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
01851452
16871384
235271384
350011380
done50011380

prune318.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes150.0ms

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

sample1.6s

Algorithm
intervals
Results
1.1s20589×body80valid