Details

Time bar (total: 17.8s)

sample88.0ms

Algorithm
intervals
Results
57.0ms653×body80valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01829
15129
215429
345529
4168129
done500129

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

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) (+ 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))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
9×associate-*r*
8×add-cube-cbrt
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 distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 81
Calls
4 calls:
81.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
55.0ms
(* (* a a) (- 1.0 a))
11.0ms
(pow (+ (* a a) (* b b)) 2.0)
72.0ms
(* (* b b) (+ 3.0 a))

series436.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
66.0ms
(* (* a a) (- 1.0 a))
156.0ms
(pow (+ (* a a) (* b b)) 2.0)
47.0ms
(* (* b b) (+ 3.0 a))

simplify3.3s

Counts
93 → 93
Iterations

Useful iterations: 2 (904.0ms)

IterNodesCost
01791446
15591337
238321209
done50001209

prune376.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 1 expressions with local error:

1.7b
(* (pow a 2) (pow b 2))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
13×add-exp-log
10×unpow2 sqr-pow
9×prod-exp
8×associate-*r* associate-*l*
6×pow-to-exp pow-exp
5×add-cube-cbrt *-un-lft-identity
3×add-cbrt-cube
1×pow1 pow-prod-down *-commutative cbrt-unprod add-log-exp
Counts
1 → 51
Calls
1 calls:
33.0ms
(* (pow a 2) (pow b 2))

series46.0ms

Counts
1 → 3
Calls
1 calls:
46.0ms
(* (pow a 2) (pow b 2))

simplify875.0ms

Counts
54 → 54
Iterations

Useful iterations: done (873.0ms)

IterNodesCost
077590
1176517
21267375
done5000367

prune158.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.5b
(* (* b b) (+ 3.0 a))
1.7b
(* (pow a 2) (pow b 2))

rewrite260.0ms

Algorithm
rewrite-expression-head
Rules
32×associate-*r/
30×add-sqr-sqrt
26×add-exp-log
20×frac-add
18×unswap-sqr
17×associate-*r*
16×add-cbrt-cube
15×prod-exp
14×pow1 unpow-prod-down *-un-lft-identity flip3-+ flip-+
10×add-cube-cbrt associate-*l* unpow2 sqr-pow
9×add-log-exp
7×pow-prod-down cbrt-unprod
6×pow-to-exp pow-exp
5×flip3-- flip--
4×distribute-rgt-in distribute-lft-in
3×sum-log *-commutative
2×sub-neg associate-+r+
1×+-commutative associate-+l+ distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 129
Calls
4 calls:
98.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
66.0ms
(* (* a a) (- 1.0 a))
56.0ms
(* (* b b) (+ 3.0 a))
28.0ms
(* (pow a 2) (pow b 2))

series345.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
77.0ms
(* (* a a) (- 1.0 a))
62.0ms
(* (* b b) (+ 3.0 a))
59.0ms
(* (pow a 2) (pow b 2))

simplify504.0ms

Counts
141 → 141
Iterations

Useful iterations: done (498.0ms)

IterNodesCost
03133806
110173314
done50003042

prune706.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.5b
(* (* b b) (+ 3.0 a))
32.4b
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))

rewrite301.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×add-sqr-sqrt
13×add-cube-cbrt
12×cbrt-prod
11×pow1 add-exp-log
10×add-cbrt-cube
9×unpow-prod-down
6×pow-unpow cube-prod
4×cube-div associate-*r* add-log-exp
3×flip3-+ pow-prod-down prod-exp cbrt-unprod flip-+ sqr-pow
2×cube-mult pow-to-exp cbrt-div pow-pow unpow3 associate-*r/ pow-exp
1×distribute-rgt-in distribute-lft-in pow1/3 associate-*l* *-commutative rem-cbrt-cube distribute-lft-out rem-cube-cbrt unswap-sqr
Counts
4 → 89
Calls
4 calls:
125.0ms
(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3)
17.0ms
(pow (+ (* a a) (* b b)) 2.0)
54.0ms
(* (* b b) (+ 3.0 a))
102.0ms
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))

series1.3s

Counts
4 → 12
Calls
4 calls:
1.0s
(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3)
141.0ms
(pow (+ (* a a) (* b b)) 2.0)
54.0ms
(* (* b b) (+ 3.0 a))
144.0ms
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))

simplify2.7s

Counts
101 → 101
Iterations

Useful iterations: 2 (705.0ms)

IterNodesCost
01953169
16112887
238372485
done50022485

prune738.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes179.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01829
12529
done2529

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.7s20608×body80valid