Details

Time bar (total: 17.1s)

sample111.0ms

Algorithm
intervals
Results
73.0ms655×body80valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01829
15129
215429
345529
4168129
done500129

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

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)))))
0.0b
(* (* a a) (- 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.2b
(* (* b b) (+ 3.0 a))

rewrite237.0ms

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:
109.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
46.0ms
(* (* a a) (- 1.0 a))
11.0ms
(pow (+ (* a a) (* b b)) 2.0)
69.0ms
(* (* b b) (+ 3.0 a))

series489.0ms

Counts
4 → 12
Calls
4 calls:
214.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
70.0ms
(* (* a a) (- 1.0 a))
161.0ms
(pow (+ (* a a) (* b b)) 2.0)
44.0ms
(* (* b b) (+ 3.0 a))

simplify4.0s

Counts
93 → 93
Iterations

Useful iterations: 2 (987.0ms)

IterNodesCost
01791446
15591337
238321209
done50001209

prune413.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (* b b) (+ 3.0 a))
20.6b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.6b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.6b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
13×*-un-lft-identity
12×add-sqr-sqrt
11×add-cube-cbrt
9×pow1 add-exp-log unpow-prod-down add-cbrt-cube
4×associate-*r* add-log-exp
3×pow1/3 pow-prod-down prod-exp cbrt-unprod sqr-pow
2×associate-*r/
1×distribute-rgt-in distribute-lft-in flip3-+ associate-*l* *-commutative flip-+ distribute-lft-out unswap-sqr
Counts
4 → 69
Calls
4 calls:
42.0ms
(* (* b b) (+ 3.0 a))
10.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
15.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
9.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series702.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (* b b) (+ 3.0 a))
225.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
244.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
189.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify1.3s

Counts
81 → 81
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01051185
12781154
217541056
done50011043

prune383.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
3.5b
(* (pow a 2) (pow b 2))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
28×prod-exp
25×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×*-un-lft-identity associate-*l* add-cbrt-cube add-log-exp
10×unpow2 sqr-pow
9×add-cube-cbrt associate-*r*
6×pow1
4×sum-log cbrt-unprod
2×+-commutative flip3-+ pow-prod-down *-commutative flip-+
1×associate-+r+ distribute-lft-out
Counts
4 → 101
Calls
4 calls:
19.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
36.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
30.0ms
(* 2 (* (pow a 2) (pow b 2)))
19.0ms
(* (pow a 2) (pow b 2))

series256.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
73.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
47.0ms
(* 2 (* (pow a 2) (pow b 2)))
55.0ms
(* (pow a 2) (pow b 2))

simplify2.0s

Counts
113 → 113
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01461649
13861443
224081245
done50011237

prune346.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
0.0b
(* (* a a) (- 1.0 a))
1.2b
(* (* b b) (+ 3.0 a))
3.5b
(* (pow a 2) (pow b 2))

rewrite234.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
28×add-exp-log
20×associate-*r*
19×unswap-sqr
18×associate-*r/ add-cbrt-cube
16×pow1 *-un-lft-identity prod-exp
14×unpow-prod-down
13×associate-*l*
12×add-cube-cbrt
10×unpow2 sqr-pow
8×pow-prod-down cbrt-unprod
6×pow-to-exp pow-exp
4×distribute-rgt-in distribute-lft-in flip3-+ frac-add *-commutative flip-+ add-log-exp
3×flip3-- flip--
2×sub-neg
1×distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 128
Calls
4 calls:
108.0ms
(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
41.0ms
(* (* a a) (- 1.0 a))
54.0ms
(* (* b b) (+ 3.0 a))
28.0ms
(* (pow a 2) (pow b 2))

series234.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
77.0ms
(* (* a a) (- 1.0 a))
37.0ms
(* (* b b) (+ 3.0 a))
43.0ms
(* (pow a 2) (pow b 2))

simplify419.0ms

Counts
140 → 140
Iterations

Useful iterations: done (414.0ms)

IterNodesCost
02431906
17581748
done50001476

prune555.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes222.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01829
12529
done2529

end0.0ms

sample3.4s

Algorithm
intervals
Results
2.7s20583×body80valid