Details

Time bar (total: 14.9s)

sample53.0ms

Algorithm
intervals
Results
31.0ms631×body80valid

simplify3.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01829
15129
215429
341029
4104729
5192929
6397029
done500029

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

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)
1.3b
(* (* b b) (+ 3.0 a))

rewrite129.0ms

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:
54.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
30.0ms
(* (* a a) (- 1.0 a))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
32.0ms
(* (* b b) (+ 3.0 a))

series319.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
52.0ms
(* (* a a) (- 1.0 a))
112.0ms
(pow (+ (* a a) (* b b)) 2.0)
39.0ms
(* (* b b) (+ 3.0 a))

simplify849.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (311.0ms)

IterNodesCost
01791446
14821329
218041209
done50001209

prune249.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* a a) (- 1.0 a))
0.2b
(/ (* (* b b) (+ (pow 3.0 3) (pow a 3))) (+ (* 3.0 3.0) (- (* a a) (* 3.0 a))))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
2.6b
(* (* b b) (+ (pow 3.0 3) (pow a 3)))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
24×add-exp-log
23×add-cbrt-cube
22×*-un-lft-identity
15×pow1
14×add-sqr-sqrt associate-*r*
10×add-cube-cbrt
9×prod-exp cbrt-unprod
7×unpow-prod-down
6×associate-*r/ pow-prod-down
5×distribute-lft-out
4×cube-prod add-log-exp
3×cbrt-undiv distribute-rgt-in pow-unpow distribute-lft-in flip3-+ times-frac div-exp associate-/r* flip-+
2×sub-neg associate-*l* associate-/r/ *-commutative associate-/l/ unswap-sqr
1×pow-to-exp flip3-- pow-pow frac-2neg pow-exp clear-num sum-cubes flip-- div-inv associate-/l* distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 100
Calls
4 calls:
31.0ms
(* (* a a) (- 1.0 a))
64.0ms
(/ (* (* b b) (+ (pow 3.0 3) (pow a 3))) (+ (* 3.0 3.0) (- (* a a) (* 3.0 a))))
9.0ms
(pow (+ (* a a) (* b b)) 2.0)
81.0ms
(* (* b b) (+ (pow 3.0 3) (pow a 3)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (* a a) (- 1.0 a))
140.0ms
(/ (* (* b b) (+ (pow 3.0 3) (pow a 3))) (+ (* 3.0 3.0) (- (* a a) (* 3.0 a))))
108.0ms
(pow (+ (* a a) (* b b)) 2.0)
91.0ms
(* (* b b) (+ (pow 3.0 3) (pow a 3)))

simplify1.5s

Counts
112 → 112
Iterations

Useful iterations: 2 (474.0ms)

IterNodesCost
02071961
15841739
225851487
done50021487

prune587.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 2 (* (pow a 2) (pow b 2)))
2.7b
(* (pow a 2) (pow b 2))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
37×add-exp-log
28×prod-exp
23×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×associate-*l*
10×unpow2 sqr-pow
9×associate-*r* add-cbrt-cube
7×add-cube-cbrt *-un-lft-identity
4×pow1 cbrt-unprod
2×pow-prod-down *-commutative add-log-exp
Counts
2 → 76
Calls
2 calls:
23.0ms
(* 2 (* (pow a 2) (pow b 2)))
19.0ms
(* (pow a 2) (pow b 2))

series72.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(* 2 (* (pow a 2) (pow b 2)))
33.0ms
(* (pow a 2) (pow b 2))

simplify3.0s

Counts
82 → 82
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0100937
1227811
2704649
33729641
done5000617

prune147.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (* b b) (+ 3.0 a))
1.3b
(* (* b b) (+ 3.0 a))
3.4b
(- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
32.3b
(/ (- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite334.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
21×*-un-lft-identity
18×times-frac
17×add-cube-cbrt
16×add-exp-log add-cbrt-cube
15×difference-of-squares
14×pow1
8×associate-*r*
6×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod associate-/l* add-log-exp
5×unpow-prod-down sqr-pow
4×associate-*r/ associate--r+
3×flip3-- associate-/r* flip--
2×flip3-+ associate-*l* associate-/r/ *-commutative flip-+ associate-/l/ distribute-lft-out unswap-sqr
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
4 → 111
Calls
4 calls:
29.0ms
(* (* b b) (+ 3.0 a))
29.0ms
(* (* b b) (+ 3.0 a))
73.0ms
(- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
198.0ms
(/ (- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series940.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (* b b) (+ 3.0 a))
35.0ms
(* (* b b) (+ 3.0 a))
465.0ms
(- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
407.0ms
(/ (- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify1.1s

Counts
123 → 123
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02156827
15946605
224536041
done50015275

prune426.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes71.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02645
13545
done3545

end0.0ms

sample1.5s

Algorithm
intervals
Results
973.0ms20101×body80valid