Details

Time bar (total: 5.6s)

sample75.0ms

Algorithm
intervals
Results
47.0ms646×body80valid

simplify69.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05114
115514
243014
3119514
4252614
5500114
done500114

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)
0.5b
(* (* b b) (+ 3.0 a))

rewrite126.0ms

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:
53.0ms
(+ (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))
9.0ms
(pow (+ (* a a) (* b b)) 2.0)
32.0ms
(* (* b b) (+ 3.0 a))

series309.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
51.0ms
(* (* a a) (- 1.0 a))
109.0ms
(pow (+ (* a a) (* b b)) 2.0)
38.0ms
(* (* b b) (+ 3.0 a))

simplify62.0ms

Counts
93 → 93
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0506651
12520583
25001583
done5001583

prune254.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* b b) (+ 3.0 a))
0.5b
(* (* b b) (+ 3.0 a))
10.8b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
10.8b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt associate-*r*
6×pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×flip3-+ sqrt-div associate-*r/ flip-+ add-log-exp
2×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 78
Calls
4 calls:
30.0ms
(* (* b b) (+ 3.0 a))
31.0ms
(* (* b b) (+ 3.0 a))
55.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
57.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series426.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (* b b) (+ 3.0 a))
33.0ms
(* (* b b) (+ 3.0 a))
179.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
173.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify47.0ms

Counts
90 → 90
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0321932
11454858
25002856
done5002856

prune520.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* b b) (+ 3.0 a))
11.4b
(cbrt (+ (* a a) (* b b)))
11.4b
(cbrt (+ (* a a) (* b b)))
11.4b
(cbrt (+ (* a a) (* b b)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cbrt-cube
8×add-cube-cbrt
6×cbrt-div
4×flip3-+ associate-*r* flip-+ add-log-exp
3×pow1/3 pow-prod-down prod-exp cbrt-unprod
2×associate-*r/
1×distribute-rgt-in distribute-lft-in associate-*l* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 63
Calls
4 calls:
32.0ms
(* (* b b) (+ 3.0 a))
5.0ms
(cbrt (+ (* a a) (* b b)))
5.0ms
(cbrt (+ (* a a) (* b b)))
5.0ms
(cbrt (+ (* a a) (* b b)))

series320.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (* b b) (+ 3.0 a))
94.0ms
(cbrt (+ (* a a) (* b b)))
93.0ms
(cbrt (+ (* a a) (* b b)))
96.0ms
(cbrt (+ (* a a) (* b b)))

simplify41.0ms

Counts
75 → 75
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0271484
11307442
25002433
done5002433

prune309.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* a a) (- (pow 1.0 3) (pow a 3)))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.5b
(* (* b b) (+ 3.0 a))
1.7b
(/ (* (* a a) (- (pow 1.0 3) (pow a 3))) (+ (* 1.0 1.0) (+ (* a a) (* 1.0 a))))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
29×associate-*r*
24×add-exp-log
23×add-cbrt-cube
22×*-un-lft-identity
16×difference-of-squares
15×pow1 unpow-prod-down
12×cube-prod
10×add-cube-cbrt
9×prod-exp cbrt-unprod sqr-pow
6×associate-*r/ pow-prod-down
5×distribute-lft-out--
4×add-log-exp
3×cbrt-undiv distribute-rgt-in pow-unpow distribute-lft-in times-frac div-exp associate-/r*
2×sub-neg flip3-- flip3-+ associate-*l* associate-/r/ *-commutative flip-- flip-+ associate-/l/ unswap-sqr
1×difference-cubes pow-to-exp pow-pow frac-2neg pow-exp clear-num div-inv distribute-lft-out associate-/l*
Counts
4 → 115
Calls
4 calls:
85.0ms
(* (* a a) (- (pow 1.0 3) (pow a 3)))
9.0ms
(pow (+ (* a a) (* b b)) 2.0)
29.0ms
(* (* b b) (+ 3.0 a))
70.0ms
(/ (* (* a a) (- (pow 1.0 3) (pow a 3))) (+ (* 1.0 1.0) (+ (* a a) (* 1.0 a))))

series428.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(* (* a a) (- (pow 1.0 3) (pow a 3)))
105.0ms
(pow (+ (* a a) (* b b)) 2.0)
33.0ms
(* (* b b) (+ 3.0 a))
178.0ms
(/ (* (* a a) (- (pow 1.0 3) (pow a 3))) (+ (* 1.0 1.0) (+ (* a a) (* 1.0 a))))

simplify107.0ms

Counts
127 → 127
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
07181002
14177853
25002839
done5002839

prune427.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes154.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03026
13026
done3026

end0.0ms

sample1.4s

Algorithm
intervals
Results
983.0ms20589×body80valid