Details

Time bar (total: 15.6s)

sample75.0ms

Algorithm
intervals
Results
48.0ms659×body80valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01931
15331
216131
349231
4171631
done500031

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize65.0ms

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)
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite169.0ms

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×pow-unpow unpow-prod-down
2×associate-+r+ sub-neg flip3-+ associate-*l* *-commutative flip-+ unswap-sqr
1×pow-to-exp +-commutative sum-log pow-pow flip3-- pow-exp flip-- distribute-lft-out sqr-pow
Counts
4 → 79
Calls
4 calls:
57.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
50.0ms
(* (* a a) (+ 1.0 a))
13.0ms
(pow (+ (* a a) (* b b)) 2.0)
47.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series466.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
77.0ms
(* (* a a) (+ 1.0 a))
143.0ms
(pow (+ (* a a) (* b b)) 2.0)
77.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify2.9s

Counts
91 → 91
Iterations

Useful iterations: 2 (935.0ms)

IterNodesCost
01751540
15521441
238921287
done50001287

prune505.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (* 3.0 a))
0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (+ (* (* a a) 1.0) (pow a 3)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log
9×add-cbrt-cube
8×add-sqr-sqrt add-log-exp
7×*-un-lft-identity add-cube-cbrt
3×distribute-rgt-in pow-unpow sub-neg unpow-prod-down distribute-lft-in associate-*r* pow-prod-down prod-exp cbrt-unprod
2×associate-+r+ flip3-- associate-*r/ flip--
1×pow-to-exp +-commutative sum-log pow-pow flip3-+ diff-log associate-*l* pow-exp *-commutative flip-+ unswap-sqr sqr-pow
Counts
4 → 67
Calls
4 calls:
9.0ms
(- 1.0 (* 3.0 a))
142.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (+ (* (* a a) 1.0) (pow a 3)) (* (* b b) (- 1.0 (* 3.0 a))))))
16.0ms
(pow (+ (* a a) (* b b)) 2.0)
47.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series450.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(- 1.0 (* 3.0 a))
143.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (+ (* (* a a) 1.0) (pow a 3)) (* (* b b) (- 1.0 (* 3.0 a))))))
163.0ms
(pow (+ (* a a) (* b b)) 2.0)
87.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.6s

Counts
79 → 79
Iterations

Useful iterations: 2 (467.0ms)

IterNodesCost
01451436
14321353
223661187
done50001187

prune493.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
8.1b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0)))
8.1b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0)))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
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 sqrt-pow1 flip3-+ flip3-- pow1/2 associate-*l* *-commutative flip-+ flip-- unswap-sqr
Counts
4 → 80
Calls
4 calls:
28.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
33.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
66.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0)))
56.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0)))

series641.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
65.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
235.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0)))
280.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0)))

simplify1.0s

Counts
92 → 92
Iterations

Useful iterations: done (997.0ms)

IterNodesCost
01212304
13382090
218251910
done50021902

prune582.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 2 (* (pow a 2) (pow b 2)))
2.0b
(* (pow a 2) (pow b 2))

rewrite57.0ms

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×add-cbrt-cube associate-*r*
7×*-un-lft-identity add-cube-cbrt
4×pow1 cbrt-unprod
2×pow-prod-down *-commutative add-log-exp
Counts
2 → 76
Calls
2 calls:
21.0ms
(* 2 (* (pow a 2) (pow b 2)))
34.0ms
(* (pow a 2) (pow b 2))

series100.0ms

Counts
2 → 6
Calls
2 calls:
59.0ms
(* 2 (* (pow a 2) (pow b 2)))
41.0ms
(* (pow a 2) (pow b 2))

simplify846.0ms

Counts
82 → 82
Iterations

Useful iterations: done (842.0ms)

IterNodesCost
0100937
1240823
21498649
done5000641

prune290.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes170.0ms

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 (1.0ms)

IterNodesCost
02133
12933
done2933

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.5s20551×body80valid