Details

Time bar (total: 16.2s)

sample47.0ms

Algorithm
intervals
Results
30.0ms717×body80valid

simplify4.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01217
12517
23917
36317
410917
525917
683117
7372717
done500017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* a a) (* b b))
0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b
(* 4.0 (* b b))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log
9×add-cbrt-cube
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt *-un-lft-identity
3×unpow-prod-down pow-unpow associate-*l* pow-prod-down prod-exp cbrt-unprod
2×+-commutative flip3-+ sum-log flip-+
1×pow-to-exp pow-pow associate-*r* pow-exp *-commutative unswap-sqr sqr-pow
Counts
4 → 58
Calls
4 calls:
3.0ms
(+ (* a a) (* b b))
25.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
7.0ms
(* 4.0 (* b b))
5.0ms
(pow (+ (* a a) (* b b)) 2.0)

series240.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* a a) (* b b))
65.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
33.0ms
(* 4.0 (* b b))
108.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify2.1s

Counts
70 → 70
Iterations

Useful iterations: 2 (121.0ms)

IterNodesCost
0117931
1317854
21043778
34092778
done5001778

prune179.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
0.0b
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
2.0b
(* (pow a 2) (pow b 2))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
28×prod-exp
27×add-sqr-sqrt
16×unswap-sqr
15×add-log-exp
14×unpow-prod-down *-un-lft-identity
12×pow-to-exp pow-exp
11×associate-*l* add-cbrt-cube
10×unpow2 sqr-pow
9×add-cube-cbrt associate-*r*
6×pow1
4×sum-log cbrt-unprod
3×diff-log
2×pow-prod-down *-commutative distribute-lft-out--
1×+-commutative sub-neg flip3-- flip3-+ associate--l+ flip-- flip-+ distribute-lft-out difference-of-squares
Counts
4 → 105
Calls
4 calls:
6.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
11.0ms
(* 2 (* (pow a 2) (pow b 2)))
147.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
13.0ms
(* (pow a 2) (pow b 2))

series187.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
37.0ms
(* 2 (* (pow a 2) (pow b 2)))
58.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
33.0ms
(* (pow a 2) (pow b 2))

simplify1000.0ms

Counts
117 → 117
Iterations

Useful iterations: 2 (253.0ms)

IterNodesCost
01571770
13831595
215051379
done50001379

prune265.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (pow a 2) (pow b 2))
2.0b
(* (pow a 2) (pow b 2))
14.7b
(sqrt (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))))
14.7b
(sqrt (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
32×unswap-sqr
28×add-exp-log unpow-prod-down
20×unpow2 sqr-pow
18×*-un-lft-identity prod-exp
16×associate-*r* associate-*l*
14×add-cube-cbrt
12×pow-to-exp pow-exp
8×sqrt-prod add-cbrt-cube
6×pow1
4×sqrt-div add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow-prod-down *-commutative cbrt-unprod flip-+ distribute-lft-out
Counts
4 → 134
Calls
4 calls:
10.0ms
(* (pow a 2) (pow b 2))
9.0ms
(* (pow a 2) (pow b 2))
30.0ms
(sqrt (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))))
29.0ms
(sqrt (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))))

series225.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (pow a 2) (pow b 2))
33.0ms
(* (pow a 2) (pow b 2))
80.0ms
(sqrt (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))))
79.0ms
(sqrt (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))))

simplify3.2s

Counts
146 → 146
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
01132138
12571854
210181546
339891530
done50001530

prune641.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* b b))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
3.2b
(exp (log (pow (+ (* a a) (* b b)) 2.0)))
24.9b
(log (pow (+ (* a a) (* b b)) 2.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
14×log-prod
13×add-sqr-sqrt
12×add-exp-log add-cube-cbrt *-un-lft-identity
10×pow1
9×unpow-prod-down add-cbrt-cube
7×exp-sum
4×exp-prod add-log-exp
3×pow-unpow rem-log-exp associate-*l* pow-prod-down prod-exp cbrt-unprod sqr-pow
2×pow-to-exp pow-exp log-pow
1×pow-pow associate-*r* *-commutative rem-exp-log unswap-sqr
Counts
4 → 73
Calls
4 calls:
9.0ms
(* 4.0 (* b b))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
5.0ms
(exp (log (pow (+ (* a a) (* b b)) 2.0)))
5.0ms
(log (pow (+ (* a a) (* b b)) 2.0))

series320.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* 4.0 (* b b))
100.0ms
(pow (+ (* a a) (* b b)) 2.0)
99.0ms
(exp (log (pow (+ (* a a) (* b b)) 2.0)))
96.0ms
(log (pow (+ (* a a) (* b b)) 2.0))

simplify1.5s

Counts
85 → 85
Iterations

Useful iterations: 3 (317.0ms)

IterNodesCost
01241084
12501002
2644901
31968878
done5000878

prune209.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes127.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01217
11517
done1517

end0.0ms

sample1.2s

Algorithm
intervals
Results
796.0ms20641×body80valid