Details

Time bar (total: 13.1s)

sample41.0ms

Algorithm
intervals
Results
26.0ms660×body80valid

simplify3.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01217
12517
23917
36317
410917
524517
681517
7374717
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
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b
(+ (* a a) (* b b))
0.0b
(* 4.0 (* b b))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite39.0ms

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:
24.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
3.0ms
(+ (* a a) (* b b))
6.0ms
(* 4.0 (* b b))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series225.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
26.0ms
(+ (* a a) (* b b))
24.0ms
(* 4.0 (* b b))
108.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify2.0s

Counts
70 → 70
Iterations

Useful iterations: 2 (119.0ms)

IterNodesCost
0117931
1317838
21046778
34057778
done5000778

prune170.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
19.5b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.5b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.5b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
73×cbrt-prod
46×add-sqr-sqrt
29×unpow-prod-down
22×add-cube-cbrt *-un-lft-identity
16×unswap-sqr
15×sqr-pow
11×pow1
10×swap-sqr associate-*r* associate-*l*
9×pow1/3
6×add-exp-log
4×add-cbrt-cube add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 109
Calls
4 calls:
38.0ms
(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series772.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
336.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
148.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
146.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify2.0s

Counts
121 → 121
Iterations

Useful iterations: 4 (1.0s)

IterNodesCost
01192918
12082763
25052621
313882425
437492413
done50002413

prune356.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

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))))) 1.0)
0.0b
(* 2 (* (pow a 2) (pow b 2)))
3.0b
(* (pow a 2) (pow b 2))

rewrite172.0ms

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))))
143.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
10.0ms
(* 2 (* (pow a 2) (pow b 2)))
9.0ms
(* (pow a 2) (pow b 2))

series177.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
52.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
39.0ms
(* 2 (* (pow a 2) (pow b 2)))
32.0ms
(* (pow a 2) (pow b 2))

simplify785.0ms

Counts
117 → 117
Iterations

Useful iterations: done (782.0ms)

IterNodesCost
01571770
13831595
215021379
done50001377

prune255.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 2 (* a a))
0.0b
(- (+ (* (* b b) (+ 4.0 (* 2 (* a a)))) (pow a 4)) 1.0)
0.0b
(+ (* (* b b) (+ 4.0 (* 2 (* a a)))) (pow a 4))
1.0b
(* (* b b) (+ 4.0 (* 2 (* a a))))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1 add-exp-log add-cbrt-cube
11×add-log-exp
10×add-sqr-sqrt
8×*-un-lft-identity
6×add-cube-cbrt pow-prod-down prod-exp cbrt-unprod
4×associate-*r* associate-*l*
2×distribute-rgt-in associate-+l+ distribute-lft-in flip3-+ diff-log associate-*r/ sum-log *-commutative flip-+ unswap-sqr
1×+-commutative sub-neg flip3-- associate--l+ flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 71
Calls
4 calls:
6.0ms
(* 2 (* a a))
91.0ms
(- (+ (* (* b b) (+ 4.0 (* 2 (* a a)))) (pow a 4)) 1.0)
11.0ms
(+ (* (* b b) (+ 4.0 (* 2 (* a a)))) (pow a 4))
14.0ms
(* (* b b) (+ 4.0 (* 2 (* a a))))

series263.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* 2 (* a a))
83.0ms
(- (+ (* (* b b) (+ 4.0 (* 2 (* a a)))) (pow a 4)) 1.0)
78.0ms
(+ (* (* b b) (+ 4.0 (* 2 (* a a)))) (pow a 4))
78.0ms
(* (* b b) (+ 4.0 (* 2 (* a a))))

simplify771.0ms

Counts
83 → 83
Iterations

Useful iterations: 2 (204.0ms)

IterNodesCost
01361387
13751253
215591163
done50001163

prune174.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes120.0ms

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
821.0ms20612×body80valid