Details

Time bar (total: 14.3s)

sample37.0ms

Algorithm
intervals
Results
22.0ms620×body80valid

simplify6.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01217
12517
23917
36317
411017
525717
6111817
7495217
done500017

prune2.0ms

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

rewrite40.0ms

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))
7.0ms
(* 4.0 (* b b))
25.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
5.0ms
(pow (+ (* a a) (* b b)) 2.0)

series212.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (* a a) (* b b))
23.0ms
(* 4.0 (* b b))
64.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
99.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify509.0ms

Counts
70 → 70
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
0117931
1322854
21256778
done5001778

prune170.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
15.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
15.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
15.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
123.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
15.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
15.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
17.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series663.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
176.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
177.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
177.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify2.1s

Counts
99 → 99
Iterations

Useful iterations: 3 (502.0ms)

IterNodesCost
01213626
12663295
29423029
337662636
done50002636

prune318.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

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)))
2.6b
(* (pow a 2) (pow b 2))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
28×prod-exp
26×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
13×*-un-lft-identity
12×pow-to-exp pow-exp add-log-exp
11×associate-*l*
10×add-cbrt-cube unpow2 sqr-pow
9×associate-*r*
8×add-cube-cbrt
5×pow1
4×cbrt-unprod
3×diff-log sum-log
2×pow-prod-down *-commutative distribute-lft-out--
1×sub-neg flip3-- associate--l+ flip-- distribute-lft-out difference-of-squares
Counts
3 → 94
Calls
3 calls:
147.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
13.0ms
(* 2 (* (pow a 2) (pow b 2)))
9.0ms
(* (pow a 2) (pow b 2))

series118.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
34.0ms
(* 2 (* (pow a 2) (pow b 2)))
31.0ms
(* (pow a 2) (pow b 2))

simplify715.0ms

Counts
103 → 103
Iterations

Useful iterations: 2 (117.0ms)

IterNodesCost
01421478
13291344
214641144
done50011144

prune204.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 2.0 (* (pow a 2) (pow b 2)))
0.0b
(* 4.0 (* b b))
0.0b
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
2.6b
(* (pow a 2) (pow b 2))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
44×add-exp-log
31×prod-exp
27×add-sqr-sqrt
17×unswap-sqr
16×add-cbrt-cube
14×unpow-prod-down associate-*l*
12×pow-to-exp pow-exp
11×pow1
10×add-cube-cbrt *-un-lft-identity associate-*r* unpow2 sqr-pow
9×add-log-exp
7×cbrt-unprod
5×pow-prod-down
3×sum-log *-commutative
1×+-commutative associate-+l+ flip3-+ flip-+
Counts
4 → 108
Calls
4 calls:
11.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
9.0ms
(* 4.0 (* b b))
28.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
9.0ms
(* (pow a 2) (pow b 2))

series159.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
24.0ms
(* 4.0 (* b b))
64.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
33.0ms
(* (pow a 2) (pow b 2))

simplify809.0ms

Counts
120 → 120
Iterations

Useful iterations: 2 (144.0ms)

IterNodesCost
01601554
13991400
217911118
done50011118

prune234.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes112.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01552
11952
done1952

end0.0ms

sample1.1s

Algorithm
intervals
Results
747.0ms20313×body80valid