Details

Time bar (total: 16.8s)

sample101.0ms

Algorithm
intervals
Results
64.0ms626×body80valid

simplify5.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01931
15331
216031
345131
4122331
5246931
6461831
done500131

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

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)
0.9b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite164.0ms

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×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 sqr-pow
Counts
4 → 79
Calls
4 calls:
72.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
33.0ms
(* (* a a) (+ 1.0 a))
19.0ms
(pow (+ (* a a) (* b b)) 2.0)
38.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
75.0ms
(* (* a a) (+ 1.0 a))
141.0ms
(pow (+ (* a a) (* b b)) 2.0)
59.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.3s

Counts
91 → 91
Iterations

Useful iterations: 2 (404.0ms)

IterNodesCost
01751540
14791431
218381287
done50001287

prune316.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (+ 1.0 a) (pow a 2)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (+ 1.0 a) (pow a 2))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.9b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×add-exp-log
12×*-un-lft-identity
11×associate-*r* add-cbrt-cube
10×pow1 add-cube-cbrt
7×unpow-prod-down
6×prod-exp add-log-exp
5×associate-*l* unswap-sqr
4×cbrt-unprod
3×distribute-rgt-in pow-unpow distribute-lft-in pow-prod-down sqr-pow
2×pow-to-exp sub-neg associate-+r+ flip3-+ associate-*r/ associate-*l/ pow-exp *-commutative flip-+ unpow2
1×+-commutative flip3-- pow-pow sum-log flip-- distribute-lft-out
Counts
4 → 85
Calls
4 calls:
82.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (+ 1.0 a) (pow a 2)) (* (* b b) (- 1.0 (* 3.0 a))))))
26.0ms
(* (+ 1.0 a) (pow a 2))
11.0ms
(pow (+ (* a a) (* b b)) 2.0)
39.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series458.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (+ 1.0 a) (pow a 2)) (* (* b b) (- 1.0 (* 3.0 a))))))
54.0ms
(* (+ 1.0 a) (pow a 2))
132.0ms
(pow (+ (* a a) (* b b)) 2.0)
77.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.1s

Counts
97 → 97
Iterations

Useful iterations: 2 (372.0ms)

IterNodesCost
01881607
14811504
216781343
done50011343

prune377.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
3.1b
(* (pow a 2) (pow b 2))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
28×prod-exp
25×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×*-un-lft-identity associate-*l* add-cbrt-cube add-log-exp
10×unpow2 sqr-pow
9×add-cube-cbrt associate-*r*
6×pow1
4×sum-log cbrt-unprod
2×+-commutative flip3-+ pow-prod-down *-commutative flip-+
1×associate-+r+ distribute-lft-out
Counts
4 → 101
Calls
4 calls:
42.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
32.0ms
(* 2 (* (pow a 2) (pow b 2)))
19.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
21.0ms
(* (pow a 2) (pow b 2))

series627.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
463.0ms
(* 2 (* (pow a 2) (pow b 2)))
57.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
37.0ms
(* (pow a 2) (pow b 2))

simplify974.0ms

Counts
113 → 113
Iterations

Useful iterations: done (971.0ms)

IterNodesCost
01461649
13731431
212371245
done50011231

prune329.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (/ -1 a) -4.0) (* 4.0 (+ (* (+ 1.0 a) (pow a 2)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (+ 1.0 a) (pow a 2))
0.3b
(pow (/ -1 a) -4.0)
0.9b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
18×*-un-lft-identity
17×add-exp-log unpow-prod-down
16×add-cube-cbrt
11×associate-*r* add-cbrt-cube
10×pow1
9×times-frac
6×prod-exp add-log-exp
5×associate-*l* unswap-sqr
4×cbrt-unprod
3×distribute-rgt-in pow-unpow distribute-lft-in pow-prod-down pow-exp sqr-pow
2×pow-to-exp sub-neg associate-+r+ flip3-+ associate-*r/ associate-*l/ *-commutative flip-+ unpow2
1×+-commutative flip3-- pow-pow div-exp sum-log flip-- div-inv distribute-lft-out
Counts
4 → 96
Calls
4 calls:
35.0ms
(+ (pow (/ -1 a) -4.0) (* 4.0 (+ (* (+ 1.0 a) (pow a 2)) (* (* b b) (- 1.0 (* 3.0 a))))))
52.0ms
(* (+ 1.0 a) (pow a 2))
12.0ms
(pow (/ -1 a) -4.0)
58.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(+ (pow (/ -1 a) -4.0) (* 4.0 (+ (* (+ 1.0 a) (pow a 2)) (* (* b b) (- 1.0 (* 3.0 a))))))
55.0ms
(* (+ 1.0 a) (pow a 2))
202.0ms
(pow (/ -1 a) -4.0)
70.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify935.0ms

Counts
108 → 108
Iterations

Useful iterations: 2 (317.0ms)

IterNodesCost
02251589
15631498
218371323
done50001323

prune343.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes90.0ms

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
02131
12931
done2931

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.3s20293×body80valid