Details

Time bar (total: 18.2s)

sample145.0ms

Algorithm
intervals
Results
100.0ms656×body80valid

simplify5.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01829
15129
215429
341029
4104729
5192929
6397029
done500029

prune6.0ms

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) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.5b
(* (* b b) (+ 3.0 a))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
9×associate-*r*
8×add-cube-cbrt
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 distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 81
Calls
4 calls:
63.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
43.0ms
(* (* a a) (- 1.0 a))
14.0ms
(pow (+ (* a a) (* b b)) 2.0)
42.0ms
(* (* b b) (+ 3.0 a))

series452.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
74.0ms
(* (* a a) (- 1.0 a))
137.0ms
(pow (+ (* a a) (* b b)) 2.0)
43.0ms
(* (* b b) (+ 3.0 a))

simplify1.4s

Counts
93 → 93
Iterations

Useful iterations: 2 (543.0ms)

IterNodesCost
01791446
14821329
218041209
done50001209

prune325.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* b b) (+ 3.0 a))
0.5b
(* (* b b) (+ 3.0 a))
8.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite287.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt associate-*r*
6×pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×flip3-+ sqrt-div associate-*r/ flip-+ add-log-exp
2×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 78
Calls
4 calls:
51.0ms
(* (* b b) (+ 3.0 a))
35.0ms
(* (* b b) (+ 3.0 a))
81.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
115.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series564.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (* b b) (+ 3.0 a))
42.0ms
(* (* b b) (+ 3.0 a))
227.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
237.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify1.2s

Counts
90 → 90
Iterations

Useful iterations: 2 (262.0ms)

IterNodesCost
01152030
13111800
211941654
done50011654

prune485.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

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)))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
2.3b
(* (pow a 2) (pow b 2))

rewrite141.0ms

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:
18.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
47.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
44.0ms
(* 2 (* (pow a 2) (pow b 2)))
27.0ms
(* (pow a 2) (pow b 2))

series234.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
78.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
42.0ms
(* 2 (* (pow a 2) (pow b 2)))
38.0ms
(* (pow a 2) (pow b 2))

simplify1.3s

Counts
113 → 113
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01461649
13731431
212391245
done50001231

prune371.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 2.0 (* (pow a 2) (pow b 2)))
0.1b
(* (* a a) (- 1.0 a))
0.5b
(* (* b b) (+ 3.0 a))
2.3b
(* (pow a 2) (pow b 2))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
34×prod-exp
31×add-sqr-sqrt
21×add-cbrt-cube
18×associate-*r* unswap-sqr
16×pow1
15×*-un-lft-identity
14×unpow-prod-down
13×associate-*l*
12×pow-to-exp pow-exp
11×add-cube-cbrt
10×cbrt-unprod unpow2 sqr-pow
8×pow-prod-down
4×associate-*r/ *-commutative add-log-exp
3×distribute-rgt-in distribute-lft-in
2×sub-neg
1×flip3-- flip3-+ flip-- flip-+ distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 127
Calls
4 calls:
47.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
57.0ms
(* (* a a) (- 1.0 a))
47.0ms
(* (* b b) (+ 3.0 a))
19.0ms
(* (pow a 2) (pow b 2))

series203.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
75.0ms
(* (* a a) (- 1.0 a))
36.0ms
(* (* b b) (+ 3.0 a))
48.0ms
(* (pow a 2) (pow b 2))

simplify1.7s

Counts
139 → 139
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01951528
14911350
218191116
done50011104

prune474.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes192.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02059
12759
done2759

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.6s20728×body80valid