Details

Time bar (total: 20.8s)

sample112.0ms

Algorithm
intervals
Results
74.0ms680×body80valid

simplify5.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01829
15129
215429
341029
4104729
5192929
6397029
done500029

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

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)
0.7b
(* (* b b) (+ 3.0 a))

rewrite183.0ms

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:
79.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
44.0ms
(* (* a a) (- 1.0 a))
12.0ms
(pow (+ (* a a) (* b b)) 2.0)
45.0ms
(* (* b b) (+ 3.0 a))

series379.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
68.0ms
(* (* a a) (- 1.0 a))
139.0ms
(pow (+ (* a a) (* b b)) 2.0)
36.0ms
(* (* b b) (+ 3.0 a))

simplify1.3s

Counts
93 → 93
Iterations

Useful iterations: 2 (498.0ms)

IterNodesCost
01791446
14821329
218041209
done50001209

prune333.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* b b) (+ 3.0 a))
25.5b
(cbrt (* (* a a) (- 1.0 a)))
25.5b
(cbrt (* (* a a) (- 1.0 a)))
25.5b
(cbrt (* (* a a) (- 1.0 a)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log add-cbrt-cube
8×associate-*r/
7×*-un-lft-identity
6×add-sqr-sqrt cbrt-div
5×add-cube-cbrt
4×associate-*r* add-log-exp
3×cbrt-prod flip3-- pow1/3 pow-prod-down prod-exp flip-- cbrt-unprod
1×distribute-rgt-in distribute-lft-in flip3-+ associate-*l* *-commutative flip-+ distribute-lft-out unswap-sqr
Counts
4 → 57
Calls
4 calls:
41.0ms
(* (* b b) (+ 3.0 a))
36.0ms
(cbrt (* (* a a) (- 1.0 a)))
20.0ms
(cbrt (* (* a a) (- 1.0 a)))
26.0ms
(cbrt (* (* a a) (- 1.0 a)))

series377.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (* b b) (+ 3.0 a))
110.0ms
(cbrt (* (* a a) (- 1.0 a)))
102.0ms
(cbrt (* (* a a) (- 1.0 a)))
124.0ms
(cbrt (* (* a a) (- 1.0 a)))

simplify2.6s

Counts
69 → 69
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01221068
13211034
21032905
33656788
done5000755

prune365.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* b b) (+ 3.0 a))
10.2b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
10.2b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
10.2b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cbrt-cube
8×add-cube-cbrt
6×cbrt-div
4×flip3-+ associate-*r* flip-+ add-log-exp
3×pow1/3 pow-prod-down prod-exp cbrt-unprod
2×associate-*r/
1×distribute-rgt-in distribute-lft-in associate-*l* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 63
Calls
4 calls:
32.0ms
(* (* b b) (+ 3.0 a))
32.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
38.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
44.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series710.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (* b b) (+ 3.0 a))
200.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
214.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
262.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify1.1s

Counts
75 → 75
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01222535
13302399
212082156
done50002111

prune431.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize90.0ms

Local error

Found 4 expressions with local error:

10.2b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
10.2b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
10.2b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
10.2b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log flip3-+ pow1/3 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 52
Calls
4 calls:
43.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
49.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
51.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
52.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series876.0ms

Counts
4 → 12
Calls
4 calls:
238.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
218.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
204.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
216.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify2.1s

Counts
64 → 64
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0803004
12012848
26152580
328242520
done50022516

prune450.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes207.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02148
12948
done2948

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.9s20632×body80valid