Details

Time bar (total: 21.7s)

sample104.0ms

Algorithm
intervals
Results
72.0ms680×body80valid

simplify6.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01931
15331
216031
345131
4122331
5246931
6461831
done500131

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

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)
0.6b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite168.0ms

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:
68.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
42.0ms
(* (* a a) (+ 1.0 a))
11.0ms
(pow (+ (* a a) (* b b)) 2.0)
43.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series482.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
57.0ms
(* (* a a) (+ 1.0 a))
191.0ms
(pow (+ (* a a) (* b b)) 2.0)
75.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.3s

Counts
91 → 91
Iterations

Useful iterations: 2 (524.0ms)

IterNodesCost
01751540
14791431
218381287
done50001287

prune397.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1 add-exp-log
16×add-cbrt-cube
13×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt associate-*r*
7×pow-prod-down prod-exp cbrt-unprod
6×associate-*r/
5×associate-*l*
4×add-log-exp
3×distribute-rgt-in unpow-prod-down pow-unpow distribute-lft-in *-commutative
2×sub-neg flip3-- associate-*l/ flip-- unswap-sqr
1×pow-to-exp pow-pow flip3-+ pow-exp flip-+ distribute-lft-out sqr-pow
Counts
4 → 85
Calls
4 calls:
21.0ms
(* b (- 1.0 (* 3.0 a)))
47.0ms
(* (* b (- 1.0 (* 3.0 a))) b)
34.0ms
(* (* a a) (+ 1.0 a))
16.0ms
(pow (+ (* a a) (* b b)) 2.0)

series408.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* b (- 1.0 (* 3.0 a)))
69.0ms
(* (* b (- 1.0 (* 3.0 a))) b)
75.0ms
(* (* a a) (+ 1.0 a))
170.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify1.7s

Counts
97 → 97
Iterations

Useful iterations: 2 (359.0ms)

IterNodesCost
01581115
13941066
21339924
done5000924

prune397.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* b b) (- 1.0 (* 3.0 a)))
0.6b
(* (* b b) (- 1.0 (* 3.0 a)))
9.6b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.6b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite257.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-div associate-*r/ add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 associate-*l* *-commutative flip-- flip-+ unswap-sqr
Counts
4 → 80
Calls
4 calls:
45.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
35.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
81.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
93.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series639.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
69.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
269.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
236.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify1.6s

Counts
92 → 92
Iterations

Useful iterations: 2 (350.0ms)

IterNodesCost
01202304
13222090
211531892
done50001892

prune512.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* b b) (- 1.0 (* 3.0 a)))
10.1b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.1b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.1b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×add-log-exp
3×flip3-+ pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod flip-+
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 64
Calls
4 calls:
58.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
43.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
68.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
40.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series886.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
265.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
244.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
294.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify1.2s

Counts
76 → 76
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01262764
13402636
211662390
done50012330

prune505.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes260.0ms

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
02031
12931
done2931

end0.0ms

sample4.0s

Algorithm
intervals
Results
3.3s20632×body80valid