Details

Time bar (total: 10.7s)

sample52.0ms

Algorithm
intervals
Results
35.0ms620×body80valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01829
15129
213429
331729
469429
5146729
6319429
done500029

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

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))

rewrite58.0ms

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:
24.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
14.0ms
(* (* a a) (- 1.0 a))
5.0ms
(pow (+ (* a a) (* b b)) 2.0)
14.0ms
(* (* b b) (+ 3.0 a))

series304.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
54.0ms
(* (* a a) (- 1.0 a))
102.0ms
(pow (+ (* a a) (* b b)) 2.0)
38.0ms
(* (* b b) (+ 3.0 a))

simplify1.1s

Counts
93 → 93
Iterations

Useful iterations: 2 (316.0ms)

IterNodesCost
01791446
14911329
219821209
done50001209

prune245.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* b b) (+ 3.0 a))
0.7b
(* (* b b) (+ 3.0 a))
9.6b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
9.6b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite89.0ms

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:
14.0ms
(* (* b b) (+ 3.0 a))
14.0ms
(* (* b b) (+ 3.0 a))
27.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
30.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series396.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* b b) (+ 3.0 a))
35.0ms
(* (* b b) (+ 3.0 a))
166.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
164.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify567.0ms

Counts
90 → 90
Iterations

Useful iterations: done (564.0ms)

IterNodesCost
01152030
13151800
212351654
done50001650

prune306.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* b b) (+ 3.0 a))
9.6b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
9.6b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
9.6b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1 add-sqr-sqrt
10×*-un-lft-identity
9×add-exp-log sqrt-prod add-cbrt-cube
8×add-cube-cbrt
6×sqrt-div
4×flip3-+ associate-*r* flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 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 → 69
Calls
4 calls:
14.0ms
(* (* b b) (+ 3.0 a))
27.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
29.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
28.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series522.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (* b b) (+ 3.0 a))
160.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
163.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
165.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify573.0ms

Counts
81 → 81
Iterations

Useful iterations: done (570.0ms)

IterNodesCost
01152481
13152174
212352039
done50002033

prune317.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log cbrt-div flip3-+ sqrt-div add-cbrt-cube flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
27.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
29.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
14.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
14.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series696.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
170.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
179.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
173.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify1.1s

Counts
68 → 68
Iterations

Useful iterations: 3 (266.0ms)

IterNodesCost
01142968
12722698
27862502
330782468
done50002468

prune360.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes148.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02290
13090
done3090

end0.0ms

sample1.3s

Algorithm
intervals
Results
999.0ms20313×body80valid