Details

Time bar (total: 8.4s)

sample16.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify16.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12817
23717
34117
done4117

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 0.99229 (* x 0.04481))
0.0b
(- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)
0.1b
(* x (+ 0.99229 (* x 0.04481)))
14.8b
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
10×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
6×pow1
4×flip3-+ flip-+
3×associate-*r* associate-*l* associate-/r* associate-/l*
2×associate-*r/ associate-/r/ associate-/l/ difference-of-squares
1×cbrt-undiv +-commutative distribute-rgt-in sub-neg flip3-- frac-2neg distribute-lft-in diff-log div-exp pow-prod-down prod-exp clear-num sum-log *-commutative flip-- cbrt-unprod div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 79
Calls
4 calls:
2.0ms
(+ 0.99229 (* x 0.04481))
32.0ms
(- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)
10.0ms
(* x (+ 0.99229 (* x 0.04481)))
9.0ms
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series249.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ 0.99229 (* x 0.04481))
87.0ms
(- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)
68.0ms
(* x (+ 0.99229 (* x 0.04481)))
61.0ms
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify552.0ms

Counts
91 → 91
Iterations

Useful iterations: 2 (129.0ms)

IterNodesCost
01721656
14481580
216081474
done50001474

prune209.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
0.2b
(/ (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
14.8b
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
14.8b
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×add-cube-cbrt *-un-lft-identity
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×flip3-+ associate-/r* flip-+
11×add-exp-log add-cbrt-cube
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 264
Calls
4 calls:
10.0ms
(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
24.0ms
(/ (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
3.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
3.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series384.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
61.0ms
(/ (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
81.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
82.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify1.4s

Counts
276 → 276
Iterations

Useful iterations: 2 (284.0ms)

IterNodesCost
038412269
193411071
2333010277
done500010277

prune580.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) (+ 2.30753 (* x 0.27061)))
0.2b
(/ (/ 1 (/ (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) (+ 2.30753 (* x 0.27061)))) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
14.8b
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
14.8b
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
1362×times-frac
627×add-sqr-sqrt
625×add-cube-cbrt *-un-lft-identity
441×sqrt-prod
83×associate-/l*
53×associate-/r/
30×div-inv
26×flip3-+ flip-+
25×add-exp-log
15×div-exp add-cbrt-cube
9×associate-/r*
8×sqrt-div
7×cbrt-undiv
6×pow1
4×add-log-exp
3×associate-/l/
2×rem-sqrt-square rec-exp frac-2neg sqrt-pow1 pow1/2 1-exp clear-num
Counts
4 → 641
Calls
4 calls:
8.0ms
(/ (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) (+ 2.30753 (* x 0.27061)))
41.0ms
(/ (/ 1 (/ (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) (+ 2.30753 (* x 0.27061)))) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
3.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
3.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series389.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(/ (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) (+ 2.30753 (* x 0.27061)))
60.0ms
(/ (/ 1 (/ (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) (+ 2.30753 (* x 0.27061)))) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
79.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
81.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify1.1s

Counts
653 → 653
Iterations

Useful iterations: done (1.0s)

IterNodesCost
094035589
1233531596
done500130594

prune884.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* x (+ 0.99229 (* x 0.04481)))
0.2b
(* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))
2.7b
(/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))))
20.7b
(* (/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481)))))) (- 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1
31×add-sqr-sqrt
25×add-exp-log times-frac add-cbrt-cube
24×add-cube-cbrt *-un-lft-identity
22×associate-*l*
19×pow-prod-down
18×associate-*r/
11×prod-exp cbrt-unprod
8×flip3-+ flip-+
7×distribute-rgt-in distribute-lft-in associate-*r* difference-of-squares
6×frac-times
4×flip3-- associate-/r* associate-/r/ pow-sqr pow-prod-up flip-- add-log-exp
3×associate-*l/ *-commutative associate-/l* unswap-sqr
2×cbrt-undiv sub-neg pow-plus div-exp div-inv associate-/l/
1×pow2 frac-2neg swap-sqr clear-num
Counts
4 → 148
Calls
4 calls:
7.0ms
(* x (+ 0.99229 (* x 0.04481)))
19.0ms
(* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))
10.0ms
(/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))))
25.0ms
(* (/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481)))))) (- 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series306.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* x (+ 0.99229 (* x 0.04481)))
39.0ms
(* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))
75.0ms
(/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))))
126.0ms
(* (/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481)))))) (- 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify1.3s

Counts
160 → 160
Iterations

Useful iterations: 2 (279.0ms)

IterNodesCost
02764710
17894439
238803961
done50003961

prune375.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes15.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01831
12631
done2631

end0.0ms

sample334.0ms

Algorithm
intervals
Results
247.0ms8000×body80valid