Details

Time bar (total: 8.8s)

sample17.0ms

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))
0.1b
(* x (+ 0.99229 (* x 0.04481)))
15.8b
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
9×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
6×pow1
5×flip3-+ flip-+
3×associate-*r* associate-*l* associate-/r* associate-/l*
2×+-commutative associate-*r/ sum-log associate-/r/ associate-/l/
1×cbrt-undiv distribute-rgt-in frac-2neg distribute-lft-in div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod div-inv unswap-sqr
Counts
4 → 75
Calls
4 calls:
2.0ms
(+ 0.99229 (* x 0.04481))
2.0ms
(+ 2.30753 (* x 0.27061))
7.0ms
(* x (+ 0.99229 (* x 0.04481)))
13.0ms
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series199.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ 0.99229 (* x 0.04481))
38.0ms
(+ 2.30753 (* x 0.27061))
69.0ms
(* x (+ 0.99229 (* x 0.04481)))
58.0ms
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify2.3s

Counts
87 → 87
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
01551315
13951267
212171163
342771161
done50001161

prune204.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

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))))))
15.7b
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
15.7b
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite54.0ms

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:
9.0ms
(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
22.0ms
(/ (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
5.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
3.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series381.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
59.0ms
(/ (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
79.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
86.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify1.0s

Counts
276 → 276
Iterations

Useful iterations: done (995.0ms)

IterNodesCost
038412269
193110977
2237010279
done500110277

prune553.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

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))))
1.4b
(/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))))
21.2b
(* (/ (+ 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)))))

rewrite69.0ms

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)))
20.0ms
(* (* 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))))))
24.0ms
(* (/ (+ 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)))))

series296.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* x (+ 0.99229 (* x 0.04481)))
40.0ms
(* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))
73.0ms
(/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))))
117.0ms
(* (/ (+ 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)))))

simplify1.1s

Counts
160 → 160
Iterations

Useful iterations: 2 (402.0ms)

IterNodesCost
02764710
17684439
231703961
done50003961

prune353.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.4b
(/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))))
21.2b
(* (/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481)))))) (- 1.0 (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ 0.99229 (* x 0.04481))))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×times-frac
24×add-cube-cbrt *-un-lft-identity
18×associate-*l*
11×add-exp-log add-cbrt-cube
7×difference-of-squares
6×pow1 cbrt-prod
4×flip3-- associate-/r* associate-/r/ flip-- add-log-exp
3×associate-*r* associate-/l*
2×cbrt-undiv distribute-rgt-in frac-times sub-neg distribute-lft-in pow1/3 associate-*r/ div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×frac-2neg flip3-+ pow-prod-down associate-*l/ clear-num *-commutative flip-+
Counts
4 → 102
Calls
4 calls:
0.0ms
(cbrt x)
0.0ms
(cbrt x)
12.0ms
(/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))))
24.0ms
(* (/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481)))))) (- 1.0 (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ 0.99229 (* x 0.04481))))))

series562.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(cbrt x)
180.0ms
(cbrt x)
72.0ms
(/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))))
136.0ms
(* (/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481)))))) (- 1.0 (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ 0.99229 (* x 0.04481))))))

simplify830.0ms

Counts
114 → 114
Iterations

Useful iterations: 2 (283.0ms)

IterNodesCost
02144035
15773974
224403334
done50003334

prune407.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes13.0ms

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
01629
12229
done2229

end0.0ms

sample327.0ms

Algorithm
intervals
Results
238.0ms8000×body80valid