Details

Time bar (total: 24.3s)

sample116.0ms

Algorithm
intervals
Results
51.0ms282×body80valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03037
15537
211637
333737
4113037
done500037

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize79.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (* (+ z 15.234687407) z) 31.4690115749) z)
0.1b
(* (+ (* z 3.13060547623) 11.1667541262) z)
3.1b
(* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
28.4b
(/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

rewrite590.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity
10×pow1
9×associate-*r* associate-*l*
5×flip3-+ flip-+
4×associate-*r/ associate-*l/ prod-exp cbrt-unprod add-log-exp
3×times-frac pow-prod-down associate-/r* *-commutative unswap-sqr
2×cbrt-undiv div-exp associate-/r/ associate-/l/
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num div-inv associate-/l*
Counts
4 → 87
Calls
4 calls:
74.0ms
(* (+ (* (+ z 15.234687407) z) 31.4690115749) z)
54.0ms
(* (+ (* z 3.13060547623) 11.1667541262) z)
233.0ms
(* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
225.0ms
(/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

series1.2s

Counts
4 → 12
Calls
4 calls:
70.0ms
(* (+ (* (+ z 15.234687407) z) 31.4690115749) z)
127.0ms
(* (+ (* z 3.13060547623) 11.1667541262) z)
287.0ms
(* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
765.0ms
(/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

simplify2.8s

Counts
99 → 99
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02082415
16102393
232462049
done50022041

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.8b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (* 1.6453555072203998 (* y b)))
0.2b
(* 1.6453555072203998 (* y b))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
4×add-log-exp
3×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*l* pow-prod-down prod-exp cbrt-unprod
1×+-commutative flip3-+ associate-*r* sum-log *-commutative flip-+
Counts
2 → 29
Calls
2 calls:
13.0ms
(+ x (* 1.6453555072203998 (* y b)))
32.0ms
(* 1.6453555072203998 (* y b))

series108.0ms

Counts
2 → 6
Calls
2 calls:
66.0ms
(+ x (* 1.6453555072203998 (* y b)))
42.0ms
(* 1.6453555072203998 (* y b))

simplify2.8s

Counts
35 → 35
Iterations

Useful iterations: 2 (138.0ms)

IterNodesCost
057314
1152294
2583260
32897260
done5000260

prune375.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.8b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (* (sqrt 1.6453555072203998) (* (sqrt 1.6453555072203998) (* y b))))
0.2b
(* (sqrt 1.6453555072203998) (* y b))
0.2b
(* (sqrt 1.6453555072203998) (* (sqrt 1.6453555072203998) (* y b)))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1 add-exp-log add-cbrt-cube
12×associate-*l*
9×pow-prod-down prod-exp cbrt-unprod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×sqrt-prod
5×add-log-exp
2×associate-*r* *-commutative
1×+-commutative flip3-+ sum-log flip-+
Counts
3 → 56
Calls
3 calls:
17.0ms
(+ x (* (sqrt 1.6453555072203998) (* (sqrt 1.6453555072203998) (* y b))))
35.0ms
(* (sqrt 1.6453555072203998) (* y b))
103.0ms
(* (sqrt 1.6453555072203998) (* (sqrt 1.6453555072203998) (* y b)))

series360.0ms

Counts
3 → 9
Calls
3 calls:
165.0ms
(+ x (* (sqrt 1.6453555072203998) (* (sqrt 1.6453555072203998) (* y b))))
76.0ms
(* (sqrt 1.6453555072203998) (* y b))
119.0ms
(* (sqrt 1.6453555072203998) (* (sqrt 1.6453555072203998) (* y b)))

simplify2.0s

Counts
65 → 65
Iterations

Useful iterations: done (2.0s)

IterNodesCost
081776
1228551
21321491
done5000471

prune540.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 2.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ x (* (* y b) 1.6453555072203998))) (cbrt (+ x (* (* y b) 1.6453555072203998))))
3.2b
(cbrt (+ x (* (* y b) 1.6453555072203998)))
3.2b
(cbrt (+ x (* (* y b) 1.6453555072203998)))
3.2b
(cbrt (+ x (* (* y b) 1.6453555072203998)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
55.0ms
(* (cbrt (+ x (* (* y b) 1.6453555072203998))) (cbrt (+ x (* (* y b) 1.6453555072203998))))
5.0ms
(cbrt (+ x (* (* y b) 1.6453555072203998)))
5.0ms
(cbrt (+ x (* (* y b) 1.6453555072203998)))
6.0ms
(cbrt (+ x (* (* y b) 1.6453555072203998)))

series1.1s

Counts
4 → 12
Calls
4 calls:
272.0ms
(* (cbrt (+ x (* (* y b) 1.6453555072203998))) (cbrt (+ x (* (* y b) 1.6453555072203998))))
290.0ms
(cbrt (+ x (* (* y b) 1.6453555072203998)))
268.0ms
(cbrt (+ x (* (* y b) 1.6453555072203998)))
253.0ms
(cbrt (+ x (* (* y b) 1.6453555072203998)))

simplify1.4s

Counts
99 → 99
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01191997
12781846
29731732
done50011616

prune881.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.8b

regimes2.4s

Accuracy

94.6% (1.3b remaining)

Error of 4.4b against oracle of 3.1b and baseline of 27.1b

bsearch505.0ms

Steps
ItersRangePoint
5
1.0816333686123665e+44
2.6599497145365887e+44
2.4817666994432834e+44
10
-1.1186547819190151e+38
-2.0000046046006454e+25
-1.7564580588938436e+37

simplify16.0ms

Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
04783
17265
done7265

end0.0ms

sample3.4s

Algorithm
intervals
Results
2.5s8874×body80valid