Details

sample23.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify716.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	21
1	35	21
2	63	21
3	120	21
4	203	21
5	291	21
6	366	21
7	472	21
8	574	21
9	610	21
10	612	21
done	612	21

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
2.2b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
20.5b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`pow1` `associate-l`
9×	`associate-r`
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` `distribute-lft-out` `associate-/l*`

Counts

4 → 88

Calls

4 calls:

10.0ms	(* (+ z 6.012459259764103) z)
10.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
20.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
20.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series299.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (+ z 6.012459259764103) z)
68.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
59.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
127.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify856.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (195.0ms)

Iter	Nodes	Cost
0	190	1538
1	523	1492
2	1791	1282
done	5001	1282

prune303.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.1b	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
15.9b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
21×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `associate-l`
5×	`flip3-+` `flip-+`
4×	`associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `div-inv` `associate-/l/`
1×	`frac-2neg` `associate-*r/` `clear-num` `distribute-lft-out`

Counts

4 → 106

Calls

4 calls:

10.0ms	(* (+ z 6.012459259764103) z)
14.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
38.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
22.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series311.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (+ z 6.012459259764103) z)
69.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
130.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
66.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify860.0ms

Counts

118 → 118

Iterations

Useful iterations: done (855.0ms)

Iter	Nodes	Cost
0	209	2226
1	544	2178
2	1705	1940
done	5000	1926

prune337.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

14.7b	(* (* y (* (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))) (/ (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
15.7b	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
15.7b	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
15.7b	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-div`
25×	`add-exp-log`
24×	`associate-r`
21×	`associate-*r/`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`cbrt-prod` `times-frac` `add-cbrt-cube`
16×	`frac-times` `flip3-+` `flip-+`
13×	`pow1`
12×	`associate-*l/` `prod-exp` `cbrt-unprod`
6×	`pow-prod-down`
4×	`add-log-exp`
3×	`cbrt-undiv` `pow1/3` `div-exp`
2×	`associate-/r/`
1×	`associate-l` `*-commutative` `div-inv`

Counts

4 → 104

Calls

4 calls:

190.0ms	(* (* y (* (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))) (/ (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
5.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
5.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
5.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

series606.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (* y (* (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))) (/ (cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
160.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
161.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
154.0ms	(cbrt (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

simplify1.0s

Counts

116 → 116

Iterations

Useful iterations: 2 (378.0ms)

Iter	Nodes	Cost
0	261	5006
1	785	4868
2	2942	3949
done	5001	3949

prune499.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) y) (* y 0.279195317918525))
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
2.2b	(* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) y)
20.5b	(/ (+ (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) y) (* y 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
9×	`times-frac`
6×	`associate-r` `associate-*l/` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`associate-/r` `associate-/l`
2×	`associate-/r/` `*-commutative` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

15.0ms	(+ (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) y) (* y 0.279195317918525))
11.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
18.0ms	(* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) y)
49.0ms	(/ (+ (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) y) (* y 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series234.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) y) (* y 0.279195317918525))
73.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
48.0ms	(* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) y)
73.0ms	(/ (+ (* (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) y) (* y 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify1.0s

Counts

94 → 94

Iterations

Useful iterations: 2 (245.0ms)

Iter	Nodes	Cost
0	172	1930
1	452	1886
2	1576	1568
done	5001	1568

prune287.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes157.0ms

Accuracy

99.1% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 16.5b

bsearch140.0ms

Steps

Iters	Range		Point
6	0.0591185632533196	0.44834868164545755	0.4426814927734349
9	-511708.7274343749	-0.04390830018224924	-505680.7086753328

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	33	59
1	49	45
done	49	45

end0.0ms

sample494.0ms

Algorithm

intervals

Results

326.0ms

8000×

body

valid