Details

sample23.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify1.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	21
1	35	21
2	64	21
3	143	21
4	276	21
5	400	21
6	481	21
7	564	21
8	728	21
9	949	21
10	955	21
done	955	21

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
4.1b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
17.8b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite133.0ms

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:

19.0ms	(* (+ z 6.012459259764103) z)
26.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
46.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
40.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series274.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (+ z 6.012459259764103) z)
62.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
54.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
117.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify840.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (282.0ms)

Iter	Nodes	Cost
0	190	1538
1	523	1492
2	1881	1284
done	5001	1284

prune265.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* y (+ (* z 0.0692910599291889) 0.4917317610505968))
0.2b	(* (* y (+ (* z 0.0692910599291889) 0.4917317610505968)) z)
17.8b	(/ (+ (* (* y (+ (* z 0.0692910599291889) 0.4917317610505968)) z) (* 0.279195317918525 y)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

20.0ms	(* (+ z 6.012459259764103) z)
24.0ms	(* y (+ (* z 0.0692910599291889) 0.4917317610505968))
38.0ms	(* (* y (+ (* z 0.0692910599291889) 0.4917317610505968)) z)
123.0ms	(/ (+ (* (* y (+ (* z 0.0692910599291889) 0.4917317610505968)) z) (* 0.279195317918525 y)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series287.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (+ z 6.012459259764103) z)
47.0ms	(* y (+ (* z 0.0692910599291889) 0.4917317610505968))
60.0ms	(* (* y (+ (* z 0.0692910599291889) 0.4917317610505968)) z)
133.0ms	(/ (+ (* (* y (+ (* z 0.0692910599291889) 0.4917317610505968)) z) (* 0.279195317918525 y)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify859.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (283.0ms)

Iter	Nodes	Cost
0	194	1830
1	520	1784
2	1878	1516
done	5002	1516

prune271.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.2b	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
15.4b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite176.0ms

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:

20.0ms	(* (+ z 6.012459259764103) z)
25.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
76.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
53.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series300.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (+ z 6.012459259764103) z)
66.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
121.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
65.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify970.0ms

Counts

118 → 118

Iterations

Useful iterations: done (965.0ms)

Iter	Nodes	Cost
0	209	2226
1	540	2178
2	1781	1942
done	5000	1922

prune292.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

7.9b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.7b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.8b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
66×	`times-frac`
47×	`add-cube-cbrt` `*-un-lft-identity`
42×	`sqrt-prod`
24×	`associate-r` `associate-l`
18×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 150

Calls

4 calls:

132.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
15.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
53.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
56.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
48.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
119.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify1.0s

Counts

162 → 162

Iterations

Useful iterations: 2 (377.0ms)

Iter	Nodes	Cost
0	258	4914
1	709	4681
2	2375	4141
done	5001	4141

prune496.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes119.0ms

Accuracy

99% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 16.4b

bsearch125.0ms

Steps

Iters	Range		Point
5	335341194.4438158	882388454.4280733	341189452.0808505
9	-1.1782931510050808e+39	-1.2139019026724813e+32	-1.2323106427377409e+32

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	35	69
1	51	55
done	51	55

end0.0ms

sample545.0ms

Algorithm

intervals

Results

317.0ms

8000×

body

valid