Details

sample42.0ms

Algorithm

intervals

Results

22.0ms

256×

body

valid

simplify5.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
12	4530
11	2981
10	1941
9	1327
8	935
7	744
6	622
5	489
4	295
3	139
2	62
1	35
0	18

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
4.0b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
21.3b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`pow1` `associate-l`
9×	`associate-r`
5×	`flip3-+` `flip-+`
4×	`associate-l/` `prod-exp` `associate-r/` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`associate-/r` `times-frac` `pow-prod-down` `-commutative` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `associate-/l/`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 92

Calls

4 calls:

34.0ms	(* (+ z 6.012459259764103) z)
50.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
58.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
49.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series431.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (+ z 6.012459259764103) z)
93.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
81.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
175.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify1.7s

Counts

104 → 104

Iterations

Iter	Nodes
done	5001
2	2021
1	560
0	196

prune571.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.3b	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
17.6b	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
64×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
60×	`add-cube-cbrt`
18×	`associate-/r*`
15×	`add-cbrt-cube` `add-exp-log`
11×	`associate-/r/`
8×	`pow1` `flip3-+` `flip-+`
7×	`associate-l`
6×	`associate-r` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp` `associate-*l/` `insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`distribute-lft-out`

Counts

4 → 154

Calls

4 calls:

19.0ms	(* (+ z 6.012459259764103) z)
45.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
83.0ms	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
98.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

series441.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (+ z 6.012459259764103) z)
105.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
181.0ms	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
99.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

simplify2.0s

Counts

166 → 166

Iterations

Iter	Nodes
done	5008
2	2769
1	805
0	307

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

7.3b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
16.8b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
16.8b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
16.9b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
66×	`times-frac`
47×	`*-un-lft-identity` `add-cube-cbrt`
42×	`sqrt-prod`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube` `add-exp-log`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`associate-/r*` `flip3-+` `associate-/r/` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 154

Calls

4 calls:

178.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
16.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
71.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
78.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
83.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
134.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify2.5s

Counts

166 → 166

Iterations

Iter	Nodes
done	5001
2	2599
1	748
0	261

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* y (/ (/ (+ (* (+ 0.4917317610505968 (* z 0.0692910599291889)) z) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
16.8b	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
16.8b	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
16.9b	(/ (+ (* (+ 0.4917317610505968 (* z 0.0692910599291889)) z) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

280×	`times-frac`
175×	`add-sqr-sqrt`
150×	`associate-r`
149×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
20×	`sqrt-div`
16×	`associate-/r/`
15×	`add-cbrt-cube` `add-exp-log`
11×	`flip3-+` `flip-+`
8×	`pow1` `div-inv`
7×	`unswap-sqr`
6×	`associate-/r*`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
3×	`associate-l` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 253

Calls

4 calls:

160.0ms	(* y (/ (/ (+ (* (+ 0.4917317610505968 (* z 0.0692910599291889)) z) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
28.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
29.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
72.0ms	(/ (+ (* (+ 0.4917317610505968 (* z 0.0692910599291889)) z) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))

series508.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(* y (/ (/ (+ (* (+ 0.4917317610505968 (* z 0.0692910599291889)) z) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
60.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
66.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
197.0ms	(/ (+ (* (+ 0.4917317610505968 (* z 0.0692910599291889)) z) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))

simplify2.5s

Counts

265 → 265

Iterations

Iter	Nodes
done	5003
2	3643
1	1207
0	421

prune1.5s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes220.0ms

Accuracy

99% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 15.4b

bsearch223.0ms

Steps

Iters	Range		Point
8	94859.26993337883	968457078.2664605	540034.0694215782
9	-0.9226745362972328	-2.2774727908477772e-07	-0.612073400392309

simplify9.0ms

Iterations

Iter	Nodes
done	53
1	53
0	36

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.0s

8000×

body

valid