Details

sample62.0ms

Algorithm

intervals

Results

32.0ms

256×

body

valid

simplify13.0s

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.2b

localize149.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
5.0b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
20.3b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite392.0ms

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:

42.0ms	(* (+ z 6.012459259764103) z)
52.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
181.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
112.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series518.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (+ z 6.012459259764103) z)
98.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
99.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
234.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify4.3s

Counts

104 → 104

Iterations

Iter	Nodes
done	5003
2	1995
1	560
0	196

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize213.0ms

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	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
17.0b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
17.0b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite673.0ms

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:

385.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
184.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
43.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
35.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series594.0ms

Counts

4 → 12

Calls

4 calls:

263.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
169.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
77.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
84.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify5.6s

Counts

166 → 166

Iterations

Iter	Nodes
done	5003
2	2707
1	752
0	261

prune2.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize226.0ms

Local error

Found 4 expressions with local error:

0.1b	(* y (/ (/ (+ (* z (+ (* 0.0692910599291889 z) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))) (sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))))
16.8b	(/ (+ (* z (+ (* 0.0692910599291889 z) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304)))
17.0b	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))
17.0b	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))

rewrite663.0ms

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:

355.0ms	(* y (/ (/ (+ (* z (+ (* 0.0692910599291889 z) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))) (sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))))
117.0ms	(/ (+ (* z (+ (* 0.0692910599291889 z) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304)))
60.0ms	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))
60.0ms	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))

series581.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(* y (/ (/ (+ (* z (+ (* 0.0692910599291889 z) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))) (sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))))
201.0ms	(/ (+ (* z (+ (* 0.0692910599291889 z) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304)))
56.0ms	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))
67.0ms	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))

simplify6.9s

Counts

265 → 265

Iterations

Iter	Nodes
done	5000
2	3624
1	1202
0	420

prune3.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize387.0ms

Local error

Found 4 expressions with local error:

17.0b	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))
17.0b	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))
17.0b	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))
17.0b	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

30.0ms	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))
50.0ms	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))
60.0ms	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))
61.0ms	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))

series292.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))
73.0ms	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))
75.0ms	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))
73.0ms	(sqrt (+ (* z (+ 6.012459259764103 z)) 3.350343815022304))

simplify4.1s

Counts

76 → 76

Iterations

Iter	Nodes
done	5002
3	2103
2	475
1	143
0	59

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes654.0ms

Accuracy

99.2% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.3b

bsearch278.0ms

Steps

Iters	Range		Point
8	32.81305289360078	23716.851585869685	23415.342663009633
7	-1128039971029451.0	-46788795361090.23	-47430921588347.03

simplify45.0ms

Iterations

Iter	Nodes
done	57
1	57
0	40

end0.0ms

sample1.3s

Algorithm

intervals

Results

977.0ms

8000×

body

valid