Details

sample40.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify6.5s

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.2b

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
2.4b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
19.5b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

38.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
34.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
47.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
48.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series700.0ms

Counts

4 → 12

Calls

4 calls:

335.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
102.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
75.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
187.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify2.0s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	1926
1	556
0	192

prune686.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
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)))
15.6b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

7.0ms	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
21.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
127.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
60.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series845.0ms

Counts

4 → 12

Calls

4 calls:

373.0ms	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
144.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
209.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
118.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify2.5s

Counts

108 → 108

Iterations

Iter	Nodes
done	5003
2	2064
1	573
0	209

prune809.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize87.0ms

Local error

Found 4 expressions with local error:

5.6b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
15.0b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.0b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.0b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite265.0ms

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` `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 → 150

Calls

4 calls:

152.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
25.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
25.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
57.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series532.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
71.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
81.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
196.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify2.3s

Counts

162 → 162

Iterations

Iter	Nodes
done	5002
2	2577
1	738
0	258

prune1.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize87.0ms

Local error

Found 4 expressions with local error:

15.0b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.0b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.0b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.0b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
21×	`sqrt-prod`
18×	`times-frac`
8×	`sqrt-div`
7×	`pow1`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

21.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
20.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
13.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
48.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series476.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
84.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
108.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
175.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify2.7s

Counts

100 → 100

Iterations

Iter	Nodes
done	5012
3	3773
2	1063
1	365
0	155

prune1.0s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes450.0ms

Accuracy

99.1% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 16.1b

bsearch226.0ms

Steps

Iters	Range		Point
8	595377.2589799166	3378812226.2511864	203544506.32119253
6	-3.236922250557709e+34	-4.17042468654624e+33	-4.2303010413466555e+33

simplify9.0ms

Iterations

Iter	Nodes
done	48
1	48
0	32

end0.0ms

sample1.2s

Algorithm

intervals

Results

936.0ms

8000×

body

valid