Details

sample42.0ms

Algorithm

intervals

Results

28.0ms

256×

body

valid

simplify5.7s

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
4.3b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
19.7b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite5.1s

Algorithm

rewrite-expression-head

Rules

253×	`*-un-lft-identity`
119×	`distribute-lft-out`
100×	`associate-l`
96×	`times-frac`
68×	`add-sqr-sqrt`
62×	`associate-r`
48×	`add-cube-cbrt`
16×	`associate-/l*`
15×	`add-cbrt-cube` `add-exp-log`
10×	`pow1` `*-commutative` `unswap-sqr`
6×	`associate-/r*`
5×	`flip3-+` `flip-+`
4×	`associate-l/` `prod-exp` `associate-r/` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow-prod-down`
2×	`distribute-rgt-in` `cbrt-undiv` `+-commutative` `distribute-lft-in` `div-exp` `associate-/r/` `associate-/l/`
1×	`clear-num` `frac-2neg` `div-inv`

Counts

4 → 211

Calls

4 calls:

26.0ms	(* (+ z 6.012459259764103) z)
84.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
1.3s	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
3.7s	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series479.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (+ z 6.012459259764103) z)
93.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
103.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
206.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify2.3s

Counts

223 → 223

Iterations

Iter	Nodes
done	5000
2	2427
1	702
0	256

prune863.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

8.3b	(* (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ y (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)))

rewrite5.6s

Algorithm

rewrite-expression-head

Rules

943×	`*-un-lft-identity`
442×	`distribute-lft-out`
354×	`sqrt-prod`
351×	`associate-/r*`
325×	`associate-l`
315×	`frac-times`
218×	`add-sqr-sqrt`
186×	`add-cube-cbrt` `associate-/l*`
165×	`times-frac`
40×	`clear-num`
39×	`frac-2neg`
34×	`associate-/l/`
33×	`associate-r`
22×	`flip3-+` `flip-+`
21×	`associate-*l/`
18×	`add-cbrt-cube` `add-exp-log`
15×	`associate-*r/`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`associate-/r/`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `un-div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 616

Calls

4 calls:

3.8s	(* (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
142.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
181.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
1.4s	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
77.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
63.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
186.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify2.5s

Counts

628 → 628

Iterations

Iter	Nodes
done	5000
1	1719
0	492

prune2.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize121.0ms

Local error

Found 4 expressions with local error:

14.7b	(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)))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

210×	`*-un-lft-identity`
104×	`distribute-lft-out`
66×	`sqrt-prod`
63×	`times-frac`
62×	`associate-l`
36×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
9×	`associate-/r*`
8×	`sqrt-div`
7×	`pow1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`flip3-+` `flip-+`
4×	`insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 153

Calls

4 calls:

189.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
176.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
188.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
1.5s	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
64.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
86.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
176.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify2.7s

Counts

165 → 165

Iterations

Iter	Nodes
done	5002
3	3856
2	1072
1	367
0	157

prune803.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.0692910599291889 y) (- (* 0.07512208616047561 (/ y z)) (* (/ 0.40462203869992125 z) (/ y z))))
0.1b	(* (/ 0.40462203869992125 z) (/ y z))
0.4b	(* 0.07512208616047561 (/ y z))
3.9b	(- (* 0.07512208616047561 (/ y z)) (* (/ 0.40462203869992125 z) (/ y z)))

rewrite901.0ms

Algorithm

rewrite-expression-head

Rules

1160×	`associate-/l*`
1111×	`frac-sub`
1067×	`associate-*r/`
1042×	`associate-/r*`
972×	`frac-times`
910×	`*-un-lft-identity`
816×	`add-sqr-sqrt`
730×	`add-cube-cbrt`
472×	`clear-num`
346×	`frac-2neg`
244×	`un-div-inv`
115×	`associate-*l/`
71×	`times-frac`
60×	`associate-r`
33×	`associate-l`
32×	`sub-div`
28×	`unswap-sqr`
21×	`add-cbrt-cube` `add-exp-log`
20×	`distribute-rgt-out--`
15×	`difference-of-squares`
13×	`distribute-lft-out--`
11×	`add-log-exp`
10×	`distribute-lft-out`
8×	`pow1`
6×	`prod-exp` `cbrt-unprod`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`*-commutative` `insert-posit16`
2×	`associate-+r+` `sum-log` `sub-neg` `diff-log` `pow-prod-down`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip3--` `flip-+` `flip--`

Counts

4 → 1414

Calls

4 calls:

455.0ms	(+ (* 0.0692910599291889 y) (- (* 0.07512208616047561 (/ y z)) (* (/ 0.40462203869992125 z) (/ y z))))
49.0ms	(* (/ 0.40462203869992125 z) (/ y z))
19.0ms	(* 0.07512208616047561 (/ y z))
268.0ms	(- (* 0.07512208616047561 (/ y z)) (* (/ 0.40462203869992125 z) (/ y z)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(+ (* 0.0692910599291889 y) (- (* 0.07512208616047561 (/ y z)) (* (/ 0.40462203869992125 z) (/ y z))))
42.0ms	(* (/ 0.40462203869992125 z) (/ y z))
23.0ms	(* 0.07512208616047561 (/ y z))
119.0ms	(- (* 0.07512208616047561 (/ y z)) (* (/ 0.40462203869992125 z) (/ y z)))

simplify2.3s

Counts

1426 → 1426

Iterations

Iter	Nodes
done	5000
0	2611

prune5.4s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes325.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.1b

bsearch224.0ms

Steps

Iters	Range		Point
8	315.1021581913647	2484744.5477507794	727958.1035308853
5	-670394737327.6124	-271299687514.82303	-273974326636.0899

simplify8.0ms

Iterations

Iter	Nodes
done	51
1	51
0	34

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.7s

8000×

body

valid