Details

sample56.0ms

Algorithm

intervals

Results

25.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.5b

localize44.0ms

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))
18.8b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite219.0ms

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:

59.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
39.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
78.0ms	(* 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))

series624.0ms

Counts

4 → 12

Calls

4 calls:

317.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
76.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
70.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
162.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify1.9s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	1926
1	556
0	192

prune572.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize36.0ms

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)
0.1b	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
14.4b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite166.0ms

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:

6.0ms	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
33.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
83.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
41.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series682.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(+ x (* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
85.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
169.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
105.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify1.7s

Counts

108 → 108

Iterations

Iter	Nodes
done	5003
2	2064
1	573
0	209

prune760.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize438.0ms

Local error

Found 4 expressions with local error:

7.6b	(* (* y (/ 1 (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
13.8b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
13.8b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
13.9b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log`
36×	`add-sqr-sqrt` `times-frac`
34×	`*-un-lft-identity` `add-cube-cbrt`
27×	`add-cbrt-cube` `sqrt-prod`
24×	`associate-r`
18×	`prod-exp`
11×	`pow1`
10×	`div-exp` `cbrt-unprod`
8×	`sqrt-div`
6×	`cbrt-undiv` `associate-/r*`
5×	`flip3-+` `flip-+`
4×	`associate-/r/` `add-log-exp`
3×	`pow-prod-down` `associate-r/` `associate-/l`
2×	`frac-times` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-*l/` `un-div-inv` `div-inv` `associate-/l/`
1×	`clear-num` `frac-2neg` `associate-l` `*-commutative`

Counts

4 → 129

Calls

4 calls:

157.0ms	(* (* y (/ 1 (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
22.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
13.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
46.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(* (* y (/ 1 (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
62.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
62.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
158.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify2.1s

Counts

141 → 141

Iterations

Iter	Nodes
done	5005
2	2681
1	719
0	250

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize76.0ms

Local error

Found 4 expressions with local error:

13.9b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
14.2b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.2b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.2b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

44.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
7.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
9.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
7.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series622.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
173.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
159.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
128.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify2.8s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
3	4122
2	1176
1	414
0	179

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes273.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.9b

bsearch318.0ms

Steps

Iters	Range		Point
11	573579.0075499975	3.0706563307201483e+25	212668326.62860867
7	-8.665460962243007e+24	-3.9554820123738635e+22	-4.069777565766241e+22

simplify20.0ms

Iterations

Iter	Nodes
done	59
1	59
0	39

end0.0ms

sample1.3s

Algorithm

intervals

Results

873.0ms

8000×

body

valid