Details

sample26.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify60.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	10
1	64	10
2	143	10
3	288	10
4	443	10
5	563	10
6	648	10
7	817	10
8	1060	10
9	1066	10
10	1066	10
done	1066	10

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.2b

localize13.0ms

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)
3.6b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
22.3b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
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×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 79

Calls

4 calls:

36.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
26.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
45.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
42.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series442.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
65.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
52.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
121.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify65.0ms

Counts

91 → 91

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	534	840
1	2452	738
2	5003	738
done	5003	738

prune228.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

7.1b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
16.4b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
16.6b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
16.6b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
66×	`times-frac`
47×	`add-cube-cbrt` `*-un-lft-identity`
42×	`sqrt-prod`
24×	`associate-r` `associate-l`
18×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`flip3-+` `associate-/r*` `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` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 150

Calls

4 calls:

130.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
53.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
15.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series334.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
114.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
51.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
47.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify84.0ms

Counts

162 → 162

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	720	2533
1	3090	2327
2	5002	2242
done	5002	2242

prune492.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

16.4b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
16.6b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
16.6b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
16.6b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`sqrt-prod`
18×	`times-frac`
8×	`sqrt-div`
7×	`pow1`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
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` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 88

Calls

4 calls:

50.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
18.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series256.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
45.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
49.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
49.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify43.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	359	1091
1	1174	1038
2	5001	1008
done	5001	1008

prune387.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 0.07512208616047561 (/ y z)) (* 0.0692910599291889 y))
0.3b	(* 0.07512208616047561 (/ y z))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `flip-+` `div-inv`

Counts

2 → 43

Calls

2 calls:

11.0ms	(+ (* 0.07512208616047561 (/ y z)) (* 0.0692910599291889 y))
17.0ms	(* 0.07512208616047561 (/ y z))

series61.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(+ (* 0.07512208616047561 (/ y z)) (* 0.0692910599291889 y))
19.0ms	(* 0.07512208616047561 (/ y z))

simplify108.0ms

Counts

49 → 49

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	242	226
1	1032	207
2	4425	206
3	5001	206
done	5001	206

prune89.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes145.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.5b

bsearch115.0ms

Steps

Iters	Range		Point
8	892369.0132880388	49821777349.62285	182633786.16382062
7	-1.836344030007439e+19	-1.8070707071506563e+17	-1.844996988886154e+17

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	21
1	48	21
done	48	21

end0.0ms

sample541.0ms

Algorithm

intervals

Results

316.0ms

8000×

body

valid