Details

sample41.0ms

Algorithm

intervals

Results

19.0ms

256×

body

valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	21
1	35	21
2	64	21
3	143	21
4	276	21
5	400	21
6	481	21
7	564	21
8	728	21
9	949	21
10	955	21
done	955	21

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.3b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
18.5b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

22.0ms	(* (+ z 6.012459259764103) z)
41.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
91.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
88.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series472.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (+ z 6.012459259764103) z)
120.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
83.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
207.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify1.3s

Counts

100 → 100

Iterations

Useful iterations: 2 (502.0ms)

Iter	Nodes	Cost
0	190	1538
1	523	1492
2	1881	1284
done	5001	1284

prune433.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
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)))
14.6b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
21×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `associate-l`
5×	`flip3-+` `flip-+`
4×	`associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `div-inv` `associate-/l/`
1×	`frac-2neg` `associate-*r/` `clear-num` `distribute-lft-out`

Counts

4 → 106

Calls

4 calls:

31.0ms	(* (+ z 6.012459259764103) z)
44.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
97.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
94.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series440.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (+ z 6.012459259764103) z)
97.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
183.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
103.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify1.5s

Counts

118 → 118

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	209	2226
1	540	2178
2	1781	1942
done	5000	1922

prune452.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.3b	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
14.7b	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

rewrite288.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
64×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
60×	`add-cube-cbrt`
18×	`associate-/r*`
15×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r/`
8×	`pow1` `flip3-+` `flip-+`
7×	`associate-l`
6×	`associate-r` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp` `associate-*l/` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`distribute-lft-out`

Counts

4 → 150

Calls

4 calls:

36.0ms	(* (+ z 6.012459259764103) z)
39.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
81.0ms	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
120.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

series398.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (+ z 6.012459259764103) z)
96.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
158.0ms	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
79.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

simplify1.8s

Counts

162 → 162

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	303	4145
1	718	4037
2	2503	3795
done	5001	3789

prune844.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 0.07512208616047561 (/ 0.40462203869992125 z))
0.0b	(+ (* 0.0692910599291889 y) (* (/ y z) (- 0.07512208616047561 (/ 0.40462203869992125 z))))
0.0b	(+ x (+ (* 0.0692910599291889 y) (* (/ y z) (- 0.07512208616047561 (/ 0.40462203869992125 z)))))
0.2b	(* (/ y z) (- 0.07512208616047561 (/ 0.40462203869992125 z)))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`associate-l` `add-log-exp`
12×	`add-cube-cbrt` `times-frac`
9×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-r`
5×	`sub-neg` `associate-+r+`
4×	`distribute-rgt-in` `distribute-lft-in` `sum-log` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`+-commutative` `frac-times` `flip3-+` `associate-*r/` `prod-exp` `cbrt-unprod` `flip-+` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `distribute-lft-out`

Counts

4 → 87

Calls

4 calls:

15.0ms	(- 0.07512208616047561 (/ 0.40462203869992125 z))
22.0ms	(+ (* 0.0692910599291889 y) (* (/ y z) (- 0.07512208616047561 (/ 0.40462203869992125 z))))
35.0ms	(+ x (+ (* 0.0692910599291889 y) (* (/ y z) (- 0.07512208616047561 (/ 0.40462203869992125 z)))))
107.0ms	(* (/ y z) (- 0.07512208616047561 (/ 0.40462203869992125 z)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- 0.07512208616047561 (/ 0.40462203869992125 z))
62.0ms	(+ (* 0.0692910599291889 y) (* (/ y z) (- 0.07512208616047561 (/ 0.40462203869992125 z))))
82.0ms	(+ x (+ (* 0.0692910599291889 y) (* (/ y z) (- 0.07512208616047561 (/ 0.40462203869992125 z)))))
86.0ms	(* (/ y z) (- 0.07512208616047561 (/ 0.40462203869992125 z)))

simplify1.2s

Counts

99 → 99

Iterations

Useful iterations: 2 (389.0ms)

Iter	Nodes	Cost
0	162	1480
1	457	1392
2	1559	1280
done	5000	1280

prune355.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes580.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.4b

bsearch245.0ms

Steps

Iters	Range		Point
8	0.5242272119756929	639.503948019383	629.303371294859
9	-9.466489429598327e+36	-2.8897456288171165e+31	-1.8560802591567945e+36

simplify10.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	33	59
1	49	45
done	49	45

end0.0ms

sample1.1s

Algorithm

intervals

Results

753.0ms

8000×

body

valid