Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	190×	body	80	valid
4.0ms	23×	body	640	valid
3.0ms	13×	body	1280	valid
2.0ms	14×	body	320	valid
1.0ms	16×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
14	4122
13	3069
12	2474
11	2032
10	1843
9	1602
8	1334
7	972
6	535
5	248
4	118
3	71
2	33
1	16
0	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.5b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
4.2b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
5.8b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
10×	`add-cbrt-cube` `add-exp-log`
7×	`add-cube-cbrt`
5×	`pow1` `associate-l` `add-log-exp`
4×	`associate-/r` `times-frac` `associate-l/`
3×	`flip3--` `associate-r` `insert-posit16` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `associate-/l/`
1×	`clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `-commutative` `flip-+` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 66

Calls

3 calls:

17.0ms	(* (- 1.0 x) y)
12.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
19.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series179.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* (- 1.0 x) y)
75.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
68.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify1.1s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
2	1305
1	349
0	131

prune264.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) (/ y (+ y 1.0)))
0.0b	(/ y (+ y 1.0))
4.2b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`times-frac`
21×	`add-cube-cbrt`
18×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
7×	`distribute-lft-out`
5×	`pow1` `associate-l` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`flip3--` `insert-posit16` `flip--` `associate-/l*`
2×	`frac-times` `cbrt-undiv` `flip3-+` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `associate-r/` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 91

Calls

3 calls:

28.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
9.0ms	(/ y (+ y 1.0))
8.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series227.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
55.0ms	(/ y (+ y 1.0))
114.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify1.3s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1646
1	428
0	160

prune369.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(* y (* y y))
7.4b	(- 1.0 (* (/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
9.2b	(/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y))))
15.1b	(* (/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-cbrt-cube` `add-exp-log`
20×	`pow1`
13×	`add-sqr-sqrt` `associate-l`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`times-frac` `prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`cbrt-undiv` `associate-/r` `flip3-+` `cube-unmult` `div-exp` `associate-r*` `pow-prod-down` `associate-/r/` `flip-+` `insert-posit16`
3×	`pow3` `associate-*l/` `sum-cubes`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `flip3--` `associate-r/` `-commutative` `div-inv` `flip--` `associate--r+` `unswap-sqr` `associate-/l/`
1×	`pow2` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `pow-sqr` `associate-/l*`

Counts

4 → 105

Calls

4 calls:

27.0ms	(* y (* y y))
8.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
46.0ms	(/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y))))
166.0ms	(* (/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

series567.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* y (* y y))
288.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
110.0ms	(/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y))))
131.0ms	(* (/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

simplify2.4s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
2	3168
1	711
0	209

prune686.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

9.2b	(/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y))))
9.2b	(/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y))))
12.4b	(* (/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y)))) (- (* 1.0 1.0) (* y 1.0)))
15.7b	(* (/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y)))) (* y y))

rewrite358.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-cbrt-cube` `add-exp-log`
20×	`associate-l`
17×	`prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt` `times-frac`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
10×	`cbrt-undiv` `div-exp`
8×	`associate-/r*` `associate-/r/`
6×	`cube-unmult` `pow3` `associate-*l/` `sum-cubes`
5×	`associate-r`
4×	`flip3-+` `flip3--` `pow-prod-down` `flip-+` `insert-posit16` `div-inv` `flip--` `add-log-exp` `associate-/l/`
2×	`distribute-rgt-in` `frac-times` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `associate-r/` `-commutative` `associate-/l*` `unswap-sqr`
1×	`distribute-rgt-out--`

Counts

4 → 132

Calls

4 calls:

44.0ms	(/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y))))
44.0ms	(/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y))))
133.0ms	(* (/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y)))) (- (* 1.0 1.0) (* y 1.0)))
135.0ms	(* (/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y)))) (* y y))

series434.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y))))
98.0ms	(/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y))))
111.0ms	(* (/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y)))) (- (* 1.0 1.0) (* y 1.0)))
105.0ms	(* (/ (* (- 1.0 x) y) (+ (* (* 1.0 1.0) 1.0) (* y (* y y)))) (* y y))

simplify2.6s

Counts

144 → 144

Iterations

Iter	Nodes
done	5001
2	3089
1	675
0	202

prune773.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

regimes315.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 23.0b

bsearch143.0ms

Steps

Iters	Range		Point
6	11120271688924408.0	6.72681328144926e+16	11305515126613318.0
9	-9.169070498365897e+20	-3361471310457274.5	-3.40118678716794e+15

simplify15.0ms

Iterations

Iter	Nodes
done	41
1	41
0	29

end0.0ms

sample1.3s

Algorithm

intervals

Results

536.0ms	676×	body	640	valid
448.0ms	6204×	body	80	valid
82.0ms	342×	body	1280	valid
70.0ms	497×	body	320	valid
26.0ms	281×	body	160	valid