Details

sample25.0ms

Algorithm

intervals

Results

8.0ms	197×	body	80	valid
4.0ms	27×	body	640	valid
2.0ms	11×	body	1280	valid
2.0ms	14×	body	320	valid
1.0ms	7×	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: 22.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
3.5b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.2b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite121.0ms

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:

40.0ms	(* (- 1.0 x) y)
36.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
42.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series232.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* (- 1.0 x) y)
108.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
62.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify1.4s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
2	1305
1	349
0	131

prune336.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ y 1.0))
0.0b	(* (- 1.0 x) y)
6.7b	(- 1.0 (* (* (- 1.0 x) y) (/ 1 (+ y 1.0))))
8.3b	(* (* (- 1.0 x) y) (/ 1 (+ y 1.0)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
32×	`add-exp-log`
27×	`add-sqr-sqrt`
24×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-cbrt-cube`
13×	`prod-exp`
12×	`pow1`
8×	`associate-*l/`
7×	`cbrt-unprod` `distribute-lft-out`
6×	`div-exp` `associate-l` `add-log-exp`
4×	`associate-/r*` `flip3--` `pow-prod-down` `associate-/r/` `insert-posit16` `flip--`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*`
2×	`frac-times` `flip3-+` `*-commutative` `flip-+` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `associate-*r/` `un-div-inv` `pow-flip` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 122

Calls

4 calls:

11.0ms	(/ 1 (+ y 1.0))
29.0ms	(* (- 1.0 x) y)
10.0ms	(- 1.0 (* (* (- 1.0 x) y) (/ 1 (+ y 1.0))))
74.0ms	(* (* (- 1.0 x) y) (/ 1 (+ y 1.0)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1 (+ y 1.0))
66.0ms	(* (- 1.0 x) y)
103.0ms	(- 1.0 (* (* (- 1.0 x) y) (/ 1 (+ y 1.0))))
64.0ms	(* (* (- 1.0 x) y) (/ 1 (+ y 1.0)))

simplify1.7s

Counts

134 → 134

Iterations

Iter	Nodes
done	5001
2	1864
1	520
0	190

prune412.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize67.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* y y) y)
7.4b	(- 1.0 (* (/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
13.0b	(/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0)))
14.3b	(* (/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

37.0ms	(* (* y y) y)
9.0ms	(- 1.0 (* (/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
75.0ms	(/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0)))
219.0ms	(* (/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

series542.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (* y y) y)
249.0ms	(- 1.0 (* (/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
101.0ms	(/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0)))
123.0ms	(* (/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

simplify2.8s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
2	3958
1	776
0	214

prune570.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize48.0ms

Local error

Found 4 expressions with local error:

9.5b	(* (- (* 1.0 1.0) (* y 1.0)) (/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0))))
13.0b	(/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0)))
13.0b	(/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0)))
15.2b	(* (* y y) (/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0))))

rewrite606.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 128

Calls

4 calls:

234.0ms	(* (- (* 1.0 1.0) (* y 1.0)) (/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0))))
90.0ms	(/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0)))
104.0ms	(/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0)))
172.0ms	(* (* y y) (/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0))))

series433.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (- (* 1.0 1.0) (* y 1.0)) (/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0))))
117.0ms	(/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0)))
113.0ms	(/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0)))
112.0ms	(* (* y y) (/ (* y (- 1.0 x)) (+ (* (* y y) y) (* (* 1.0 1.0) 1.0))))

simplify2.9s

Counts

140 → 140

Iterations

Iter	Nodes
done	5020
2	3570
1	721
0	206

prune896.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

regimes253.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 23.6b

bsearch102.0ms

Steps

Iters	Range		Point
7	451460537736783.06	6.038363079945714e+16	490339666933239.4
10	-9.360541598459243e+24	-871508905171.6743	-30415092808503.895

simplify8.0ms

Iterations

Iter	Nodes
done	40
1	40
0	28

end0.0ms

sample1.5s

Algorithm

intervals

Results

488.0ms	6052×	body	80	valid
467.0ms	296×	body	160	valid
163.0ms	762×	body	640	valid
126.0ms	362×	body	1280	valid
92.0ms	528×	body	320	valid