Details

sample48.0ms

Algorithm

intervals

Results

18.0ms	195×	body	80	valid
6.0ms	14×	body	1280	valid
6.0ms	23×	body	320	valid
6.0ms	17×	body	640	valid
1.0ms	7×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
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: 22.4b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
2.7b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.2b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite70.0ms

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:

15.0ms	(* (- 1.0 x) y)
24.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
30.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series222.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* (- 1.0 x) y)
104.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
68.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify701.0ms

Counts

75 → 75

Iterations

Iter	Nodes
done	2062
2	1305
1	349
0	131

prune256.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (+ y 1.0))
0.0b	(* (- 1.0 x) (/ y (+ y 1.0)))
2.7b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite74.0ms

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:

15.0ms	(/ y (+ y 1.0))
45.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
12.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series200.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ y (+ y 1.0))
49.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
97.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify660.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	2017
2	1630
1	427
0	160

prune279.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-log-exp`
3×	`times-frac` `difference-of-squares`
2×	`pow1` `sum-log` `flip3-+` `add-cbrt-cube` `diff-log` `add-exp-log` `frac-sub` `add-cube-cbrt` `flip-+` `insert-posit16` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--`

Counts

2 → 35

Calls

2 calls:

46.0ms	(- (+ x (/ 1.0 y)) (/ x (/ y 1.0)))
9.0ms	(+ x (/ 1.0 y))

series93.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (+ x (/ 1.0 y)) (/ x (/ y 1.0)))
42.0ms	(+ x (/ 1.0 y))

simplify477.0ms

Counts

41 → 41

Iterations

Iter	Nodes
done	2000
2	753
1	208
0	81

prune128.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ 1.0 y))
0.3b	(* (sqrt (- (+ x (/ 1.0 y)) (/ x (/ y 1.0)))) (sqrt (- (+ x (/ 1.0 y)) (/ x (/ y 1.0)))))
3.6b	(sqrt (- (+ x (/ 1.0 y)) (/ x (/ y 1.0))))
3.6b	(sqrt (- (+ x (/ 1.0 y)) (/ x (/ y 1.0))))

rewrite308.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
70×	`*-un-lft-identity`
66×	`sqrt-prod`
48×	`sqrt-div`
24×	`frac-sub`
21×	`pow1`
20×	`distribute-lft-out--`
19×	`swap-sqr`
18×	`times-frac` `difference-of-squares`
16×	`frac-times`
14×	`add-cube-cbrt`
13×	`flip3-+` `flip-+`
12×	`flip3--` `flip--`
11×	`associate-r` `associate-l` `distribute-lft-out`
10×	`sqrt-pow1` `pow1/2`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow-prod-up`
4×	`associate-l/` `associate-r/` `insert-posit16` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 154

Calls

4 calls:

6.0ms	(+ x (/ 1.0 y))
208.0ms	(* (sqrt (- (+ x (/ 1.0 y)) (/ x (/ y 1.0)))) (sqrt (- (+ x (/ 1.0 y)) (/ x (/ y 1.0)))))
51.0ms	(sqrt (- (+ x (/ 1.0 y)) (/ x (/ y 1.0))))
41.0ms	(sqrt (- (+ x (/ 1.0 y)) (/ x (/ y 1.0))))

series278.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ x (/ 1.0 y))
47.0ms	(* (sqrt (- (+ x (/ 1.0 y)) (/ x (/ y 1.0)))) (sqrt (- (+ x (/ 1.0 y)) (/ x (/ y 1.0)))))
101.0ms	(sqrt (- (+ x (/ 1.0 y)) (/ x (/ y 1.0))))
100.0ms	(sqrt (- (+ x (/ 1.0 y)) (/ x (/ y 1.0))))

simplify508.0ms

Counts

166 → 166

Iterations

Iter	Nodes
done	2002
2	1163
1	423
0	203

prune671.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes154.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 14.4b

bsearch127.0ms

Steps

Iters	Range		Point
10	0.0038666078177206752	941504501108.8118	166873327.66733637
10	-121993772661.31783	-0.22068356154967622	-119130230.14897136

simplify6.0ms

Iterations

Iter	Nodes
done	25
1	25
0	19

end0.0ms

sample1.3s

Algorithm

intervals

Results

528.0ms	6097×	body	80	valid
265.0ms	747×	body	640	valid
154.0ms	505×	body	320	valid
146.0ms	358×	body	1280	valid
44.0ms	293×	body	160	valid