Details

sample188.0ms

Algorithm

intervals

Results

79.0ms	269×	body	80	nan
68.0ms	256×	body	80	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2005
5	2005
4	1302
3	350
2	100
1	50
0	28

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.4b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.2b	(/ 2.0 (* t 3.0))
3.3b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
6.4b	(/ (* z (sqrt (+ t a))) t)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

16.0ms	(* z (sqrt (+ t a)))
6.0ms	(/ 2.0 (* t 3.0))
27.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
12.0ms	(/ (* z (sqrt (+ t a))) t)

series568.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* z (sqrt (+ t a)))
34.0ms	(/ 2.0 (* t 3.0))
306.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
144.0ms	(/ (* z (sqrt (+ t a))) t)

simplify1.3s

Counts

117 → 117

Iterations

Iter	Nodes
done	2004
2	2004
1	1044
0	350

prune2.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize127.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
2.2b	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
3.3b	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
60×	`frac-sub`
58×	`times-frac`
47×	`*-un-lft-identity`
46×	`associate-r`
39×	`frac-times`
35×	`add-cube-cbrt`
31×	`cbrt-prod`
28×	`sqrt-prod`
27×	`associate-*r/`
25×	`flip3--` `add-exp-log` `flip--`
21×	`associate-*l/`
18×	`add-cbrt-cube`
10×	`unswap-sqr`
9×	`flip3-+` `flip-+`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `associate-l`
6×	`pow1` `distribute-lft-out` `associate--r+` `add-log-exp`
4×	`insert-posit16`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
2×	`pow1/3` `associate--l+` `div-inv`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 173

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
49.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
64.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

293.0ms	(cbrt t)
259.0ms	(cbrt t)
171.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
320.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

simplify1.8s

Counts

185 → 185

Iterations

Iter	Nodes
done	2000
2	2000
1	1858
0	491

prune4.9s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize141.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
3.3b	(- (/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
6.4b	(/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t)
54.9b	(posit16->real (real->posit16 (* z (sqrt (+ t a)))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

20×	`frac-sub`
19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
9×	`times-frac` `flip3--` `flip--`
8×	`frac-times` `add-cbrt-cube` `add-exp-log`
7×	`associate-r`
6×	`pow1` `associate-*r/` `associate--r+` `add-log-exp`
5×	`sqrt-prod`
4×	`flip3-+` `flip-+` `insert-posit16`
3×	`distribute-rgt-in` `associate-/r` `sub-neg` `distribute-lft-in` `associate-l` `associate-/l`
2×	`sqrt-div` `associate-*l/` `associate--l+` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `remove-posit16` `distribute-lft-out`

Counts

4 → 96

Calls

4 calls:

22.0ms	(* z (sqrt (+ t a)))
31.0ms	(- (/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
10.0ms	(/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t)
1.0ms	(posit16->real (real->posit16 (* z (sqrt (+ t a)))))

series652.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* z (sqrt (+ t a)))
316.0ms	(- (/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
111.0ms	(/ (posit16->real (real->posit16 (* z (sqrt (+ t a))))) t)
103.0ms	(posit16->real (real->posit16 (* z (sqrt (+ t a)))))

simplify1.2s

Counts

108 → 108

Iterations

Iter	Nodes
done	2010
2	2010
1	926
0	321

prune3.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize107.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
2.2b	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
3.3b	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
49.4b	(posit16->real (real->posit16 (- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
60×	`frac-sub`
58×	`times-frac`
46×	`-un-lft-identity` `associate-r*`
39×	`frac-times`
34×	`add-cube-cbrt`
28×	`cbrt-prod` `sqrt-prod`
27×	`associate-*r/`
25×	`flip3--` `add-exp-log` `flip--`
21×	`associate-*l/`
18×	`add-cbrt-cube`
10×	`unswap-sqr`
9×	`flip3-+` `flip-+`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `associate-l`
6×	`pow1` `distribute-lft-out` `associate--r+` `add-log-exp`
4×	`insert-posit16`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
2×	`associate--l+` `div-inv`
1×	`pow1/3` `diff-log` `pow-prod-down` `*-commutative` `remove-posit16`

Counts

4 → 170

Calls

4 calls:

1.0ms	(cbrt t)
70.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
35.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
1.0ms	(posit16->real (real->posit16 (- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

251.0ms	(cbrt t)
177.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
336.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
338.0ms	(posit16->real (real->posit16 (- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))

simplify2.0s

Counts

182 → 182

Iterations

Iter	Nodes
done	2000
2	2000
1	1872
0	500

prune7.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes961.0ms

Accuracy

-7.6% (2.6b remaining)

Error of 3.1b against oracle of 0.5b and baseline of 2.9b

bsearch549.0ms

Steps

Iters	Range		Point
8	1.1593160082027975e-229	3.509697963527615e-227	1.4924055999405827e-228
7	-1.9808904324337393e-87	-5.488403640925928e-89	-7.898436796540733e-89

simplify50.0ms

Iterations

Iter	Nodes
done	62
1	62
0	47

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.5s	7941×	body	80	nan
1.9s	8000×	body	80	valid