Details

sample187.0ms

Algorithm

intervals

Results

63.0ms	256×	body	80	valid
48.0ms	243×	body	80	nan

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
5	5020
4	1334
3	350
2	100
1	50
0	28

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.5b	(/ 2.0 (* t 3.0))
2.4b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
5.4b	(/ (* z (sqrt (+ t a))) t)

rewrite120.0ms

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:

34.0ms	(* z (sqrt (+ t a)))
13.0ms	(/ 2.0 (* t 3.0))
46.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
24.0ms	(/ (* z (sqrt (+ t a))) t)

series543.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* z (sqrt (+ t a)))
20.0ms	(/ 2.0 (* t 3.0))
332.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
107.0ms	(/ (* z (sqrt (+ t a))) t)

simplify2.2s

Counts

117 → 117

Iterations

Iter	Nodes
2	4466
1	1031
0	350

prune3.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize92.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
1.4b	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
2.4b	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

rewrite136.0ms

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)
84.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
40.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

347.0ms	(cbrt t)
330.0ms	(cbrt t)
159.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
366.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

simplify4.4s

Counts

185 → 185

Iterations

Iter	Nodes
2	8957
1	1854
0	491

prune4.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize114.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
1.4b	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
2.4b	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
46.3b	(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)))))))

rewrite111.0ms

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)
61.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
45.0ms	(- (* (/ 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)))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

293.0ms	(cbrt t)
142.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
346.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
372.0ms	(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)))))))

simplify4.4s

Counts

182 → 182

Iterations

Iter	Nodes
2	8819
1	1868
0	500

prune7.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize79.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t)
2.6b	(* z (* (- a (/ 5.0 6.0)) (* t 3.0)))
9.3b	(- (* (sqrt (+ a t)) (* z (* (- a (/ 5.0 6.0)) (* t 3.0)))) (* (- b c) (* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t)))
28.2b	(/ (- (* (sqrt (+ a t)) (* z (* (- a (/ 5.0 6.0)) (* t 3.0)))) (* (- b c) (* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

rewrite2.9s

Algorithm

rewrite-expression-head

Rules

2902×	`associate-*l/`
2512×	`associate-*r/`
1776×	`frac-sub`
1551×	`flip3--` `flip--`
1528×	`frac-times`
744×	`sqrt-div`
666×	`flip3-+` `flip-+`
500×	`associate-/l/`
106×	`sub-div`
29×	`add-cbrt-cube` `add-exp-log`
15×	`pow1`
13×	`prod-exp` `cbrt-unprod`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow-prod-down`
6×	`associate-l` `add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-r` `insert-posit16`
3×	`times-frac` `associate-/l*`
2×	`associate-/r/` `*-commutative`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-inv` `unswap-sqr`

Counts

4 → 1103

Calls

4 calls:

391.0ms	(* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t)
70.0ms	(* z (* (- a (/ 5.0 6.0)) (* t 3.0)))
982.0ms	(- (* (sqrt (+ a t)) (* z (* (- a (/ 5.0 6.0)) (* t 3.0)))) (* (- b c) (* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t)))
1.3s	(/ (- (* (sqrt (+ a t)) (* z (* (- a (/ 5.0 6.0)) (* t 3.0)))) (* (- b c) (* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

series1.5s

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t)
71.0ms	(* z (* (- a (/ 5.0 6.0)) (* t 3.0)))
637.0ms	(- (* (sqrt (+ a t)) (* z (* (- a (/ 5.0 6.0)) (* t 3.0)))) (* (- b c) (* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t)))
689.0ms	(/ (- (* (sqrt (+ a t)) (* z (* (- a (/ 5.0 6.0)) (* t 3.0)))) (* (- b c) (* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

simplify10.6s

Counts

1115 → 1115

Iterations

Iter	Nodes
1	11412
0	2949

prune48.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes783.0ms

Accuracy

45.3% (1.3b remaining)

Error of 1.7b against oracle of 0.4b and baseline of 2.7b

bsearch599.0ms

Steps

Iters	Range		Point
7	6.549482153422473e-156	5.833704946244723e-154	1.5942112126605388e-155
7	-4.960756058276486e-44	-1.7458197007173568e-45	-2.730208876097712e-45

simplify39.0ms

Iterations

Iter	Nodes
2	77
1	77
0	56

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.2s	8000×	body	80	valid
2.2s	8333×	body	80	nan