Details

sample251.0ms

Algorithm

intervals

Results

113.0ms	256×	body	80	valid
83.0ms	259×	body	80	nan

simplify2.3s

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.2b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.5b	(/ 2.0 (* t 3.0))
2.1b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
7.0b	(/ (* z (sqrt (+ t a))) t)

rewrite86.0ms

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:

25.0ms	(* z (sqrt (+ t a)))
7.0ms	(/ 2.0 (* t 3.0))
29.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
23.0ms	(/ (* z (sqrt (+ t a))) t)

series592.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* z (sqrt (+ t a)))
36.0ms	(/ 2.0 (* t 3.0))
281.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
151.0ms	(/ (* z (sqrt (+ t a))) t)

simplify1.9s

Counts

117 → 117

Iterations

Iter	Nodes
2	4466
1	1031
0	350

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize101.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
2.1b	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
2.4b	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))

rewrite128.0ms

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)
64.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
56.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))

series1.0s

Counts

4 → 12

Calls

4 calls:

253.0ms	(cbrt t)
262.0ms	(cbrt t)
350.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
167.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))

simplify4.2s

Counts

185 → 185

Iterations

Iter	Nodes
2	8873
1	1848
0	491

prune2.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize112.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
2.1b	(- (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)))))
2.4b	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
52.3b	(posit16->real (real->posit16 (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
58×	`times-frac`
46×	`-un-lft-identity` `associate-r*`
34×	`add-cube-cbrt`
28×	`cbrt-prod` `sqrt-prod`
25×	`add-exp-log`
18×	`add-cbrt-cube`
10×	`unswap-sqr`
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×	`frac-times` `flip3--` `pow1/3` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `remove-posit16` `flip--`

Counts

4 → 128

Calls

4 calls:

1.0ms	(cbrt t)
9.0ms	(- (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)))))
61.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
0.0ms	(posit16->real (real->posit16 (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))))

series950.0ms

Counts

4 → 12

Calls

4 calls:

286.0ms	(cbrt t)
330.0ms	(- (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)))))
156.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
179.0ms	(posit16->real (real->posit16 (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))))

simplify1.3s

Counts

140 → 140

Iterations

Iter	Nodes
2	2767
1	790
0	272

prune1.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize72.0ms

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)
2.5b	(* z (* (- a (/ 5.0 6.0)) (* t 3.0)))
8.8b	(- (* (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)))
28.3b	(/ (- (* (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))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

rewrite2.8s

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:

394.0ms	(* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t)
65.0ms	(* z (* (- a (/ 5.0 6.0)) (* t 3.0)))
1.0s	(- (* (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)))
1.2s	(/ (- (* (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:

61.0ms	(* (- (* (+ a (/ 5.0 6.0)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* 2.0 (- a (/ 5.0 6.0)))) t)
54.0ms	(* z (* (- a (/ 5.0 6.0)) (* t 3.0)))
692.0ms	(- (* (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)))
725.0ms	(/ (- (* (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))))

simplify10.2s

Counts

1115 → 1115

Iterations

Iter	Nodes
1	11412
0	2949

prune24.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes578.0ms

Accuracy

31.7% (1.6b remaining)

Error of 2.2b against oracle of 0.5b and baseline of 3.0b

bsearch772.0ms

Steps

Iters	Range		Point
9	8.748081393432952e-296	2.635021139593418e-287	1.230296909173772e-287
11	-163048972.58857644	-1.681474053001753e-26	-9.499850531274005e-14

simplify41.0ms

Iterations

Iter	Nodes
2	77
1	77
0	56

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.2s	8000×	body	80	valid
2.1s	8094×	body	80	nan