Details

sample161.0ms

Algorithm

intervals

Results

57.0ms	256×	body	80	valid
48.0ms	259×	body	80	nan

simplify1.2s

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.2b

localize47.0ms

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)

rewrite76.0ms

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)))
6.0ms	(/ 2.0 (* t 3.0))
29.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
12.0ms	(/ (* z (sqrt (+ t a))) t)

series583.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* z (sqrt (+ t a)))
34.0ms	(/ 2.0 (* t 3.0))
313.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
141.0ms	(/ (* z (sqrt (+ t a))) t)

simplify1.3s

Counts

117 → 117

Iterations

Iter	Nodes
done	2004
2	2004
1	1044
0	350

prune2.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize85.0ms

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)))

rewrite111.0ms

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)
63.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
38.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))

series1.0s

Counts

4 → 12

Calls

4 calls:

305.0ms	(cbrt t)
297.0ms	(cbrt t)
289.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
139.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))

simplify1.7s

Counts

185 → 185

Iterations

Iter	Nodes
done	2006
2	2006
1	1852
0	491

prune5.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize156.0ms

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)))))

rewrite88.0ms

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)
11.0ms	(- (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)))))
70.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
1.0ms	(posit16->real (real->posit16 (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))))

series965.0ms

Counts

4 → 12

Calls

4 calls:

297.0ms	(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)))))
167.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
171.0ms	(posit16->real (real->posit16 (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))))

simplify1.2s

Counts

140 → 140

Iterations

Iter	Nodes
done	2003
2	2003
1	794
0	272

prune5.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize123.0ms

Local error

Found 4 expressions with local error:

3.6b	(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
4.7b	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
8.8b	(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
28.3b	(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

766×	`associate-*l/`
764×	`associate-*r/`
524×	`frac-sub`
498×	`flip3--` `flip--`
364×	`frac-times`
240×	`sqrt-div`
162×	`associate-/l/`
120×	`flip3-+` `flip-+`
28×	`add-cbrt-cube` `add-exp-log`
16×	`distribute-rgt-in` `distribute-lft-in`
14×	`pow1`
12×	`prod-exp` `cbrt-unprod`
9×	`sub-neg`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `associate--r+`
7×	`associate-l`
6×	`pow-prod-down` `add-log-exp`
4×	`cbrt-undiv` `div-exp` `insert-posit16`
3×	`times-frac` `associate-/l*`
2×	`associate-r` `associate-/r/` `*-commutative`
1×	`clear-num` `associate-/r*` `frac-2neg` `diff-log` `div-sub` `div-inv` `difference-of-squares`

Counts

4 → 441

Calls

4 calls:

393.0ms	(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
46.0ms	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
561.0ms	(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
817.0ms	(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

series2.1s

Counts

4 → 12

Calls

4 calls:

239.0ms	(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
84.0ms	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
839.0ms	(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
982.0ms	(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

simplify2.8s

Counts

453 → 453

Iterations

Iter	Nodes
done	2000
1	2000
0	1157

prune16.6s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes775.0ms

Accuracy

10.1% (2.1b remaining)

Error of 2.7b against oracle of 0.6b and baseline of 3.0b

bsearch753.0ms

Steps

Iters	Range		Point
9	8.748081393432952e-296	2.635021139593418e-287	9.422186440286068e-296
11	-163048972.58857644	-1.681474053001753e-26	-9.499850531274005e-14

simplify47.0ms

Iterations

Iter	Nodes
done	79
1	79
0	57

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.2s	8094×	body	80	nan
2.0s	8000×	body	80	valid