Details

sample196.0ms

Algorithm

intervals

Results

127.0ms	914×	body	80	nan
35.0ms	282×	body	80	valid

simplify3.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	2234
4	794
3	241
2	80
1	30
0	14

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9 (- a (/ 1.0 3.0)))
0.1b	(sqrt (* 9 (- a (/ 1.0 3.0))))
0.1b	(fma (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))) rand (- a (/ 1.0 3.0)))
0.3b	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))

rewrite348.0ms

Algorithm

rewrite-expression-head

Rules

285×	`add-sqr-sqrt`
190×	`times-frac`
180×	`*-un-lft-identity`
124×	`add-cube-cbrt`
120×	`sqrt-prod`
78×	`prod-diff`
56×	`difference-of-squares`
54×	`associate-r`
41×	`distribute-rgt-in` `distribute-lft-in`
28×	`distribute-lft-out--`
27×	`associate-l`
18×	`associate-/r*`
10×	`unswap-sqr`
9×	`pow1` `*-commutative`
8×	`add-cbrt-cube` `add-exp-log`
7×	`div-inv`
6×	`associate-r/` `associate-/l`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow-prod-down` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `pow1/2` `div-sub` `div-exp` `prod-exp` `cbrt-unprod` `fma-udef`

Counts

4 → 303

Calls

4 calls:

64.0ms	(* 9 (- a (/ 1.0 3.0)))
121.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
1.0ms	(fma (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))) rand (- a (/ 1.0 3.0)))
134.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))

series354.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* 9 (- a (/ 1.0 3.0)))
71.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
98.0ms	(fma (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))) rand (- a (/ 1.0 3.0)))
122.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify2.4s

Counts

315 → 315

Iterations

Iter	Nodes
done	5000
2	2840
1	1180
0	555

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* (/ 1 (fabs (cbrt 9))) (/ (- a (/ 1.0 3.0)) (sqrt (* (cbrt 9) (- a (/ 1.0 3.0)))))) rand (- a (/ 1.0 3.0)))
0.1b	(sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))
0.2b	(* (/ 1 (fabs (cbrt 9))) (/ (- a (/ 1.0 3.0)) (sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))))
0.3b	(/ (- a (/ 1.0 3.0)) (sqrt (* (cbrt 9) (- a (/ 1.0 3.0)))))

rewrite917.0ms

Algorithm

rewrite-expression-head

Rules

803×	`add-sqr-sqrt`
465×	`sqrt-prod`
420×	`*-un-lft-identity`
374×	`times-frac`
344×	`associate-/r*`
297×	`frac-times`
282×	`associate-r`
254×	`add-cube-cbrt`
170×	`associate-/l*`
158×	`difference-of-squares`
157×	`associate-l`
100×	`cbrt-prod`
80×	`distribute-lft-out--`
71×	`unswap-sqr`
46×	`clear-num`
45×	`frac-2neg`
39×	`associate-*r/`
28×	`add-exp-log`
25×	`*-commutative`
22×	`associate-/l/`
18×	`add-cbrt-cube`
14×	`flip3--` `flip--`
9×	`pow1` `div-exp` `associate-*l/`
8×	`prod-exp`
6×	`sqrt-div`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `associate-/r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `un-div-inv` `div-inv`
2×	`rec-exp` `sqrt-pow1` `1-exp` `pow-prod-down`
1×	`pow1/2` `div-sub` `fma-udef`

Counts

4 → 760

Calls

4 calls:

0.0ms	(fma (* (/ 1 (fabs (cbrt 9))) (/ (- a (/ 1.0 3.0)) (sqrt (* (cbrt 9) (- a (/ 1.0 3.0)))))) rand (- a (/ 1.0 3.0)))
99.0ms	(sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))
571.0ms	(* (/ 1 (fabs (cbrt 9))) (/ (- a (/ 1.0 3.0)) (sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))))
174.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* (cbrt 9) (- a (/ 1.0 3.0)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

592.0ms	(fma (* (/ 1 (fabs (cbrt 9))) (/ (- a (/ 1.0 3.0)) (sqrt (* (cbrt 9) (- a (/ 1.0 3.0)))))) rand (- a (/ 1.0 3.0)))
198.0ms	(sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))
558.0ms	(* (/ 1 (fabs (cbrt 9))) (/ (- a (/ 1.0 3.0)) (sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))))
321.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* (cbrt 9) (- a (/ 1.0 3.0)))))

simplify3.5s

Counts

772 → 772

Iterations

Iter	Nodes
done	5001
1	3736
0	1057

prune3.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (sqrt 1.0) (cbrt 3.0))
1.0b	(/ (sqrt 1.0) (cbrt 3.0))
1.0b	(/ (sqrt 1.0) (cbrt 3.0))
61.9b	(fma (- (/ (sqrt 1.0) (cbrt 3.0))) (/ (sqrt 1.0) (* (cbrt 3.0) (cbrt 3.0))) (* (/ (sqrt 1.0) (cbrt 3.0)) (/ (sqrt 1.0) (* (cbrt 3.0) (cbrt 3.0)))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
88×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
63×	`cbrt-prod` `sqrt-prod`
18×	`associate-/r` `associate-/l`
13×	`add-cbrt-cube`
10×	`add-exp-log`
6×	`cbrt-undiv`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `div-exp` `div-inv`
1×	`fma-udef`

Counts

4 → 203

Calls

4 calls:

16.0ms	(/ (sqrt 1.0) (cbrt 3.0))
16.0ms	(/ (sqrt 1.0) (cbrt 3.0))
16.0ms	(/ (sqrt 1.0) (cbrt 3.0))
1.0ms	(fma (- (/ (sqrt 1.0) (cbrt 3.0))) (/ (sqrt 1.0) (* (cbrt 3.0) (cbrt 3.0))) (* (/ (sqrt 1.0) (cbrt 3.0)) (/ (sqrt 1.0) (* (cbrt 3.0) (cbrt 3.0)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/ (sqrt 1.0) (cbrt 3.0))
0.0ms	(/ (sqrt 1.0) (cbrt 3.0))
0.0ms	(/ (sqrt 1.0) (cbrt 3.0))
0.0ms	(fma (- (/ (sqrt 1.0) (cbrt 3.0))) (/ (sqrt 1.0) (* (cbrt 3.0) (cbrt 3.0))) (* (/ (sqrt 1.0) (cbrt 3.0)) (/ (sqrt 1.0) (* (cbrt 3.0) (cbrt 3.0)))))

simplify1.9s

Counts

207 → 207

Iterations

Iter	Nodes
done	5000
4	2463
3	842
2	336
1	186
0	116

prune1.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* 9 (- a (/ 1.0 3.0))))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
0.3b	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

173×	`add-sqr-sqrt`
139×	`sqrt-prod`
124×	`times-frac`
109×	`*-un-lft-identity`
95×	`associate-l`
81×	`add-cube-cbrt`
63×	`associate-r`
36×	`associate-/r*`
26×	`associate-*l/`
20×	`difference-of-squares` `unswap-sqr`
19×	`add-exp-log`
15×	`pow1`
13×	`add-cbrt-cube`
11×	`*-commutative`
10×	`distribute-lft-out--`
8×	`associate-*r/`
6×	`flip3--` `sqrt-div` `flip--` `associate-/l*`
5×	`prod-exp`
4×	`expm1-log1p-u` `frac-times` `sqrt-pow1` `div-exp` `pow-prod-down` `associate-/r/` `insert-posit16` `log1p-expm1-u` `pow-flip` `add-log-exp`
3×	`flip3-+` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out`
2×	`distribute-rgt-in` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `distribute-lft-in` `pow1/2` `1-exp`
1×	`inv-pow`

Counts

4 → 282

Calls

4 calls:

138.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
1.5s	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
358.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
133.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

series488.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
113.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
179.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
128.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify2.6s

Counts

294 → 294

Iterations

Iter	Nodes
done	5002
2	3121
1	1102
0	417

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes173.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.9s	27682×	body	80	nan
1.3s	9061×	body	80	valid