Details

sample122.0ms

Algorithm

intervals

Results

60.0ms	967×	body	80	nan
15.0ms	288×	body	80	valid

simplify6.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	13	20
1	27	20
2	76	19
3	206	19
4	503	19
5	992	19
6	2080	19
7	3449	19
done	5000	19

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (fma (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand 1.0) (- a (/ 1.0 3.0)))
0.1b	(fma (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand 1.0)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
85×	`*-un-lft-identity`
83×	`add-cube-cbrt`
78×	`prod-diff`
67×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
7×	`div-inv`
6×	`associate-r/` `associate-r*`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `sqrt-div` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `associate-l` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-pow1` `pow-prod-down` `associate-/r/` `difference-of-squares`
1×	`cbrt-undiv` `frac-2neg` `pow1/2` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 167

Calls

4 calls:

69.0ms	(* (fma (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand 1.0) (- a (/ 1.0 3.0)))
1.0ms	(fma (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand 1.0)
36.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
66.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series843.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(* (fma (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand 1.0) (- a (/ 1.0 3.0)))
213.0ms	(fma (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand 1.0)
257.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
127.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify2.5s

Counts

179 → 179

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	453	7178
1	946	6698
2	2958	5557
done	5002	5038

prune465.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(* (fma (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand 1.0) (- a (/ 1.0 3.0)))
0.1b	(fma (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand 1.0)
0.4b	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

457×	`times-frac`
379×	`add-sqr-sqrt`
301×	`*-un-lft-identity`
251×	`add-cube-cbrt`
234×	`sqrt-prod`
78×	`prod-diff`
50×	`difference-of-squares`
41×	`distribute-rgt-in` `distribute-lft-in`
25×	`distribute-lft-out--`
22×	`associate-/l*`
17×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*`
7×	`pow1`
6×	`associate-r`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-l` `flip--`
2×	`sub-neg` `associate-*r/` `associate-/r/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `associate-/l/` `unswap-sqr`

Counts

4 → 385

Calls

4 calls:

35.0ms	(sqrt (- a (/ 1.0 3.0)))
74.0ms	(* (fma (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand 1.0) (- a (/ 1.0 3.0)))
1.0ms	(fma (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand 1.0)
63.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series973.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(sqrt (- a (/ 1.0 3.0)))
288.0ms	(* (fma (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand 1.0) (- a (/ 1.0 3.0)))
344.0ms	(fma (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand 1.0)
262.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify3.1s

Counts

397 → 397

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	707	13146
1	1529	12096
2	4188	10934
done	5002	10583

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 9.0)) (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0))))) rand 1.0) (- a (/ 1.0 3.0)))
0.1b	(fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 9.0)) (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0))))) rand 1.0)
0.2b	(/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0))))
0.4b	(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 9.0)) (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0)))))

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

256×	`add-sqr-sqrt`
204×	`times-frac`
170×	`*-un-lft-identity`
142×	`add-cube-cbrt`
92×	`sqrt-prod`
78×	`prod-diff`
66×	`associate-r`
63×	`cbrt-prod`
41×	`distribute-rgt-in` `distribute-lft-in`
29×	`add-exp-log`
28×	`difference-of-squares`
21×	`add-cbrt-cube`
16×	`unswap-sqr`
14×	`distribute-lft-out--`
13×	`associate-l`
9×	`prod-exp` `associate-/r*` `cbrt-unprod` `div-inv`
8×	`pow1` `cbrt-undiv` `div-exp`
6×	`associate-/l*`
4×	`expm1-log1p-u` `sqrt-div` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `associate-*r/` `flip--`
2×	`sub-neg` `pow-prod-down` `*-commutative`
1×	`frac-times` `frac-2neg` `associate-*l/` `clear-num` `fma-udef`

Counts

4 → 313

Calls

4 calls:

71.0ms	(* (fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 9.0)) (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0))))) rand 1.0) (- a (/ 1.0 3.0)))
1.0ms	(fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 9.0)) (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0))))) rand 1.0)
25.0ms	(/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0))))
138.0ms	(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 9.0)) (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

325.0ms	(* (fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 9.0)) (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0))))) rand 1.0) (- a (/ 1.0 3.0)))
308.0ms	(fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 9.0)) (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0))))) rand 1.0)
149.0ms	(/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0))))
267.0ms	(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 9.0)) (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0)))))

simplify1.0s

Counts

325 → 325

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	610	12383
1	1431	11625
done	5001	9487

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
0.2b	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
0.3b	(/ (pow (cbrt 1.0) 3) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
0.3b	(/ (pow (cbrt 1.0) 3) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
38×	`times-frac`
36×	`-un-lft-identity` `associate-/l`
34×	`add-exp-log`
32×	`add-cube-cbrt`
26×	`sqrt-prod`
24×	`cbrt-prod` `unpow-prod-down` `cube-prod`
18×	`associate-r` `add-cbrt-cube`
12×	`pow1` `div-exp` `associate-l`
8×	`sqrt-div` `associate-*r/` `prod-exp` `unswap-sqr`
6×	`pow-prod-down`
4×	`cbrt-undiv` `expm1-log1p-u` `cube-mult` `pow-to-exp` `flip3--` `sqrt-pow1` `pow1/2` `unpow3` `pow-exp` `associate-/r/` `flip--` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `difference-of-squares` `sqr-pow`
2×	`frac-2neg` `sqrt-unprod` `clear-num` `associate-/r` `-commutative` `div-inv` `distribute-lft-out--`

Counts

4 → 192

Calls

4 calls:

67.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
66.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
45.0ms	(/ (pow (cbrt 1.0) 3) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
48.0ms	(/ (pow (cbrt 1.0) 3) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))

series776.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
124.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
246.0ms	(/ (pow (cbrt 1.0) 3) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
278.0ms	(/ (pow (cbrt 1.0) 3) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))

simplify1.4s

Counts

204 → 204

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	212	3430
1	496	2842
2	1724	2700
done	5000	2672

prune1.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes133.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	20
1	14	20
done	14	20

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.5s	27325×	body	80	nan
1.2s	9148×	body	80	valid