Details

sample96.0ms

Algorithm

intervals

Results

31.0ms	812×	body	80	nan
13.0ms	293×	body	80	valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	2429
5	1149
4	547
3	208
2	76
1	27
0	13

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- a (/ 1.0 3.0)) 9.0)
0.1b	(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (* 1.0 (- a (/ 1.0 3.0))) (* 1.0 (- a (/ 1.0 3.0))))
0.1b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
0.2b	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-l` `associate-*l/`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `associate-/r*` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `associate-r` `flip--` `associate-/l*`
2×	`sqrt-pow1` `pow-prod-down` `associate-/r/` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `pow1/2` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

58.0ms	(* (- a (/ 1.0 3.0)) 9.0)
0.0ms	(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (* 1.0 (- a (/ 1.0 3.0))) (* 1.0 (- a (/ 1.0 3.0))))
11.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
14.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (- a (/ 1.0 3.0)) 9.0)
124.0ms	(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (* 1.0 (- a (/ 1.0 3.0))) (* 1.0 (- a (/ 1.0 3.0))))
79.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
243.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

simplify1.6s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	2200
1	559
0	230

prune561.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(fma (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) (* 1.0 (- a (/ 1.0 3.0))) (* 1.0 (- a (/ 1.0 3.0))))
0.3b	(/ rand (sqrt (- a (/ 1.0 3.0))))
0.3b	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

440×	`times-frac`
334×	`add-sqr-sqrt`
258×	`sqrt-prod`
255×	`*-un-lft-identity`
203×	`add-cube-cbrt`
52×	`difference-of-squares`
36×	`associate-/l*`
26×	`distribute-lft-out--`
18×	`sqrt-div`
16×	`associate-/r/`
15×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`flip3--` `div-inv` `flip--`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef` `associate-/l/`

Counts

4 → 339

Calls

4 calls:

25.0ms	(sqrt (- a (/ 1.0 3.0)))
0.0ms	(fma (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) (* 1.0 (- a (/ 1.0 3.0))) (* 1.0 (- a (/ 1.0 3.0))))
19.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
41.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

series695.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (- a (/ 1.0 3.0)))
227.0ms	(fma (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) (* 1.0 (- a (/ 1.0 3.0))) (* 1.0 (- a (/ 1.0 3.0))))
123.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
278.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

simplify1.1s

Counts

351 → 351

Iterations

Iter	Nodes
done	5000
1	1253
0	513

prune2.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (/ rand (fabs (cbrt (- a (/ 1.0 3.0))))) (sqrt (cbrt (- a (/ 1.0 3.0))))) (sqrt 9.0))
0.3b	(/ (/ rand (fabs (cbrt (- a (/ 1.0 3.0))))) (sqrt (cbrt (- a (/ 1.0 3.0)))))
0.6b	(cbrt (- a (/ 1.0 3.0)))
0.6b	(cbrt (- a (/ 1.0 3.0)))

rewrite384.0ms

Algorithm

rewrite-expression-head

Rules

3200×	`times-frac`
1868×	`add-sqr-sqrt`
1547×	`*-un-lft-identity`
1434×	`sqrt-prod`
1333×	`add-cube-cbrt`
642×	`cbrt-prod`
214×	`difference-of-squares`
175×	`associate-/l*`
107×	`distribute-lft-out--`
106×	`div-inv`
20×	`cbrt-div`
18×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
16×	`sqrt-div` `associate-/r/`
10×	`flip3--` `flip--`
9×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow1/3` `associate-/l/`

Counts

4 → 1395

Calls

4 calls:

112.0ms	(/ (/ (/ rand (fabs (cbrt (- a (/ 1.0 3.0))))) (sqrt (cbrt (- a (/ 1.0 3.0))))) (sqrt 9.0))
56.0ms	(/ (/ rand (fabs (cbrt (- a (/ 1.0 3.0))))) (sqrt (cbrt (- a (/ 1.0 3.0)))))
7.0ms	(cbrt (- a (/ 1.0 3.0)))
7.0ms	(cbrt (- a (/ 1.0 3.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

425.0ms	(/ (/ (/ rand (fabs (cbrt (- a (/ 1.0 3.0))))) (sqrt (cbrt (- a (/ 1.0 3.0))))) (sqrt 9.0))
344.0ms	(/ (/ rand (fabs (cbrt (- a (/ 1.0 3.0))))) (sqrt (cbrt (- a (/ 1.0 3.0)))))
162.0ms	(cbrt (- a (/ 1.0 3.0)))
129.0ms	(cbrt (- a (/ 1.0 3.0)))

simplify4.0s

Counts

1407 → 1407

Iterations

Iter	Nodes
done	5001
1	3851
0	1654

prune8.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ rand (fabs (cbrt (- a (/ 1.0 3.0))))) (fabs (cbrt 9.0))) (/ (/ 1 (sqrt (cbrt (- a (/ 1.0 3.0))))) (sqrt (cbrt 9.0))))
0.4b	(/ (/ 1 (sqrt (cbrt (- a (/ 1.0 3.0))))) (sqrt (cbrt 9.0)))
0.6b	(cbrt (- a (/ 1.0 3.0)))
0.6b	(cbrt (- a (/ 1.0 3.0)))

rewrite595.0ms

Algorithm

rewrite-expression-head

Rules

1748×	`times-frac`
1298×	`add-sqr-sqrt`
1101×	`sqrt-prod`
860×	`*-un-lft-identity`
715×	`add-cube-cbrt`
648×	`cbrt-prod`
382×	`associate-r`
118×	`difference-of-squares`
73×	`add-exp-log`
66×	`unswap-sqr`
59×	`distribute-lft-out--`
45×	`add-cbrt-cube`
43×	`associate-l`
42×	`cbrt-div` `associate-/l*`
39×	`div-exp`
38×	`sqrt-div` `associate-/r/`
25×	`div-inv`
21×	`cbrt-undiv` `flip3--` `flip--`
15×	`prod-exp`
9×	`associate-/r*` `cbrt-unprod`
6×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 1013

Calls

4 calls:

360.0ms	(* (/ (/ rand (fabs (cbrt (- a (/ 1.0 3.0))))) (fabs (cbrt 9.0))) (/ (/ 1 (sqrt (cbrt (- a (/ 1.0 3.0))))) (sqrt (cbrt 9.0))))
66.0ms	(/ (/ 1 (sqrt (cbrt (- a (/ 1.0 3.0))))) (sqrt (cbrt 9.0)))
7.0ms	(cbrt (- a (/ 1.0 3.0)))
14.0ms	(cbrt (- a (/ 1.0 3.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

551.0ms	(* (/ (/ rand (fabs (cbrt (- a (/ 1.0 3.0))))) (fabs (cbrt 9.0))) (/ (/ 1 (sqrt (cbrt (- a (/ 1.0 3.0))))) (sqrt (cbrt 9.0))))
277.0ms	(/ (/ 1 (sqrt (cbrt (- a (/ 1.0 3.0))))) (sqrt (cbrt 9.0)))
111.0ms	(cbrt (- a (/ 1.0 3.0)))
154.0ms	(cbrt (- a (/ 1.0 3.0)))

simplify4.4s

Counts

1025 → 1025

Iterations

Iter	Nodes
done	5000
1	4222
0	1217

prune6.6s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes259.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	14
1	14
0	12

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.5s	26714×	body	80	nan
927.0ms	9159×	body	80	valid