Details

sample117.0ms

Algorithm

intervals

Results

52.0ms	946×	body	80	nan
18.0ms	295×	body	80	valid

simplify6.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	2855
6	1644
5	941
4	490
3	203
2	76
1	27
0	13

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

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

rewrite100.0ms

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:

66.0ms	(* (- a (/ 1.0 3.0)) 9.0)
0.0ms	(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
17.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
14.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

series510.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (- a (/ 1.0 3.0)) 9.0)
148.0ms	(fma (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
110.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
193.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))

simplify1.6s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	1711
1	545
0	227

prune577.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

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)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.2b	(/ rand (sqrt (- a (/ 1.0 3.0))))
0.2b	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

rewrite118.0ms

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:

31.0ms	(sqrt (- a (/ 1.0 3.0)))
0.0ms	(fma (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) (- a (/ 1.0 3.0)) (- 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))

series567.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(sqrt (- a (/ 1.0 3.0)))
170.0ms	(fma (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
111.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
237.0ms	(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) (sqrt 9.0))

simplify2.1s

Counts

351 → 351

Iterations

Iter	Nodes
done	5001
2	2915
1	1209
0	510

prune1.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(fma (/ rand (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.2b	(/ rand (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
0.3b	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

44.0ms	(sqrt (- a (/ 1.0 3.0)))
1.0ms	(fma (/ rand (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
22.0ms	(/ rand (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
57.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

series682.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (- a (/ 1.0 3.0)))
210.0ms	(fma (/ rand (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
298.0ms	(/ rand (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
120.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

simplify1.9s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	1835
1	552
0	224

prune815.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(fma (* (/ 1 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.2b	(/ rand (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ 1 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

139×	`add-sqr-sqrt`
102×	`times-frac`
74×	`*-un-lft-identity`
68×	`sqrt-prod`
52×	`add-cube-cbrt`
33×	`associate-r`
28×	`add-exp-log`
22×	`associate-l`
18×	`add-cbrt-cube`
16×	`difference-of-squares`
15×	`unswap-sqr`
9×	`associate-/r*` `div-exp`
8×	`prod-exp` `distribute-lft-out--`
7×	`pow1`
6×	`sqrt-div`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `div-inv` `flip--` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`frac-times` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef`

Counts

4 → 181

Calls

4 calls:

38.0ms	(sqrt (- a (/ 1.0 3.0)))
1.0ms	(fma (* (/ 1 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
37.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
100.0ms	(* (/ 1 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

series633.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt (- a (/ 1.0 3.0)))
186.0ms	(fma (* (/ 1 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
112.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
277.0ms	(* (/ 1 (sqrt 9.0)) (/ rand (sqrt (- a (/ 1.0 3.0)))))

simplify2.4s

Counts

193 → 193

Iterations

Iter	Nodes
done	5001
2	2932
1	922
0	339

prune998.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0.0b

regimes176.0ms

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	14
1	14
0	12

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.4s	27405×	body	80	nan
737.0ms	9135×	body	80	valid