Details

sample189.0ms

Algorithm

intervals

Results

105.0ms	1052×	body	80	nan
47.0ms	300×	body	80	valid

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	4878
3	463
2	80
1	30
0	14

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
0.2b	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9 (- a (/ 1.0 3.0))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `times-frac`
24×	`associate-l` `add-cube-cbrt`
19×	`add-exp-log`
15×	`pow1`
13×	`add-cbrt-cube`
8×	`associate-*r/` `sqrt-prod`
6×	`flip3--` `sqrt-div` `associate-r` `flip--`
5×	`prod-exp`
4×	`frac-times` `associate-/r*` `sqrt-pow1` `div-exp` `pow-prod-down` `associate-/r/` `insert-posit16` `pow-flip` `add-log-exp` `unswap-sqr`
3×	`flip3-+` `associate-l/` `cbrt-unprod` `flip-+` `associate-/l`
2×	`cbrt-undiv` `rec-exp` `pow1/2` `1-exp` `*-commutative` `div-inv` `difference-of-squares`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `distribute-lft-out--` `inv-pow`

Counts

4 → 128

Calls

4 calls:

28.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
71.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
17.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
13.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
187.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
115.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
66.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify2.6s

Counts

140 → 140

Iterations

Iter	Nodes
done	5001
2	4851
1	788
0	281

prune571.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1 (* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)))
0.2b	(* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1 (sqrt (- a (/ 1.0 3.0))))
0.4b	(* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0)))))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
66×	`times-frac`
60×	`*-un-lft-identity`
44×	`sqrt-prod`
42×	`add-cube-cbrt`
39×	`associate-r`
34×	`add-exp-log`
22×	`add-cbrt-cube`
16×	`difference-of-squares`
15×	`pow1`
14×	`prod-exp`
10×	`associate-l`
9×	`associate-/r*`
8×	`cbrt-unprod` `distribute-lft-out--`
6×	`div-exp` `unswap-sqr`
5×	`flip3--` `pow-prod-down` `flip--`
4×	`frac-times` `sqrt-div` `associate-l/` `associate-r/` `associate-/r/` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `-commutative` `flip-+` `pow-flip` `associate-/l`
2×	`un-div-inv` `div-inv`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `inv-pow`

Counts

4 → 176

Calls

4 calls:

41.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)))
73.0ms	(* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)
15.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))
44.0ms	(* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0)))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)))
162.0ms	(* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)
76.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))
84.0ms	(* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0)))))

simplify872.0ms

Counts

188 → 188

Iterations

Iter	Nodes
done	5001
1	928
0	328

prune715.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1/3 (sqrt (- a (/ 1.0 3.0)))) rand)))
0.2b	(* (/ 1/3 (sqrt (- a (/ 1.0 3.0)))) rand)
0.4b	(/ 1/3 (sqrt (- a (/ 1.0 3.0))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
65×	`times-frac`
60×	`*-un-lft-identity`
49×	`sqrt-prod`
42×	`add-cube-cbrt`
39×	`associate-l`
18×	`difference-of-squares`
13×	`add-cbrt-cube` `add-exp-log`
9×	`pow1` `associate-/r*` `distribute-lft-out--`
6×	`flip3--` `sqrt-div` `associate-r` `flip--`
4×	`frac-times` `associate-/r/` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`flip3-+` `associate-l/` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 159

Calls

4 calls:

7.0ms	(sqrt (- a (/ 1.0 3.0)))
34.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1/3 (sqrt (- a (/ 1.0 3.0)))) rand)))
26.0ms	(* (/ 1/3 (sqrt (- a (/ 1.0 3.0)))) rand)
19.0ms	(/ 1/3 (sqrt (- a (/ 1.0 3.0))))

series437.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (- a (/ 1.0 3.0)))
80.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1/3 (sqrt (- a (/ 1.0 3.0)))) rand)))
212.0ms	(* (/ 1/3 (sqrt (- a (/ 1.0 3.0)))) rand)
104.0ms	(/ 1/3 (sqrt (- a (/ 1.0 3.0))))

simplify2.4s

Counts

171 → 171

Iterations

Iter	Nodes
done	5000
2	4426
1	821
0	306

prune705.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9 (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1 (/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))))
0.2b	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9 (- a (/ 1.0 3.0))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
17×	`add-cube-cbrt`
14×	`times-frac`
11×	`pow1`
10×	`add-cbrt-cube` `associate-r` `add-exp-log`
9×	`associate-l`
8×	`associate-*r/`
6×	`flip3--` `flip--`
5×	`sqrt-prod`
4×	`frac-times` `associate-/r*` `sqrt-div` `insert-posit16` `add-log-exp` `difference-of-squares`
3×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `flip-+` `associate-/l*`
2×	`sub-neg` `sqrt-pow1` `associate-l/` `prod-exp` `associate-/r/` `-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `pow1/2` `div-exp` `div-inv` `distribute-lft-out`

Counts

4 → 109

Calls

4 calls:

21.0ms	(* 9 (- a (/ 1.0 3.0)))
58.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))))
10.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
6.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* 9 (- a (/ 1.0 3.0)))
116.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))))
148.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
58.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify2.1s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
2	3884
1	688
0	251

prune509.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes109.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	18
1	18
0	13

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.6s	27169×	body	80	nan
1.5s	9178×	body	80	valid