Details

sample231.0ms

Algorithm

intervals

Results

152.0ms	895×	body	80	nan
39.0ms	291×	body	80	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2003
5	2003
4	806
3	225
2	76
1	30
0	14

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

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))))
0.2b	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
9.2b	(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

40.0ms	(* 9 (- a (/ 1.0 3.0)))
13.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
11.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
80.0ms	(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* 9 (- a (/ 1.0 3.0)))
62.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
167.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
177.0ms	(* (- a (/ 1.0 3.0)) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))))

simplify1.1s

Counts

133 → 133

Iterations

Iter	Nodes
done	2000
2	2000
1	624
0	249

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize34.0ms

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

rewrite165.0ms

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:

39.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
10.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
93.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
21.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
65.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
191.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
95.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify1.2s

Counts

140 → 140

Iterations

Iter	Nodes
done	2001
2	2001
1	769
0	281

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9 (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1 (* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)))
0.1b	(pow (* 9 (- a (/ 1.0 3.0))) -1/2)
0.2b	(* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
19×	`add-exp-log`
15×	`*-un-lft-identity`
14×	`associate-l`
12×	`associate-r`
11×	`pow1` `add-cube-cbrt`
10×	`add-cbrt-cube`
8×	`prod-exp`
4×	`frac-times` `flip3--` `pow-exp` `associate-*r/` `insert-posit16` `flip--` `add-log-exp` `difference-of-squares` `unswap-sqr`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `flip3-+` `pow-prod-down` `*-commutative` `cbrt-unprod` `flip-+` `sqr-pow`
2×	`pow-to-exp` `sub-neg` `unpow-prod-down` `pow-pow` `times-frac` `associate-*l/` `distribute-lft-out--`

Counts

4 → 102

Calls

4 calls:

29.0ms	(* 9 (- a (/ 1.0 3.0)))
46.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)))
13.0ms	(pow (* 9 (- a (/ 1.0 3.0))) -1/2)
13.0ms	(* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)

series521.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* 9 (- a (/ 1.0 3.0)))
120.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)))
136.0ms	(pow (* 9 (- a (/ 1.0 3.0))) -1/2)
188.0ms	(* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)

simplify1.1s

Counts

114 → 114

Iterations

Iter	Nodes
done	2000
2	2000
1	726
0	251

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.2b	(/ rand (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (- a (/ 1.0 3.0)) 1/3)
9.2b	(* (* (- a (/ 1.0 3.0)) 1/3) (/ rand (sqrt (- a (/ 1.0 3.0)))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
63×	`times-frac`
59×	`*-un-lft-identity`
48×	`sqrt-prod`
41×	`add-cube-cbrt`
36×	`associate-r`
20×	`add-cbrt-cube` `add-exp-log`
18×	`difference-of-squares`
12×	`pow1`
9×	`associate-/r*` `distribute-lft-out--`
8×	`associate-*l/`
7×	`associate-l` `prod-exp` `cbrt-unprod`
6×	`flip3--` `sqrt-div` `flip--`
4×	`pow-prod-down` `associate-/r/` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`frac-times` `*-commutative` `div-inv`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-*r/` `unswap-sqr`

Counts

4 → 155

Calls

4 calls:

7.0ms	(sqrt (- a (/ 1.0 3.0)))
11.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
24.0ms	(* (- a (/ 1.0 3.0)) 1/3)
60.0ms	(* (* (- a (/ 1.0 3.0)) 1/3) (/ rand (sqrt (- a (/ 1.0 3.0)))))

series346.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (- a (/ 1.0 3.0)))
104.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
63.0ms	(* (- a (/ 1.0 3.0)) 1/3)
139.0ms	(* (* (- a (/ 1.0 3.0)) 1/3) (/ rand (sqrt (- a (/ 1.0 3.0)))))

simplify828.0ms

Counts

167 → 167

Iterations

Iter	Nodes
done	2001
2	2001
1	719
0	277

prune1.6s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes117.0ms

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	20
1	20
0	14

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.6s	27625×	body	80	nan
1.3s	9120×	body	80	valid