Details

sample172.0ms

Algorithm

intervals

Results

98.0ms	914×	body	80	nan
39.0ms	282×	body	80	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	2319
4	806
3	225
2	76
1	30
0	14

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite143.0ms

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:

6.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
41.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
76.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
17.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

series419.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
87.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
178.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
83.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify1.9s

Counts

140 → 140

Iterations

Iter	Nodes
done	5001
2	2701
1	770
0	281

prune664.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- a (/ 1.0 3.0)) 9)
0.1b	(sqrt (* (- a (/ 1.0 3.0)) 9))
0.2b	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9)))
7.0b	(* (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9))) (- a (/ 1.0 3.0)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`times-frac`
24×	`associate-l` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
11×	`pow1`
9×	`associate-r` `associate-*l/`
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-r/` `-commutative` `div-inv` `distribute-lft-out--`
1×	`clear-num` `frac-2neg` `pow1/2`

Counts

4 → 121

Calls

4 calls:

21.0ms	(* (- a (/ 1.0 3.0)) 9)
7.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9))
11.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9)))
77.0ms	(* (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9))) (- a (/ 1.0 3.0)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (- a (/ 1.0 3.0)) 9)
71.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9))
142.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9)))
140.0ms	(* (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9))) (- a (/ 1.0 3.0)))

simplify1.8s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	2102
1	648
0	251

prune588.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize37.0ms

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))))
0.3b	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.3b	(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 144

Calls

4 calls:

22.0ms	(* 9 (- a (/ 1.0 3.0)))
11.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
36.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
72.0ms	(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))

series340.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* 9 (- a (/ 1.0 3.0)))
63.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
95.0ms	(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
132.0ms	(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))

simplify1.4s

Counts

156 → 156

Iterations

Iter	Nodes
done	5000
2	2141
1	676
0	256

prune706.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize19.0ms

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

rewrite84.0ms

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)))
30.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1/3 (sqrt (- a (/ 1.0 3.0)))) rand)))
28.0ms	(* (/ 1/3 (sqrt (- a (/ 1.0 3.0)))) rand)
15.0ms	(/ 1/3 (sqrt (- a (/ 1.0 3.0))))

series453.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt (- a (/ 1.0 3.0)))
98.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1/3 (sqrt (- a (/ 1.0 3.0)))) rand)))
195.0ms	(* (/ 1/3 (sqrt (- a (/ 1.0 3.0)))) rand)
103.0ms	(/ 1/3 (sqrt (- a (/ 1.0 3.0))))

simplify2.0s

Counts

171 → 171

Iterations

Iter	Nodes
done	5002
2	2828
1	814
0	306

prune780.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes128.0ms

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	15
1	15
0	12

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.9s	27682×	body	80	nan
1.6s	9061×	body	80	valid