Details

sample96.0ms

Algorithm

intervals

Results

45.0ms	959×	body	80	nan
15.0ms	295×	body	80	valid

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	325
1	27	325
2	72	325
3	190	325
4	462	325
5	891	325
6	1760	325
7	3827	325
done	5000	325

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

43.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
73.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
13.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
10.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series627.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
195.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
169.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
107.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify2.8s

Counts

126 → 126

Iterations

Useful iterations: 2 (1.4s)

Iter	Nodes	Cost
0	303	51903
1	857	45905
2	4501	44901
done	5000	44901

prune731.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.3b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
8.5b	(* (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand) (- a (/ 1.0 3.0)))

rewrite633.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

57.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
13.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
9.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
548.0ms	(* (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand) (- a (/ 1.0 3.0)))

series706.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
192.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
100.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
207.0ms	(* (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand) (- a (/ 1.0 3.0)))

simplify2.4s

Counts

127 → 127

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	298	49863
1	814	44084
2	4295	42640
done	5000	42640

prune781.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))
0.3b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.3b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
8.5b	(* a (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

33×	`associate-l`
22×	`add-cbrt-cube` `add-exp-log`
20×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`prod-exp` `cbrt-unprod`
8×	`pow-prod-down`
6×	`associate-*r/`
4×	`sqrt-pow1` `sqrt-div` `associate-*l/` `add-log-exp`
2×	`cbrt-undiv` `flip3--` `pow1/2` `div-exp` `associate-r` `*-commutative` `sqrt-prod` `div-inv` `flip--` `distribute-neg-frac`
1×	`distribute-lft-neg-out` `frac-times` `neg-mul-1`

Counts

4 → 98

Calls

4 calls:

135.0ms	(* (- (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))
9.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
9.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
142.0ms	(* a (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

series676.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(* (- (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))
106.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
82.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
257.0ms	(* a (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify1.7s

Counts

110 → 110

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	263	43147
1	759	37835
2	3387	37191
done	5000	36551

prune705.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.3b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
8.5b	(* (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

61.0ms	(* 9.0 (- a (/ 1.0 3.0)))
32.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
16.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
125.0ms	(* (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))

series684.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* 9.0 (- a (/ 1.0 3.0)))
259.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
90.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
254.0ms	(* (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))

simplify2.4s

Counts

118 → 118

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	263	41004
1	761	35859
2	4064	35257
done	5000	34777

prune635.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes181.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	365
1	19	365
done	19	365

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.6s	26968×	body	80	nan
832.0ms	9189×	body	80	valid