Details

sample74.0ms

Algorithm

intervals

Results

32.0ms	978×	body	80	nan
9.0ms	286×	body	80	valid

simplify3.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	13	20
1	27	20
2	76	19
3	206	19
4	503	19
5	992	19
6	2080	19
7	3449	19
done	5000	19

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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)))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
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)))))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
26×	`*-un-lft-identity` `times-frac`
24×	`add-cube-cbrt` `associate-l`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
8×	`associate-*r/` `sqrt-prod`
6×	`flip3--` `sqrt-div` `associate-r` `flip--`
4×	`expm1-log1p-u` `frac-times` `associate-/r*` `associate-/r/` `log1p-expm1-u` `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` `frac-2neg` `distribute-lft-in` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 122

Calls

4 calls:

48.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
41.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
63.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
16.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series515.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
71.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
179.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
148.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify1.6s

Counts

134 → 134

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	311	2723
1	860	2576
2	3117	2342
done	5000	2340

prune413.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

795×	`times-frac`
608×	`add-sqr-sqrt`
452×	`sqrt-prod`
440×	`*-un-lft-identity`
346×	`add-cube-cbrt`
210×	`associate-l`
94×	`difference-of-squares`
47×	`distribute-lft-out--`
22×	`associate-/l*`
21×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `associate-/r*`
8×	`unswap-sqr`
6×	`cbrt-undiv` `flip3--` `sqrt-div` `div-exp` `associate-r` `flip--`
4×	`expm1-log1p-u` `frac-times` `prod-exp` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `associate-*l/` `flip-+`
2×	`associate-r/` `pow-prod-down` `-commutative`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 533

Calls

4 calls:

23.0ms	(sqrt (- a (/ 1.0 3.0)))
51.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
116.0ms	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
34.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series598.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(sqrt (- a (/ 1.0 3.0)))
149.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
222.0ms	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
183.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify749.0ms

Counts

545 → 545

Iterations

Useful iterations: done (722.0ms)

Iter	Nodes	Cost
0	646	11648
1	1704	10914
done	5000	10635

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
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)))))
7.5b	(* (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand) (- a (/ 1.0 3.0)))

rewrite351.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
91×	`add-cube-cbrt`
80×	`times-frac`
78×	`prod-diff`
41×	`distribute-rgt-in` `distribute-lft-in`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-l`
14×	`pow1`
9×	`associate-r`
8×	`associate-*r/` `sqrt-prod` `div-inv`
7×	`prod-exp` `cbrt-unprod`
6×	`sqrt-div`
5×	`flip3--` `pow-prod-down` `associate-*l/` `flip--`
4×	`expm1-log1p-u` `associate-/r*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`frac-times` `sub-neg` `sqrt-pow1` `*-commutative` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 201

Calls

4 calls:

40.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
62.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
16.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
223.0ms	(* (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand) (- a (/ 1.0 3.0)))

series568.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
184.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
149.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
161.0ms	(* (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand) (- a (/ 1.0 3.0)))

simplify1.8s

Counts

213 → 213

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	518	7655
1	1363	7130
2	4474	5893
done	5000	5888

prune444.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (/ (sqrt 1.0) (cbrt (sqrt 9.0))) (sqrt (- a (/ 1.0 3.0)))) rand)
0.2b	(* (/ (/ (sqrt 1.0) (* (cbrt (sqrt 9.0)) (cbrt (sqrt 9.0)))) (sqrt 1)) (* (/ (/ (sqrt 1.0) (cbrt (sqrt 9.0))) (sqrt (- a (/ 1.0 3.0)))) rand))
0.4b	(/ (/ (sqrt 1.0) (cbrt (sqrt 9.0))) (sqrt (- a (/ 1.0 3.0))))
1.0b	(/ (sqrt 1.0) (cbrt (sqrt 9.0)))

rewrite644.0ms

Algorithm

rewrite-expression-head

Rules

2363×	`times-frac`
1673×	`sqrt-prod`
1664×	`add-sqr-sqrt`
1257×	`*-un-lft-identity`
1023×	`add-cube-cbrt`
734×	`cbrt-prod`
592×	`associate-l`
234×	`difference-of-squares`
117×	`distribute-lft-out--`
100×	`add-exp-log`
85×	`add-cbrt-cube`
64×	`associate-/l*`
39×	`cbrt-undiv` `div-exp`
35×	`prod-exp` `cbrt-unprod`
29×	`div-inv`
18×	`associate-/r*`
15×	`unswap-sqr`
11×	`pow1`
4×	`expm1-log1p-u` `sqrt-div` `associate-r` `pow-prod-down` `associate-*l/` `associate-/r/` `log1p-expm1-u` `add-log-exp`
2×	`flip3--` `frac-2neg` `clear-num` `*-commutative` `flip--`
1×	`frac-times` `associate-*r/` `associate-/l/`

Counts

4 → 1367

Calls

4 calls:

214.0ms	(* (/ (/ (sqrt 1.0) (cbrt (sqrt 9.0))) (sqrt (- a (/ 1.0 3.0)))) rand)
222.0ms	(* (/ (/ (sqrt 1.0) (* (cbrt (sqrt 9.0)) (cbrt (sqrt 9.0)))) (sqrt 1)) (* (/ (/ (sqrt 1.0) (cbrt (sqrt 9.0))) (sqrt (- a (/ 1.0 3.0)))) rand))
51.0ms	(/ (/ (sqrt 1.0) (cbrt (sqrt 9.0))) (sqrt (- a (/ 1.0 3.0))))
9.0ms	(/ (sqrt 1.0) (cbrt (sqrt 9.0)))

series1.3s

Counts

4 → 10

Calls

4 calls:

635.0ms	(* (/ (/ (sqrt 1.0) (cbrt (sqrt 9.0))) (sqrt (- a (/ 1.0 3.0)))) rand)
355.0ms	(* (/ (/ (sqrt 1.0) (* (cbrt (sqrt 9.0)) (cbrt (sqrt 9.0)))) (sqrt 1)) (* (/ (/ (sqrt 1.0) (cbrt (sqrt 9.0))) (sqrt (- a (/ 1.0 3.0)))) rand))
309.0ms	(/ (/ (sqrt 1.0) (cbrt (sqrt 9.0))) (sqrt (- a (/ 1.0 3.0))))
0.0ms	(/ (sqrt 1.0) (cbrt (sqrt 9.0)))

simplify1.6s

Counts

1377 → 1377

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	1088	34237
1	2835	31678
done	5000	30573

prune3.8s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes71.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	17	21
done	17	21

end0.0ms

sample1.9s

Algorithm

intervals

Results

833.0ms	27779×	body	80	nan
312.0ms	9172×	body	80	valid