Details

sample164.0ms

Algorithm

intervals

Results

70.0ms	907×	body	80	nan
25.0ms	293×	body	80	valid

simplify4.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	20
1	27	20
2	72	20
3	190	20
4	459	20
5	929	20
6	1800	20
7	3828	20
done	5000	20

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

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)))))
0.6b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite281.0ms

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×	`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` `frac-2neg` `distribute-lft-in` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 114

Calls

4 calls:

97.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
113.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
28.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
35.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series888.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
319.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
243.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
120.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify3.7s

Counts

126 → 126

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	303	2615
1	857	2480
2	4527	2306
done	5002	2304

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
0.2b	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.6b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`add-cube-cbrt`
14×	`times-frac`
11×	`pow1`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-r` `associate-l`
8×	`associate-*r/`
6×	`flip3--` `flip--`
5×	`sqrt-prod`
4×	`frac-times` `sqrt-div` `associate-/r*` `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` `frac-2neg` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 104

Calls

4 calls:

80.0ms	(* 9.0 (- a (/ 1.0 3.0)))
111.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
34.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
23.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series742.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* 9.0 (- a (/ 1.0 3.0)))
229.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
297.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
135.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify2.7s

Counts

116 → 116

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	271	2223
1	764	2134
2	3569	1974
done	5000	1970

prune950.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite526.0ms

Algorithm

rewrite-expression-head

Rules

161×	`add-sqr-sqrt`
132×	`times-frac`
103×	`*-un-lft-identity`
83×	`sqrt-prod`
76×	`associate-l`
75×	`add-cube-cbrt`
59×	`cbrt-prod`
49×	`add-exp-log`
38×	`add-cbrt-cube`
28×	`difference-of-squares`
21×	`prod-exp` `cbrt-unprod`
14×	`distribute-lft-out--`
13×	`pow1`
11×	`cbrt-undiv` `div-exp`
9×	`associate-/r*`
7×	`associate-r`
6×	`associate-l/` `associate-/l` `unswap-sqr`
5×	`frac-times` `flip3--` `pow-prod-down` `flip--`
4×	`sqrt-div` `associate-/r/` `add-log-exp`
3×	`flip3-+` `associate-r/` `-commutative` `flip-+` `div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 238

Calls

4 calls:

104.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 9.0)) (* (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand))))
53.0ms	(/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0))))
138.0ms	(* (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand)
202.0ms	(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 9.0)) (* (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand))

series1.5s

Counts

4 → 12

Calls

4 calls:

381.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 9.0)) (* (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand))))
210.0ms	(/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0))))
444.0ms	(* (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand)
509.0ms	(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 9.0)) (* (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0)))) rand))

simplify1.1s

Counts

250 → 250

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	432	5683
1	1227	5361
done	5000	4925

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite429.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

21.0ms	(- a (/ 1.0 3.0))
191.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt 1.0) rand)) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
115.0ms	(/ (* (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt 1.0) rand)) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
93.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

37.0ms	(- a (/ 1.0 3.0))
355.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt 1.0) rand)) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))))
555.0ms	(/ (* (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt 1.0) rand)) (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
160.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))

simplify732.0ms

Counts

129 → 129

Iterations

Useful iterations: done (724.0ms)

Iter	Nodes	Cost
0	281	3372
1	899	3091
done	5000	2433

prune965.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes269.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	28
1	21	28
done	21	28

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.9s	27297×	body	80	nan
985.0ms	9138×	body	80	valid