Details

sample148.0ms

Algorithm

intervals

Results

63.0ms	967×	body	80	nan
25.0ms	288×	body	80	valid

simplify5.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

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

prune9.0ms

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)))
0.3b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite230.0ms

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:

57.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
96.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
21.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
52.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series701.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
273.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
165.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
80.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify2.7s

Counts

134 → 134

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	311	2723
1	860	2576
2	3111	2342
done	5001	2340

prune624.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

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)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite280.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
85×	`add-cube-cbrt`
78×	`prod-diff`
68×	`times-frac`
42×	`distribute-rgt-in` `distribute-lft-in`
11×	`pow1`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-r` `associate-l`
8×	`associate-*r/`
7×	`div-inv`
6×	`flip3--` `flip--`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `frac-times` `sqrt-div` `associate-/r*` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`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`

Counts

4 → 190

Calls

4 calls:

94.0ms	(* 9.0 (- a (/ 1.0 3.0)))
71.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
17.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
87.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series557.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* 9.0 (- a (/ 1.0 3.0)))
161.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
238.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
94.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify2.5s

Counts

202 → 202

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	495	5689
1	1127	5171
2	3647	3969
done	5000	3617

prune666.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.2b	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
5.7b	(* (- a (/ 1.0 3.0)) (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))

rewrite412.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 187

Calls

4 calls:

89.0ms	(* 9.0 (- a (/ 1.0 3.0)))
16.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
52.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
244.0ms	(* (- a (/ 1.0 3.0)) (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))

series690.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* 9.0 (- a (/ 1.0 3.0)))
256.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
113.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
234.0ms	(* (- a (/ 1.0 3.0)) (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))

simplify2.3s

Counts

199 → 199

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	492	5414
1	1070	4914
2	3195	3723
done	5001	3200

prune632.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

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)))
0.3b	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
0.4b	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

rewrite430.0ms

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:

34.0ms	(sqrt (- a (/ 1.0 3.0)))
71.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
148.0ms	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
74.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series928.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(sqrt (- a (/ 1.0 3.0)))
228.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)))
306.0ms	(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
330.0ms	(/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify1.0s

Counts

545 → 545

Iterations

Useful iterations: done (976.0ms)

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

prune2.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes127.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	26
1	19	26
done	19	26

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.1s	27325×	body	80	nan
829.0ms	9148×	body	80	valid