Details

sample124.0ms

Algorithm

intervals

Results

63.0ms	854×	body	80	nan
15.0ms	289×	body	80	valid

simplify3.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	13	20
1	27	20
2	76	19
3	208	19
4	553	19
5	1150	19
6	2491	19
done	5000	19

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

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

rewrite261.0ms

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:

87.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
93.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
20.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
57.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series736.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
277.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
190.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
116.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify2.7s

Counts

134 → 134

Iterations

Useful iterations: 2 (996.0ms)

Iter	Nodes	Cost
0	311	2723
1	894	2576
2	4710	2372
done	5000	2372

prune803.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

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

rewrite316.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 183

Calls

4 calls:

54.0ms	(* 9.0 (- a (/ 1.0 3.0)))
160.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
27.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
64.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series612.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* 9.0 (- a (/ 1.0 3.0)))
163.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
294.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
101.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify834.0ms

Counts

195 → 195

Iterations

Useful iterations: done (818.0ms)

Iter	Nodes	Cost
0	489	5591
1	1320	5049
done	5000	4126

prune926.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite492.0ms

Algorithm

rewrite-expression-head

Rules

163×	`times-frac`
126×	`add-sqr-sqrt`
102×	`sqrt-prod`
86×	`*-un-lft-identity`
58×	`add-cube-cbrt`
26×	`difference-of-squares`
14×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--`
11×	`div-inv`
10×	`associate-/l*`
9×	`associate-/r*`
6×	`pow1` `associate-l`
5×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
4×	`frac-times` `sqrt-div` `associate-r`
3×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`associate-r/` `associate-l/` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `*-commutative` `associate-/l/` `distribute-lft-out` `unswap-sqr`

Counts

3 → 184

Calls

3 calls:

30.0ms	(sqrt (- a (/ 1.0 3.0)))
396.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
48.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

series616.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(sqrt (- a (/ 1.0 3.0)))
204.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))))
363.0ms	(/ (/ (* 1.0 rand) (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0))))

simplify705.0ms

Counts

193 → 193

Iterations

Useful iterations: done (691.0ms)

Iter	Nodes	Cost
0	373	4691
1	1043	4305
done	5000	4166

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite579.0ms

Algorithm

rewrite-expression-head

Rules

234×	`prod-diff`
222×	`add-sqr-sqrt`
215×	`*-un-lft-identity`
213×	`add-cube-cbrt`
205×	`distribute-rgt-in` `distribute-lft-in`
167×	`times-frac`
31×	`pow1`
23×	`add-exp-log`
19×	`div-inv`
17×	`pow-prod-down`
16×	`add-cbrt-cube`
14×	`associate-*r/`
10×	`prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-l`
6×	`sub-neg`
5×	`sqrt-pow1`
4×	`cbrt-prod` `expm1-log1p-u` `flip3--` `sqrt-div` `associate-/r*` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `*-commutative` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `associate-/l*` `distribute-lft-out--`

Counts

4 → 346

Calls

4 calls:

71.0ms	(* (cbrt 9.0) (- a (/ 1.0 3.0)))
69.0ms	(/ (* 1.0 rand) (sqrt (* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0))))))
169.0ms	(* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0))))
211.0ms	(sqrt (* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0)))))

series774.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (cbrt 9.0) (- a (/ 1.0 3.0)))
343.0ms	(/ (* 1.0 rand) (sqrt (* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0))))))
176.0ms	(* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0))))
134.0ms	(sqrt (* (* (cbrt 9.0) (cbrt 9.0)) (* (cbrt 9.0) (- a (/ 1.0 3.0)))))

simplify1.5s

Counts

358 → 358

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	655	14694
1	2211	13355
done	5001	9530

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes171.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	21	27
done	21	27

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.7s	27625×	body	80	nan
771.0ms	9180×	body	80	valid