Details

sample221.0ms

Algorithm

intervals

Results

140.0ms	1044×	body	80	nan
37.0ms	303×	body	80	valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
6	3095
5	1346
4	543
3	191
2	75
1	28
0	14

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
0.1b	(sqrt (* 9 (- a (/ 1.0 3.0))))
0.2b	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `times-frac`
24×	`associate-l` `add-cube-cbrt`
19×	`add-exp-log`
15×	`pow1`
13×	`add-cbrt-cube`
8×	`associate-*r/` `sqrt-prod`
6×	`flip3--` `sqrt-div` `associate-r` `flip--`
5×	`prod-exp`
4×	`expm1-log1p-u` `frac-times` `associate-/r*` `sqrt-pow1` `div-exp` `pow-prod-down` `associate-/r/` `insert-posit16` `log1p-expm1-u` `pow-flip` `add-log-exp` `unswap-sqr`
3×	`flip3-+` `associate-l/` `cbrt-unprod` `flip-+` `associate-/l`
2×	`cbrt-undiv` `rec-exp` `pow1/2` `1-exp` `*-commutative` `div-inv` `difference-of-squares`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `distribute-lft-out--` `inv-pow`

Counts

4 → 136

Calls

4 calls:

59.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
29.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
118.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
30.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

series495.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
61.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
214.0ms	(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
137.0ms	(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify2.3s

Counts

148 → 148

Iterations

Iter	Nodes
2	2489
1	777
0	289

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1 (* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)))
0.2b	(* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1 (sqrt (- a (/ 1.0 3.0))))
0.4b	(* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0)))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
66×	`times-frac`
60×	`*-un-lft-identity`
44×	`sqrt-prod`
42×	`add-cube-cbrt`
39×	`associate-r`
34×	`add-exp-log`
22×	`add-cbrt-cube`
16×	`difference-of-squares`
15×	`pow1`
14×	`prod-exp`
10×	`associate-l`
9×	`associate-/r*`
8×	`cbrt-unprod` `distribute-lft-out--`
6×	`div-exp` `unswap-sqr`
5×	`flip3--` `pow-prod-down` `flip--`
4×	`expm1-log1p-u` `frac-times` `sqrt-div` `associate-l/` `associate-r/` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `-commutative` `flip-+` `pow-flip` `associate-/l`
2×	`un-div-inv` `div-inv`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `inv-pow`

Counts

4 → 184

Calls

4 calls:

28.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)))
56.0ms	(* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)
25.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))
54.0ms	(* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0)))))

series512.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (- a (/ 1.0 3.0)) (+ 1 (* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)))
235.0ms	(* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)
86.0ms	(/ 1 (sqrt (- a (/ 1.0 3.0))))
84.0ms	(* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0)))))

simplify2.2s

Counts

196 → 196

Iterations

Iter	Nodes
2	2836
1	914
0	336

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.3b	(/ (* 1/3 rand) (sqrt (- a (/ 1.0 3.0))))
0.3b	(* 1/3 rand)
7.9b	(* (/ (* 1/3 rand) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
83×	`add-cube-cbrt`
78×	`prod-diff`
77×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
24×	`sqrt-prod`
20×	`add-cbrt-cube` `add-exp-log`
18×	`associate-l`
10×	`difference-of-squares`
9×	`pow1` `associate-/r` `associate-r*`
8×	`div-inv`
6×	`sqrt-div` `prod-exp` `cbrt-unprod`
5×	`flip3--` `flip--` `distribute-lft-out--`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `sub-neg` `pow-prod-down` `associate-r/` `-commutative` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l/` `associate-/l`

Counts

4 → 207

Calls

4 calls:

19.0ms	(sqrt (- a (/ 1.0 3.0)))
29.0ms	(/ (* 1/3 rand) (sqrt (- a (/ 1.0 3.0))))
10.0ms	(* 1/3 rand)
78.0ms	(* (/ (* 1/3 rand) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt (- a (/ 1.0 3.0)))
157.0ms	(/ (* 1/3 rand) (sqrt (- a (/ 1.0 3.0))))
29.0ms	(* 1/3 rand)
130.0ms	(* (/ (* 1/3 rand) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))

simplify2.9s

Counts

219 → 219

Iterations

Iter	Nodes
2	4402
1	1360
0	466

prune2.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.2b	(/ rand (sqrt (- a (/ 1.0 3.0))))
0.3b	(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
7.9b	(* (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

163×	`add-sqr-sqrt`
127×	`*-un-lft-identity`
119×	`times-frac`
109×	`add-cube-cbrt`
78×	`prod-diff`
49×	`sqrt-prod`
41×	`distribute-rgt-in` `distribute-lft-in`
39×	`associate-r`
20×	`add-cbrt-cube` `add-exp-log`
18×	`difference-of-squares`
12×	`pow1`
9×	`associate-/r*` `distribute-lft-out--`
8×	`div-inv`
7×	`prod-exp` `cbrt-unprod`
6×	`sqrt-div` `associate-*r/`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*` `unswap-sqr`
2×	`frac-times` `sub-neg` `*-commutative`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-*l/`

Counts

4 → 246

Calls

4 calls:

11.0ms	(sqrt (- a (/ 1.0 3.0)))
17.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
27.0ms	(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
69.0ms	(* (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (- a (/ 1.0 3.0)))
133.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
165.0ms	(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
158.0ms	(* (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))

simplify2.3s

Counts

258 → 258

Iterations

Iter	Nodes
2	4192
1	1461
0	511

prune2.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes137.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	18
1	18
0	14

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.4s	28021×	body	80	nan
1.1s	9201×	body	80	valid