Details

sample100.0ms

Algorithm

intervals

Results

39.0ms	899×	body	80	nan
29.0ms	293×	body	80	valid

simplify9.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	27	20
2	72	20
3	188	20
4	417	20
5	772	20
6	1496	20
7	2490	20
8	3402	20
9	4724	20
done	5000	20

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

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)))))

rewrite224.0ms

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:

59.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
24.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
98.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
38.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series717.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
94.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
282.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
181.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify2.0s

Counts

126 → 126

Iterations

Useful iterations: 2 (698.0ms)

Iter	Nodes	Cost
0	303	2615
1	823	2480
2	2960	2274
done	5002	2274

prune508.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize26.0ms

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

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `associate-r`
9×	`associate-l`
8×	`associate-*r/`
6×	`flip3--` `times-frac` `flip--`
4×	`frac-times` `sqrt-div` `associate-/r*` `add-log-exp` `difference-of-squares`
3×	`distribute-rgt-in` `distribute-lft-in` `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` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 97

Calls

4 calls:

61.0ms	(* 9.0 (- a (/ 1.0 3.0)))
149.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
12.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
31.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series601.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* 9.0 (- a (/ 1.0 3.0)))
151.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
98.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
280.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify1.8s

Counts

109 → 109

Iterations

Useful iterations: 2 (526.0ms)

Iter	Nodes	Cost
0	264	2121
1	744	1996
2	2820	1812
done	5002	1812

prune403.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize22.0ms

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

rewrite479.0ms

Algorithm

rewrite-expression-head

Rules

189×	`add-sqr-sqrt`
150×	`times-frac`
103×	`*-un-lft-identity`
92×	`sqrt-prod`
75×	`add-cube-cbrt`
66×	`associate-r`
63×	`cbrt-prod`
58×	`add-exp-log`
43×	`add-cbrt-cube`
28×	`difference-of-squares`
24×	`prod-exp` `cbrt-unprod`
17×	`associate-l`
16×	`unswap-sqr`
15×	`cbrt-undiv` `div-exp`
14×	`distribute-lft-out--`
13×	`pow1`
9×	`associate-/r*`
7×	`associate-*l/`
6×	`frac-times` `associate-/l*`
5×	`flip3--` `pow-prod-down` `flip--`
4×	`sqrt-div` `associate-*r/` `associate-/r/` `add-log-exp`
3×	`flip3-+` `*-commutative` `flip-+` `div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 254

Calls

4 calls:

91.0ms	(* (- 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)))
199.0ms	(* (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 9.0)) (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0))))) rand)
26.0ms	(/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0))))
147.0ms	(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 9.0)) (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

270.0ms	(* (- 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)))
357.0ms	(* (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 9.0)) (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0))))) rand)
144.0ms	(/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0))))
268.0ms	(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 9.0)) (/ (cbrt 1.0) (sqrt (- a (/ 1.0 3.0)))))

simplify775.0ms

Counts

266 → 266

Iterations

Useful iterations: done (765.0ms)

Iter	Nodes	Cost
0	457	6866
1	1307	6380
done	5001	5530

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.4b	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))

rewrite323.0ms

Algorithm

rewrite-expression-head

Rules

46×	`sqrt-div`
32×	`frac-times`
25×	`add-sqr-sqrt`
23×	`flip3--` `flip--`
20×	`associate-*r/`
18×	`associate-l`
17×	`*-un-lft-identity`
16×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
14×	`pow1`
12×	`flip3-+` `flip-+`
11×	`add-cube-cbrt`
10×	`associate-*l/`
6×	`times-frac`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`associate-/r*` `add-log-exp` `difference-of-squares`
2×	`cbrt-undiv` `sqrt-pow1` `div-exp` `associate-/r/` `*-commutative` `distribute-lft-out--` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 128

Calls

4 calls:

103.0ms	(* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
14.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
26.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
170.0ms	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))

series845.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
80.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
335.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
204.0ms	(* (sqrt (- a (/ 1.0 3.0))) (* (sqrt (- a (/ 1.0 3.0))) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))

simplify1.9s

Counts

140 → 140

Iterations

Useful iterations: 2 (682.0ms)

Iter	Nodes	Cost
0	319	4861
1	897	4255
2	3435	3803
done	5001	3803

prune694.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes114.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.4s	27268×	body	80	nan
1.8s	9112×	body	80	valid