Details

sample152.0ms

Algorithm

intervals

Results

82.0ms	810×	body	80	nan
38.0ms	292×	body	80	valid

simplify3.1s

Counts

1 → 1

Iterations

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9 (- a (/ 1.0 3.0)))
0.1b	(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.1b	(sqrt (* 9 (- a (/ 1.0 3.0))))
0.2b	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 167

Calls

4 calls:

33.0ms	(* 9 (- a (/ 1.0 3.0)))
0.0ms	(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
13.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
14.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* 9 (- a (/ 1.0 3.0)))
123.0ms	(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
67.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
156.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify895.0ms

Counts

179 → 179

Iterations

Iter	Nodes
2	2140
1	876
0	428

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.1b	(sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))
0.2b	(/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))))
0.2b	(* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

164×	`distribute-rgt-in` `distribute-lft-in`
156×	`prod-diff`
151×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
120×	`times-frac`
15×	`pow1`
13×	`div-inv`
12×	`associate-*r/`
11×	`add-cbrt-cube` `add-exp-log`
8×	`sqrt-prod`
6×	`associate-l` `pow-prod-down`
4×	`expm1-log1p-u` `associate-/r*` `sub-neg` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `flip3--` `prod-exp` `cbrt-unprod` `flip--` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `pow1/2` `div-exp` `associate-r` `*-commutative` `fma-udef`

Counts

4 → 250

Calls

4 calls:

0.0ms	(fma (/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
61.0ms	(sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))
46.0ms	(/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))))
51.0ms	(* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))

series428.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(fma (/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
94.0ms	(sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))
164.0ms	(/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))))
59.0ms	(* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))

simplify4.3s

Counts

262 → 262

Iterations

Iter	Nodes
2	2903
1	1258
0	649

prune3.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 9 (- a (/ 1.0 3.0)))
0.1b	(sqrt (* 9 (- a (/ 1.0 3.0))))
0.2b	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
7.4b	(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

177×	`add-sqr-sqrt`
164×	`*-un-lft-identity`
160×	`add-cube-cbrt`
156×	`prod-diff`
135×	`times-frac`
82×	`distribute-rgt-in` `distribute-lft-in`
21×	`associate-l`
14×	`div-inv`
13×	`add-cbrt-cube` `add-exp-log`
12×	`associate-r`
11×	`pow1`
10×	`associate-*r/`
8×	`sqrt-prod`
6×	`flip3--` `sqrt-div` `flip--`
4×	`expm1-log1p-u` `associate-/r*` `sub-neg` `associate-/r/` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `sqrt-pow1` `div-exp` `*-commutative` `distribute-lft-out--`
1×	`clear-num` `frac-2neg` `pow1/2` `associate-*l/`

Counts

4 → 285

Calls

4 calls:

22.0ms	(* 9 (- a (/ 1.0 3.0)))
24.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
21.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
79.0ms	(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* 9 (- a (/ 1.0 3.0)))
95.0ms	(sqrt (* 9 (- a (/ 1.0 3.0))))
140.0ms	(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
122.0ms	(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))

simplify1.8s

Counts

297 → 297

Iterations

Iter	Nodes
2	3673
1	1454
0	575

prune3.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* (- a (/ 1.0 3.0)) 9))
0.1b	(sqrt (* (- a (/ 1.0 3.0)) 9))
0.2b	(/ (sqrt (* (- a (/ 1.0 3.0)) 9)) rand)
8.6b	(/ (- a (/ 1.0 3.0)) (/ (sqrt (* (- a (/ 1.0 3.0)) 9)) rand))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

209×	`times-frac`
171×	`add-sqr-sqrt`
120×	`*-un-lft-identity`
86×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`sqrt-prod`
19×	`associate-/r*`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`pow1` `associate-/l*`
9×	`div-inv`
6×	`sqrt-div` `associate-*l/`
4×	`expm1-log1p-u` `cbrt-undiv` `sqrt-pow1` `flip3--` `div-exp` `log1p-expm1-u` `flip--` `add-log-exp` `associate-/l/`
2×	`clear-num` `frac-2neg` `pow1/2` `pow-prod-down`
1×	`div-sub` `associate-/r/`

Counts

4 → 203

Calls

4 calls:

10.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9))
8.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9))
10.0ms	(/ (sqrt (* (- a (/ 1.0 3.0)) 9)) rand)
27.0ms	(/ (- a (/ 1.0 3.0)) (/ (sqrt (* (- a (/ 1.0 3.0)) 9)) rand))

series454.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9))
81.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9))
174.0ms	(/ (sqrt (* (- a (/ 1.0 3.0)) 9)) rand)
136.0ms	(/ (- a (/ 1.0 3.0)) (/ (sqrt (* (- a (/ 1.0 3.0)) 9)) rand))

simplify4.4s

Counts

215 → 215

Iterations

Iter	Nodes
2	3550
1	1091
0	366

prune2.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes220.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
2	23
1	23
0	19

end0.0ms

sample6.8s

Algorithm

intervals

Results

4.5s	27547×	body	80	nan
1.4s	9085×	body	80	valid