Details

sample204.0ms

Algorithm

intervals

Results

102.0ms	815×	body	80	nan
26.0ms	288×	body	80	valid

simplify13.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
8	4921
7	2072
6	1149
5	738
4	406
3	185
2	72
1	27
0	13

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize116.0ms

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)))))

rewrite399.0ms

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:

96.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
26.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
183.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
81.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series1.8s

Counts

4 → 12

Calls

4 calls:

444.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
157.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
660.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
533.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify10.9s

Counts

126 → 126

Iterations

Iter	Nodes
done	5028
2	3360
1	858
0	303

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize146.0ms

Local error

Found 4 expressions with local error:

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)))))
6.2b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite707.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
24×	`associate-l`
23×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
8×	`sqrt-prod`
7×	`associate-*r/` `prod-exp` `cbrt-unprod`
6×	`sqrt-div` `associate-*l/`
5×	`flip3--` `pow-prod-down` `flip--`
4×	`associate-r` `associate-/r*` `associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`frac-times` `sqrt-pow1` `*-commutative` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 111

Calls

4 calls:

30.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
178.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
36.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
455.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

series1.9s

Counts

4 → 12

Calls

4 calls:

179.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
636.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
315.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
777.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify6.6s

Counts

123 → 123

Iterations

Iter	Nodes
done	5000
2	2814
1	768
0	291

prune1.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

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

rewrite352.0ms

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:

85.0ms	(* 9.0 (- a (/ 1.0 3.0)))
192.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
25.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
44.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series878.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* 9.0 (- a (/ 1.0 3.0)))
220.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
142.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
421.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify3.7s

Counts

109 → 109

Iterations

Iter	Nodes
done	5028
2	3150
1	779
0	264

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.4b	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))
6.2b	(* (- a (/ 1.0 3.0)) (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

139×	`add-sqr-sqrt`
103×	`add-exp-log`
102×	`times-frac`
75×	`*-un-lft-identity`
62×	`sqrt-prod`
61×	`add-cbrt-cube`
53×	`add-cube-cbrt`
52×	`prod-exp`
37×	`associate-r`
29×	`associate-l`
28×	`cbrt-unprod`
25×	`div-exp`
20×	`pow1`
19×	`associate-*l/`
16×	`difference-of-squares`
15×	`unswap-sqr`
13×	`cbrt-undiv`
11×	`frac-times`
10×	`pow-prod-down`
9×	`associate-/r*`
8×	`associate-*r/` `distribute-lft-out--`
6×	`rec-exp` `flip3--` `1-exp` `flip--`
4×	`sqrt-div` `associate-/r/` `add-log-exp`
3×	`-commutative` `div-inv` `associate-/l`
1×	`frac-2neg` `clear-num`

Counts

4 → 223

Calls

4 calls:

219.0ms	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
43.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
148.0ms	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))
861.0ms	(* (- a (/ 1.0 3.0)) (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand))

series1.6s

Counts

4 → 12

Calls

4 calls:

521.0ms	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
231.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
477.0ms	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))
401.0ms	(* (- a (/ 1.0 3.0)) (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand))

simplify7.4s

Counts

235 → 235

Iterations

Iter	Nodes
done	5004
2	4288
1	1216
0	423

prune2.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes622.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample16.1s

Algorithm

intervals

Results

10.6s	27203×	body	80	nan
4.2s	9111×	body	80	valid