Details

sample99.0ms

Algorithm

intervals

Results

46.0ms	894×	body	80	nan
17.0ms	290×	body	80	valid

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	2025
6	1131
5	730
4	405
3	185
2	72
1	27
0	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

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)))))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
26×	`*-un-lft-identity` `times-frac`
24×	`associate-l` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
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` `clear-num` `frac-2neg` `distribute-lft-in` `pow1/2` `distribute-lft-out--`

Counts

4 → 114

Calls

4 calls:

62.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
20.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
95.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
31.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series665.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
83.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
232.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
187.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify2.1s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	3356
1	858
0	303

prune782.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))))
0.3b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
0.3b	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-sqr-sqrt`
82×	`times-frac`
70×	`*-un-lft-identity`
61×	`associate-l`
54×	`add-cube-cbrt`
52×	`add-exp-log` `sqrt-prod`
34×	`add-cbrt-cube`
23×	`prod-exp`
16×	`difference-of-squares`
13×	`pow1` `cbrt-unprod`
12×	`div-exp`
9×	`associate-/r*`
8×	`distribute-lft-out--`
7×	`cbrt-undiv` `associate-r`
6×	`associate-*l/`
5×	`frac-times` `flip3--` `pow-prod-down` `flip--`
4×	`sqrt-div` `associate-/r/` `add-log-exp` `unswap-sqr`
3×	`rec-exp` `flip3-+` `1-exp` `associate-r/` `-commutative` `flip-+` `div-inv` `associate-/l*`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in`

Counts

4 → 191

Calls

4 calls:

64.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))))
19.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
88.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
89.0ms	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

series846.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))))
113.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
225.0ms	(* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand)
275.0ms	(* (/ 1 (sqrt 9.0)) (* (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) rand))

simplify2.7s

Counts

203 → 203

Iterations

Iter	Nodes
done	5004
2	3820
1	1122
0	401

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

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

rewrite658.0ms

Algorithm

rewrite-expression-head

Rules

1222×	`times-frac`
877×	`add-sqr-sqrt`
780×	`sqrt-prod`
659×	`*-un-lft-identity`
537×	`add-cube-cbrt`
317×	`associate-l`
204×	`cbrt-prod`
122×	`difference-of-squares`
80×	`add-exp-log`
61×	`distribute-lft-out--`
52×	`add-cbrt-cube`
40×	`sqrt-div` `associate-/r/`
36×	`associate-/l*`
31×	`prod-exp`
27×	`div-exp`
23×	`div-inv`
20×	`flip3--` `flip--`
18×	`associate-/r*`
17×	`cbrt-undiv` `cbrt-unprod`
11×	`pow1`
10×	`unswap-sqr`
4×	`rec-exp` `1-exp` `associate-r` `pow-prod-down` `associate-*l/` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`frac-times` `associate-*r/` `associate-/l/`

Counts

4 → 791

Calls

4 calls:

207.0ms	(* (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt (cbrt 9.0))) rand)
221.0ms	(* (/ 1 (sqrt (* (cbrt 9.0) (cbrt 9.0)))) (* (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt (cbrt 9.0))) rand))
36.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
62.0ms	(/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt (cbrt 9.0)))

series1.8s

Counts

4 → 12

Calls

4 calls:

855.0ms	(* (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt (cbrt 9.0))) rand)
369.0ms	(* (/ 1 (sqrt (* (cbrt 9.0) (cbrt 9.0)))) (* (/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt (cbrt 9.0))) rand))
145.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
386.0ms	(/ (/ 1.0 (sqrt (- a (/ 1.0 3.0)))) (sqrt (cbrt 9.0)))

simplify2.3s

Counts

803 → 803

Iterations

Iter	Nodes
done	5001
1	2327
0	903

prune5.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* 1.0 (/ rand (sqrt (- a (/ 1.0 3.0))))))))
0.2b	(/ rand (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (/ 1 (sqrt 9.0)) (* 1.0 (/ rand (sqrt (- a (/ 1.0 3.0))))))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt`
51×	`times-frac`
50×	`*-un-lft-identity`
47×	`add-exp-log`
39×	`sqrt-prod`
38×	`add-cube-cbrt`
29×	`add-cbrt-cube`
28×	`associate-l`
21×	`prod-exp`
12×	`pow1` `difference-of-squares`
11×	`div-exp` `cbrt-unprod`
9×	`associate-/r*`
6×	`cbrt-undiv` `distribute-lft-out--`
5×	`frac-times` `flip3--` `associate-*r/` `flip--`
4×	`sqrt-div` `associate-r` `pow-prod-down` `add-log-exp`
3×	`rec-exp` `flip3-+` `1-exp` `associate-l/` `flip-+` `associate-/l`
2×	`associate-/r/` `*-commutative` `div-inv`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `unswap-sqr`

Counts

4 → 156

Calls

4 calls:

23.0ms	(sqrt (- a (/ 1.0 3.0)))
59.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* 1.0 (/ rand (sqrt (- a (/ 1.0 3.0))))))))
22.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
101.0ms	(* (/ 1 (sqrt 9.0)) (* 1.0 (/ rand (sqrt (- a (/ 1.0 3.0))))))

series707.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (- a (/ 1.0 3.0)))
238.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1 (sqrt 9.0)) (* 1.0 (/ rand (sqrt (- a (/ 1.0 3.0))))))))
118.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
307.0ms	(* (/ 1 (sqrt 9.0)) (* 1.0 (/ rand (sqrt (- a (/ 1.0 3.0))))))

simplify2.0s

Counts

168 → 168

Iterations

Iter	Nodes
done	5000
2	3682
1	988
0	363

prune932.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes291.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	22
1	22
0	16

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.9s	26876×	body	80	nan
746.0ms	9113×	body	80	valid