Details

sample137.0ms

Algorithm

intervals

Results

68.0ms	979×	body	80	nan
18.0ms	293×	body	80	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	3827
6	1760
5	891
4	462
3	190
2	72
1	27
0	13

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite173.0ms

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:

16.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
47.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
79.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
24.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series690.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
157.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
238.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
217.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify2.3s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	4506
1	858
0	303

prune779.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

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)))))
6.5b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite281.0ms

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-cbrt-cube` `add-exp-log`
14×	`pow1`
8×	`sqrt-prod`
7×	`prod-exp` `associate-*r/` `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×	`clear-num` `frac-2neg` `pow1/2` `distribute-lft-out--`

Counts

4 → 111

Calls

4 calls:

10.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
72.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
13.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
182.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

series863.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
262.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
249.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
244.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify1.9s

Counts

123 → 123

Iterations

Iter	Nodes
done	5002
2	3545
1	768
0	291

prune951.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- a (/ 1.0 3.0)) 9.0)
0.1b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
0.2b	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
6.5b	(* (- a (/ 1.0 3.0)) (* 1.0 (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

45.0ms	(* (- a (/ 1.0 3.0)) 9.0)
14.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
25.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
160.0ms	(* (- a (/ 1.0 3.0)) (* 1.0 (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))))

series606.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (- a (/ 1.0 3.0)) 9.0)
97.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))
223.0ms	(/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
214.0ms	(* (- a (/ 1.0 3.0)) (* 1.0 (/ rand (sqrt (* (- a (/ 1.0 3.0)) 9.0)))))

simplify2.0s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	3063
1	673
0	261

prune585.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
0.3b	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
6.5b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand))

rewrite415.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

64.0ms	(* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)
17.0ms	(/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
42.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
288.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand))

series1.1s

Counts

4 → 12

Calls

4 calls:

332.0ms	(* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand)
288.0ms	(/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0)))))
109.0ms	(* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))
322.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (* (sqrt 9.0) (sqrt (- a (/ 1.0 3.0))))) rand))

simplify2.6s

Counts

129 → 129

Iterations

Iter	Nodes
done	5000
2	4440
1	803
0	290

prune755.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes282.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	19
1	19
0	14

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.7s	27152×	body	80	nan
709.0ms	9133×	body	80	valid