Details

sample161.0ms

Algorithm

intervals

Results

60.0ms	812×	body	80	nan
23.0ms	293×	body	80	valid

simplify3.5s

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

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)))))

rewrite209.0ms

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:

78.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
19.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
79.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
26.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series820.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
96.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
314.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
241.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify2.9s

Counts

126 → 126

Iterations

Iter	Nodes
done	5002
2	4508
1	858
0	303

prune812.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

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)))))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube` `add-exp-log`
11×	`pow1`
10×	`associate-r` `add-cube-cbrt`
9×	`associate-l`
8×	`associate-*r/`
6×	`times-frac` `flip3--` `flip--`
4×	`frac-times` `associate-/r*` `sqrt-div` `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×	`clear-num` `frac-2neg` `pow1/2` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 97

Calls

4 calls:

37.0ms	(* 9.0 (- a (/ 1.0 3.0)))
95.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
15.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
40.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series647.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* 9.0 (- a (/ 1.0 3.0)))
176.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
106.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
277.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify2.4s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
2	4224
1	782
0	263

prune578.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

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

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

142×	`add-sqr-sqrt`
102×	`times-frac`
76×	`*-un-lft-identity`
62×	`add-exp-log` `sqrt-prod`
54×	`add-cube-cbrt`
39×	`associate-r`
38×	`add-cbrt-cube`
29×	`associate-l`
26×	`prod-exp`
17×	`div-exp`
16×	`difference-of-squares` `unswap-sqr`
14×	`cbrt-unprod`
13×	`pow1`
9×	`cbrt-undiv` `associate-/r*`
8×	`distribute-lft-out--`
7×	`associate-*l/`
6×	`frac-times`
5×	`flip3--` `pow-prod-down` `flip--`
4×	`rec-exp` `sqrt-div` `1-exp` `associate-*r/` `associate-/r/` `add-log-exp`
3×	`flip3-+` `-commutative` `flip-+` `div-inv` `associate-/l`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in`

Counts

4 → 209

Calls

4 calls:

48.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)))
118.0ms	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
34.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
121.0ms	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

281.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)))
332.0ms	(* (* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) rand)
123.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
273.0ms	(* (/ 1 (sqrt 9.0)) (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))

simplify1.3s

Counts

221 → 221

Iterations

Iter	Nodes
done	5001
1	1254
0	415

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
0.3b	(/ (* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) (sqrt 9.0))
0.3b	(* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))
9.1b	(* (/ (* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) (sqrt 9.0)) (- a (/ 1.0 3.0)))

rewrite287.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt`
76×	`times-frac`
63×	`*-un-lft-identity`
52×	`sqrt-prod`
47×	`add-cube-cbrt`
39×	`associate-r`
34×	`add-cbrt-cube` `add-exp-log`
16×	`difference-of-squares`
15×	`associate-/r*`
13×	`associate-l`
10×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
8×	`pow1` `distribute-lft-out--`
4×	`flip3--` `sqrt-div` `associate-r/` `associate-/r/` `div-inv` `flip--` `associate-/l` `add-log-exp` `unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `pow-prod-down` `*-commutative`
1×	`associate-*l/` `associate-/l/`

Counts

4 → 179

Calls

4 calls:

36.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
42.0ms	(/ (* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) (sqrt 9.0))
88.0ms	(* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))
105.0ms	(* (/ (* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) (sqrt 9.0)) (- a (/ 1.0 3.0)))

series889.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ 1.0 (sqrt (- a (/ 1.0 3.0))))
314.0ms	(/ (* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) (sqrt 9.0))
158.0ms	(* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0)))))
331.0ms	(* (/ (* rand (/ 1.0 (sqrt (- a (/ 1.0 3.0))))) (sqrt 9.0)) (- a (/ 1.0 3.0)))

simplify1.1s

Counts

191 → 191

Iterations

Iter	Nodes
done	5000
1	1031
0	372

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes252.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.6s	26714×	body	80	nan
657.0ms	9159×	body	80	valid