Details

sample117.0ms

Algorithm

intervals

Results

38.0ms	47×	body	1280	valid
24.0ms	55×	body	640	valid
13.0ms	148×	body	80	valid
9.0ms	29×	body	320	valid
7.0ms	103×	body	80	nan
3.0ms	16×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	8	11
1	15	11
2	24	9
3	51	9
4	148	9
5	485	9
6	1979	9
done	5000	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp (* x (log (/ x (+ x y))))) x)
0.0b	(exp (* x (log (/ x (+ x y)))))
0.1b	(* x (log (/ x (+ x y))))
9.2b	(log (/ x (+ x y)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac`
234×	`log-prod`
232×	`*-un-lft-identity`
180×	`exp-sum`
156×	`add-sqr-sqrt`
154×	`add-cube-cbrt`
108×	`distribute-rgt-in` `distribute-lft-in`
39×	`distribute-lft-out` `associate-/l*`
26×	`associate-/r/`
14×	`div-inv`
13×	`flip3-+` `flip-+`
10×	`add-exp-log`
8×	`pow1` `add-cbrt-cube`
6×	`add-log-exp`
4×	`associate-r`
3×	`associate-l` `associate-/r*`
2×	`div-exp` `rem-log-exp` `log-pow`
1×	`cbrt-undiv` `log-div` `exp-prod` `exp-to-pow` `frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 301

Calls

4 calls:

80.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
30.0ms	(exp (* x (log (/ x (+ x y)))))
25.0ms	(* x (log (/ x (+ x y))))
6.0ms	(log (/ x (+ x y)))

series621.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
283.0ms	(exp (* x (log (/ x (+ x y)))))
103.0ms	(* x (log (/ x (+ x y))))
68.0ms	(log (/ x (+ x y)))

simplify1.6s

Counts

313 → 313

Iterations

Useful iterations: 2 (797.0ms)

Iter	Nodes	Cost
0	472	6157
1	889	5532
2	3163	4948
done	5000	4948

prune785.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow (exp x) (log (/ x (+ x y)))) x)
0.0b	(/ x (+ x y))
0.3b	(pow (exp x) (log (/ x (+ x y))))
9.2b	(log (/ x (+ x y)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
142×	`*-un-lft-identity`
108×	`log-prod`
98×	`add-sqr-sqrt` `add-cube-cbrt`
90×	`unpow-prod-up`
28×	`associate-/l*`
22×	`distribute-lft-out`
15×	`unpow-prod-down`
14×	`associate-/r/`
13×	`add-exp-log`
8×	`add-cbrt-cube` `div-inv`
7×	`pow1` `flip3-+` `associate-/r*` `flip-+`
5×	`div-exp` `sqr-pow`
4×	`pow-unpow` `pow-pow` `add-log-exp`
3×	`log-div` `exp-prod`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `pow-sub`
1×	`associate-/l/`

Counts

4 → 220

Calls

4 calls:

63.0ms	(/ (pow (exp x) (log (/ x (+ x y)))) x)
19.0ms	(/ x (+ x y))
18.0ms	(pow (exp x) (log (/ x (+ x y))))
11.0ms	(log (/ x (+ x y)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (pow (exp x) (log (/ x (+ x y)))) x)
79.0ms	(/ x (+ x y))
172.0ms	(pow (exp x) (log (/ x (+ x y))))
92.0ms	(log (/ x (+ x y)))

simplify2.0s

Counts

232 → 232

Iterations

Useful iterations: 2 (705.0ms)

Iter	Nodes	Cost
0	331	4057
1	728	3820
2	3193	3685
done	5000	3685

prune886.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize62.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
1.1b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
5.2b	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

53×	`cbrt-prod`
51×	`*-un-lft-identity`
48×	`unpow-prod-down`
43×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
18×	`cbrt-div`
13×	`log-prod`
10×	`associate-/r/`
9×	`flip3-+` `flip-+`
8×	`distribute-lft-out`
6×	`pow1`
5×	`div-exp` `rem-log-exp`
4×	`frac-times` `prod-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow`
2×	`pow1/3` `associate-r/` `associate-l/` `pow-exp` `div-inv`
1×	`pow-to-exp` `log-div` `pow-pow` `log-pow` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

4.0ms	(cbrt (+ x y))
4.0ms	(cbrt (+ x y))
18.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
32.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

series832.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(cbrt (+ x y))
181.0ms	(cbrt (+ x y))
388.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
95.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

simplify1.2s

Counts

130 → 130

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	280	2249
1	824	2128
2	2572	1945
done	5001	1930

prune751.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (- y)) x)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`add-exp-log` `associate-/l/`
1×	`pow1` `cbrt-undiv` `neg-sub0` `exp-neg` `frac-2neg` `exp-diff` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

20.0ms

(/ (exp (- y)) x)

series28.0ms

Counts

1 → 3

Calls

1 calls:

28.0ms

(/ (exp (- y)) x)

simplify3.0s

Counts

32 → 32

Iterations

Useful iterations: 3 (725.0ms)

Iter	Nodes	Cost
0	64	299
1	125	289
2	488	271
3	3657	267
done	5001	267

prune65.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes98.0ms

Accuracy

95.3% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 5.9b

bsearch120.0ms

Steps

Iters	Range		Point
8	7.329791909597432e-11	2.3700091904683387e-07	2.3427008122301183e-07
9	-4159660869929146.0	-4282433023.162024	-27740047836885.016

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	17	29
1	21	25
done	21	25

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	1528×	body	1280	valid
661.0ms	1423×	body	640	valid
356.0ms	4866×	body	80	valid
212.0ms	824×	body	320	valid
202.0ms	2969×	body	80	nan
106.0ms	467×	body	160	valid