Details

sample95.0ms

Algorithm

intervals

Results

25.0ms	47×	body	1280	valid
23.0ms	176×	body	80	valid
14.0ms	43×	body	640	valid
6.0ms	29×	body	320	valid
5.0ms	118×	body	80	nan
2.0ms	15×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	8	11
1	15	11
2	24	9
3	49	9
4	105	9
5	241	9
6	578	9
7	1854	9
done	5000	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp (* x (log (/ x (+ x y))))) x)
0.0b	(/ x (+ x y))
0.1b	(* x (log (/ x (+ x y))))
8.7b	(log (/ x (+ x y)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

261×	`times-frac`
221×	`*-un-lft-identity`
198×	`log-prod`
149×	`add-sqr-sqrt`
147×	`add-cube-cbrt`
144×	`exp-sum`
90×	`distribute-rgt-in` `distribute-lft-in`
42×	`associate-/l*`
37×	`distribute-lft-out`
24×	`associate-/r/`
13×	`div-inv`
12×	`add-exp-log` `flip3-+` `flip-+`
10×	`add-cbrt-cube`
8×	`pow1`
7×	`associate-/r*`
4×	`associate-r` `add-log-exp`
3×	`div-exp` `associate-l`
2×	`cbrt-undiv` `frac-2neg` `rem-log-exp` `clear-num` `log-pow`
1×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 288

Calls

4 calls:

71.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
11.0ms	(/ x (+ x y))
26.0ms	(* x (log (/ x (+ x y))))
7.0ms	(log (/ x (+ x y)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
46.0ms	(/ x (+ x y))
117.0ms	(* x (log (/ x (+ x y))))
57.0ms	(log (/ x (+ x y)))

simplify2.8s

Counts

300 → 300

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	470	5564
1	821	4720
2	1642	4540
3	4790	4449
done	5001	4421

prune864.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
3.9b	(log (/ (cbrt x) (cbrt (+ x y))))
3.9b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod` `log-prod`
84×	`*-un-lft-identity` `times-frac`
60×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`distribute-lft-out`
10×	`add-exp-log`
6×	`pow1`
4×	`cbrt-div` `rem-log-exp` `associate-/r/` `add-cbrt-cube` `add-log-exp`
2×	`log-div` `flip3-+` `pow1/3` `div-exp` `log-pow` `flip-+` `div-inv`

Counts

4 → 140

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
13.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
9.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series744.0ms

Counts

4 → 12

Calls

4 calls:

306.0ms	(cbrt x)
225.0ms	(cbrt x)
118.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
95.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify1.9s

Counts

152 → 152

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	173	2258
1	314	2100
2	563	2014
3	1074	1940
4	2377	1936
done	5000	1924

prune840.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sqrt (/ x (+ x y))) x)
0.3b	(pow (sqrt (/ x (+ x y))) x)
4.8b	(sqrt (/ x (+ x y)))
4.8b	(sqrt (/ x (+ x y)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
64×	`*-un-lft-identity`
50×	`times-frac`
46×	`add-sqr-sqrt`
42×	`unpow-prod-down`
40×	`add-cube-cbrt`
12×	`distribute-lft-out`
10×	`pow1`
8×	`associate-/r/`
6×	`add-exp-log` `pow-unpow` `pow-pow`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `div-inv` `add-log-exp`
2×	`pow-to-exp` `sqrt-div` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

4 → 136

Calls

4 calls:

15.0ms	(pow (sqrt (/ x (+ x y))) x)
15.0ms	(pow (sqrt (/ x (+ x y))) x)
26.0ms	(sqrt (/ x (+ x y)))
21.0ms	(sqrt (/ x (+ x y)))

series1.0s

Counts

4 → 12

Calls

4 calls:

415.0ms	(pow (sqrt (/ x (+ x y))) x)
402.0ms	(pow (sqrt (/ x (+ x y))) x)
89.0ms	(sqrt (/ x (+ x y)))
111.0ms	(sqrt (/ x (+ x y)))

simplify2.1s

Counts

148 → 148

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	163	2032
1	349	1872
2	808	1774
3	2750	1752
done	5000	1736

prune597.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite21.0ms

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)

series31.0ms

Counts

1 → 3

Calls

1 calls:

31.0ms

(/ (exp (- y)) x)

simplify2.9s

Counts

32 → 32

Iterations

Useful iterations: 3 (212.0ms)

Iter	Nodes	Cost
0	64	299
1	117	289
2	281	269
3	680	267
4	2766	267
done	5001	267

prune112.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes99.0ms

Accuracy

94.3% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 5.8b

bsearch133.0ms

Steps

Iters	Range		Point
6	1.6549904719812824e-10	1.1362596833603348e-09	1.1158984721914147e-09
8	-1.1610098128388504e+53	-3.2818405371306287e+50	-4.12015628866316e+50

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	23	44
1	33	39
done	33	39

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	1484×	body	1280	valid
669.0ms	1464×	body	640	valid
564.0ms	4912×	body	80	valid
269.0ms	798×	body	320	valid
231.0ms	3128×	body	80	nan
90.0ms	507×	body	160	valid