Details

sample82.0ms

Algorithm

intervals

Results

26.0ms	48×	body	1280	valid
18.0ms	46×	body	640	valid
8.0ms	142×	body	80	valid
6.0ms	29×	body	320	valid
4.0ms	91×	body	80	nan
3.0ms	19×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize16.0ms

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))))
8.6b	(log (/ x (+ x y)))

rewrite129.0ms

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:

65.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
11.0ms	(/ x (+ x y))
21.0ms	(* x (log (/ x (+ x y))))
13.0ms	(log (/ x (+ x y)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
49.0ms	(/ x (+ x y))
91.0ms	(* x (log (/ x (+ x y))))
60.0ms	(log (/ x (+ x y)))

simplify2.7s

Counts

300 → 300

Iterations

Useful iterations: done (2.7s)

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

prune762.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
2.9b	(log (/ (cbrt x) (cbrt (+ x y))))
2.9b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite30.0ms

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)
9.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
11.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series761.0ms

Counts

4 → 12

Calls

4 calls:

280.0ms	(cbrt x)
274.0ms	(cbrt x)
103.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
104.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify1.7s

Counts

152 → 152

Iterations

Useful iterations: done (1.7s)

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

prune695.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite26.0ms

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:

24.0ms

(/ (exp (- y)) x)

series42.0ms

Counts

1 → 3

Calls

1 calls:

42.0ms

(/ (exp (- y)) x)

simplify3.1s

Counts

32 → 32

Iterations

Useful iterations: 3 (213.0ms)

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

prune77.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
23×	`sqrt-prod`
22×	`sqrt-pow1` `times-frac` `associate-r`
20×	`exp-prod`
8×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
7×	`pow1`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-l` `unswap-sqr`
4×	`neg-sub0` `exp-neg` `exp-diff`
3×	`add-log-exp`
2×	`frac-times` `neg-mul-1` `rem-sqrt-square` `pow1/2` `associate-*l/` `prod-exp` `cbrt-unprod`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`

Counts

3 → 102

Calls

3 calls:

7.0ms	(sqrt (exp (- y)))
7.0ms	(sqrt (exp (- y)))
70.0ms	(* (sqrt (exp (- y))) (/ (sqrt (exp (- y))) x))

series91.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(sqrt (exp (- y)))
30.0ms	(sqrt (exp (- y)))
33.0ms	(* (sqrt (exp (- y))) (/ (sqrt (exp (- y))) x))

simplify3.2s

Counts

111 → 111

Iterations

Useful iterations: 3 (1.9s)

Iter	Nodes	Cost
0	128	1160
1	259	936
2	772	830
3	2433	799
done	5001	799

prune425.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes489.0ms

Accuracy

98.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 5.8b

bsearch184.0ms

Steps

Iters	Range		Point
8	0.021902447110590684	639.503948019383	51.97466445904304
9	-2.4520752562547516e+37	-3.956185314329236e+31	-6.855000109145469e+33

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	30	60
1	37	60
done	37	60

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.2s	1531×	body	1280	valid
712.0ms	1482×	body	640	valid
648.0ms	3004×	body	80	nan
503.0ms	4793×	body	80	valid
250.0ms	860×	body	320	valid
75.0ms	422×	body	160	valid