Details

sample68.0ms

Algorithm

intervals

Results

23.0ms	48×	body	1280	valid
12.0ms	46×	body	640	valid
7.0ms	142×	body	80	valid
5.0ms	29×	body	320	valid
3.0ms	91×	body	80	nan
2.0ms	19×	body	160	valid

simplify107.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize10.0ms

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)))

rewrite141.0ms

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:

62.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
12.0ms	(/ x (+ x y))
39.0ms	(* x (log (/ x (+ x y))))
7.0ms	(log (/ x (+ x y)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
43.0ms	(/ x (+ x y))
82.0ms	(* x (log (/ x (+ x y))))
58.0ms	(log (/ x (+ x y)))

simplify81.0ms

Counts: 300 → 300

prune580.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (* -1 y)) x)

rewrite13.0ms

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`
1×	`pow1` `cbrt-undiv` `exp-neg` `frac-2neg` `mul-1-neg` `div-exp` `clear-num` `div-inv` `associate-/l/` `add-log-exp`

Counts

1 → 28

Calls

1 calls:

12.0ms

(/ (exp (* -1 y)) x)

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

(/ (exp (* -1 y)) x)

simplify42.0ms

Counts: 31 → 31

prune74.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (exp (* -1 y)))
0.0b	(sqrt (exp (* -1 y)))
0.0b	(* (sqrt (exp (* -1 y))) (/ (sqrt (exp (* -1 y))) x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
23×	`sqrt-prod`
22×	`times-frac` `associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`sqrt-pow1` `associate-l` `unswap-sqr`
5×	`add-log-exp`
4×	`exp-neg` `mul-1-neg` `sqrt-div`
2×	`rem-sqrt-square` `exp-prod` `exp-to-pow` `pow1/2` `prod-exp` `cbrt-unprod`
1×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `*-commutative` `div-inv`

Counts

3 → 82

Calls

3 calls:

3.0ms	(sqrt (exp (* -1 y)))
3.0ms	(sqrt (exp (* -1 y)))
35.0ms	(* (sqrt (exp (* -1 y))) (/ (sqrt (exp (* -1 y))) x))

series53.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(sqrt (exp (* -1 y)))
16.0ms	(sqrt (exp (* -1 y)))
22.0ms	(* (sqrt (exp (* -1 y))) (/ (sqrt (exp (* -1 y))) x))

simplify35.0ms

Counts: 91 → 91

prune200.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* -1 y)))
0.0b	(* (sqrt (sqrt (exp (* -1 y)))) (/ (pow (sqrt (sqrt (exp (* -1 y)))) 3) x))
0.0b	(pow (sqrt (sqrt (exp (* -1 y)))) 3)
0.0b	(/ (pow (sqrt (sqrt (exp (* -1 y)))) 3) x)

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

201×	`sqrt-prod`
190×	`add-sqr-sqrt`
168×	`times-frac`
114×	`add-cube-cbrt` `*-un-lft-identity`
81×	`unpow-prod-down` `cube-prod`
76×	`associate-r`
27×	`unswap-sqr`
24×	`associate-/l*`
20×	`add-exp-log`
12×	`add-cbrt-cube`
11×	`sqrt-pow1` `sqr-pow`
10×	`pow1`
9×	`sqrt-div` `associate-l`
8×	`cube-mult` `unpow3`
7×	`pow-pow`
6×	`div-exp` `add-log-exp`
5×	`exp-neg` `mul-1-neg`
4×	`prod-exp`
3×	`pow-to-exp` `pow-unpow` `pow1/2` `pow-exp` `associate-/r*`
2×	`cbrt-undiv` `cube-div` `exp-prod` `exp-to-pow` `cbrt-unprod` `div-inv`
1×	`frac-times` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `sqrt-pow2` `associate-/l/` `rem-cube-cbrt`

Counts

4 → 303

Calls

4 calls:

4.0ms	(sqrt (exp (* -1 y)))
77.0ms	(* (sqrt (sqrt (exp (* -1 y)))) (/ (pow (sqrt (sqrt (exp (* -1 y)))) 3) x))
9.0ms	(pow (sqrt (sqrt (exp (* -1 y)))) 3)
23.0ms	(/ (pow (sqrt (sqrt (exp (* -1 y)))) 3) x)

series227.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (exp (* -1 y)))
21.0ms	(* (sqrt (sqrt (exp (* -1 y)))) (/ (pow (sqrt (sqrt (exp (* -1 y)))) 3) x))
107.0ms	(pow (sqrt (sqrt (exp (* -1 y)))) 3)
82.0ms	(/ (pow (sqrt (sqrt (exp (* -1 y)))) 3) x)

simplify131.0ms

Counts: 315 → 315

prune542.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes129.0ms

Accuracy

96% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 12.4b

bsearch109.0ms

Steps

Iters	Range		Point
8	0.021902447110590684	639.503948019383	0.5062656618457485
9	-2.4520752562547516e+37	-3.956185314329236e+31	-6.855000109145469e+33

simplify1.0ms

end0.0ms

sample2.7s

Algorithm

intervals

Results

853.0ms	1531×	body	1280	valid
756.0ms	1482×	body	640	valid
310.0ms	4793×	body	80	valid
228.0ms	860×	body	320	valid
113.0ms	3004×	body	80	nan
81.0ms	422×	body	160	valid