Details

sample95.0ms

Algorithm

intervals

Results

34.0ms	51×	body	1280	valid
20.0ms	53×	body	640	valid
10.0ms	145×	body	80	valid
7.0ms	26×	body	320	valid
5.0ms	88×	body	80	nan
3.0ms	19×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	1916
6	531
5	212
4	89
3	41
2	22
1	15
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x (log (/ x (+ x y)))))
0.0b	(/ x (+ x y))
0.1b	(* x (log (/ x (+ x y))))
8.0b	(log (/ x (+ x y)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

93×	`*-un-lft-identity`
90×	`log-prod`
72×	`times-frac`
57×	`add-sqr-sqrt`
55×	`add-cube-cbrt`
36×	`distribute-rgt-in` `distribute-lft-in` `exp-sum`
19×	`distribute-lft-out`
12×	`associate-/r/`
11×	`add-exp-log`
8×	`pow1` `add-cbrt-cube`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
4×	`associate-/r` `associate-r*`
3×	`associate-l` `associate-/l*`
2×	`div-exp` `rem-log-exp` `log-pow`
1×	`cbrt-undiv` `log-div` `exp-prod` `clear-num` `frac-2neg` `exp-to-pow` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 163

Calls

4 calls:

13.0ms	(exp (* x (log (/ x (+ x y)))))
16.0ms	(/ x (+ x y))
16.0ms	(* x (log (/ x (+ x y))))
5.0ms	(log (/ x (+ x y)))

series593.0ms

Counts

4 → 12

Calls

4 calls:

312.0ms	(exp (* x (log (/ x (+ x y)))))
75.0ms	(/ x (+ x y))
119.0ms	(* x (log (/ x (+ x y))))
87.0ms	(log (/ x (+ x y)))

simplify2.6s

Counts

175 → 175

Iterations

Iter	Nodes
done	5000
3	4821
2	1360
1	590
0	248

prune875.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow (exp x) (log (/ x (+ x y)))) x)
0.0b	(/ x (+ x y))
0.1b	(pow (exp x) (log (/ x (+ x y))))
8.0b	(log (/ x (+ x y)))

rewrite76.0ms

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` `associate-/r*` `flip3-+` `flip-+`
5×	`div-exp` `sqr-pow`
4×	`pow-unpow` `pow-pow` `add-log-exp`
3×	`log-div` `exp-prod`
2×	`pow-to-exp` `cbrt-undiv` `clear-num` `frac-2neg` `rem-log-exp` `pow-exp` `log-pow` `pow-sub`
1×	`associate-/l/`

Counts

4 → 220

Calls

4 calls:

25.0ms	(/ (pow (exp x) (log (/ x (+ x y)))) x)
12.0ms	(/ x (+ x y))
21.0ms	(pow (exp x) (log (/ x (+ x y))))
5.0ms	(log (/ x (+ x y)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (pow (exp x) (log (/ x (+ x y)))) x)
54.0ms	(/ x (+ x y))
189.0ms	(pow (exp x) (log (/ x (+ x y))))
71.0ms	(log (/ x (+ x y)))

simplify1.8s

Counts

232 → 232

Iterations

Iter	Nodes
done	5002
2	1976
1	717
0	331

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
8.0b	(log (/ x (+ x y)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
18×	`log-prod`
15×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
9×	`cbrt-prod`
7×	`add-exp-log`
5×	`pow1`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `distribute-lft-out`
2×	`rem-log-exp` `associate-/r/`
1×	`log-div` `flip3-+` `div-exp` `log-pow` `flip-+` `div-inv`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
6.0ms	(log (/ x (+ x y)))

series740.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(cbrt x)
202.0ms	(cbrt x)
242.0ms	(cbrt x)
64.0ms	(log (/ x (+ x y)))

simplify2.4s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
4	3741
3	962
2	381
1	195
0	101

prune401.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

2.9b	(log (sqrt (/ x (+ x y))))
2.9b	(log (sqrt (/ x (+ x y))))
5.0b	(sqrt (/ x (+ x y)))
5.0b	(sqrt (/ x (+ x y)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

8.0ms	(log (sqrt (/ x (+ x y))))
10.0ms	(log (sqrt (/ x (+ x y))))
8.0ms	(sqrt (/ x (+ x y)))
9.0ms	(sqrt (/ x (+ x y)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(log (sqrt (/ x (+ x y))))
114.0ms	(log (sqrt (/ x (+ x y))))
65.0ms	(sqrt (/ x (+ x y)))
78.0ms	(sqrt (/ x (+ x y)))

simplify3.3s

Counts

138 → 138

Iterations

Iter	Nodes
done	5003
5	2682
4	1141
3	474
2	276
1	176
0	122

prune931.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes139.0ms

Accuracy

98.9% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 6.1b

bsearch168.0ms

Steps

Iters	Range		Point
11	1.4622773167296954e-11	37605091470.942024	6.903129057972267
8	-1.8275688213906753e+41	-2.70728775310249e+38	-2.738716592497185e+38

simplify6.0ms

Iterations

Iter	Nodes
done	25
1	25
0	20

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.2s	1520×	body	1280	valid
1.0s	4767×	body	80	valid
700.0ms	1500×	body	640	valid
248.0ms	878×	body	320	valid
165.0ms	3005×	body	80	nan
140.0ms	440×	body	160	valid