Details

sample58.0ms

Algorithm

intervals

Results

20.0ms	48×	body	1280	valid
11.0ms	45×	body	640	valid
7.0ms	159×	body	80	valid
6.0ms	36×	body	320	valid
2.0ms	82×	body	80	nan
1.0ms	6×	body	160	valid

simplify1.7s

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	100	9
5	235	9
6	543	9
7	1636	9
done	5001	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
54×	`log-prod`
48×	`times-frac`
40×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
18×	`distribute-rgt-in` `distribute-lft-in`
13×	`distribute-lft-out`
10×	`add-exp-log`
8×	`associate-/r/`
7×	`pow1` `add-cbrt-cube`
4×	`flip3-+` `associate-r` `associate-/r*` `flip-+` `div-inv`
3×	`associate-l` `associate-/l*` `add-log-exp`
2×	`div-exp` `rem-log-exp` `log-pow`
1×	`cbrt-undiv` `log-div` `frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 117

Calls

3 calls:

5.0ms	(/ x (+ x y))
10.0ms	(* x (log (/ x (+ x y))))
4.0ms	(log (/ x (+ x y)))

series171.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ x (+ x y))
79.0ms	(* x (log (/ x (+ x y))))
53.0ms	(log (/ x (+ x y)))

simplify2.7s

Counts

126 → 126

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	167	1600
1	292	1512
2	606	1427
3	1533	1384
4	4475	1381
done	5001	1381

prune237.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
3.0b	(log (/ (cbrt x) (cbrt (+ x y))))
3.0b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite22.0ms

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:

0.0ms	(cbrt x)
1.0ms	(cbrt x)
6.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series488.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt x)
171.0ms	(cbrt x)
70.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
73.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify1.1s

Counts

152 → 152

Iterations

Useful iterations: 4 (568.0ms)

Iter	Nodes	Cost
0	173	2258
1	309	2100
2	558	2014
3	1206	1940
4	2543	1936
done	5000	1936

prune478.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.6b	(* (cbrt x) (cbrt x))
34.1b	(log (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
42×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
34×	`cbrt-prod`
33×	`log-prod`
30×	`add-cube-cbrt`
19×	`add-exp-log`
12×	`pow1`
8×	`pow1/3`
6×	`swap-sqr` `div-exp` `associate-r` `associate-l` `distribute-lft-out`
5×	`rem-log-exp`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`prod-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up` `div-inv`
1×	`pow2` `log-div` `pow-plus` `associate-/r/` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
5.0ms	(* (cbrt x) (cbrt x))
8.0ms	(log (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))))

series624.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt x)
174.0ms	(cbrt x)
197.0ms	(* (cbrt x) (cbrt x))
66.0ms	(log (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))))

simplify761.0ms

Counts

121 → 121

Iterations

Useful iterations: 2 (131.0ms)

Iter	Nodes	Cost
0	191	1393
1	374	1278
2	1279	1087
done	5000	1087

prune339.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (* x x) (* y y))
4.0b	(* (/ x (- (* x x) (* y y))) (- x y))
14.0b	(log (* (/ x (- (* x x) (* y y))) (- x y)))
21.2b	(/ x (- (* x x) (* y y)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`times-frac`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`associate-l`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1` `difference-of-squares`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`log-div` `associate-r`
4×	`frac-times` `associate-r/` `prod-exp` `associate-/r` `associate-/r/`
3×	`sub-neg` `div-exp` `rem-log-exp` `associate-/l*`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-*l/` `log-pow` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`log-prod` `frac-2neg` `diff-log` `clear-num` `*-commutative` `distribute-lft-out--`

Counts

4 → 111

Calls

4 calls:

2.0ms	(- (* x x) (* y y))
22.0ms	(* (/ x (- (* x x) (* y y))) (- x y))
8.0ms	(log (* (/ x (- (* x x) (* y y))) (- x y)))
5.0ms	(/ x (- (* x x) (* y y)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* x x) (* y y))
70.0ms	(* (/ x (- (* x x) (* y y))) (- x y))
78.0ms	(log (* (/ x (- (* x x) (* y y))) (- x y)))
48.0ms	(/ x (- (* x x) (* y y)))

simplify866.0ms

Counts

123 → 123

Iterations

Useful iterations: 2 (258.0ms)

Iter	Nodes	Cost
0	161	1835
1	384	1786
2	1495	1612
done	5001	1612

prune309.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

regimes44.0ms

Accuracy

8.3% (4.1b remaining)

Error of 5.3b against oracle of 1.2b and baseline of 5.7b

bsearch103.0ms

Steps

Iters	Range		Point
9	3.9952034404095503e+118	2.258742533603766e+124	5.234179426754207e+118
7	50024088429.266525	12169712469967.395	51088118733.37021

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	79
1	39	54
done	39	54

end0.0ms

sample1.7s

Algorithm

intervals

Results

676.0ms	1582×	body	1280	valid
356.0ms	1425×	body	640	valid
203.0ms	4873×	body	80	valid
131.0ms	812×	body	320	valid
88.0ms	2981×	body	80	nan
44.0ms	453×	body	160	valid