Details

sample34.0ms

Algorithm

intervals

Results

7.0ms	187×	body	80	valid
5.0ms	25×	body	1280	valid
3.0ms	107×	body	80	nan
2.0ms	17×	body	640	valid
2.0ms	13×	body	1280	nan
1.0ms	15×	body	320	valid
1.0ms	12×	body	640	nan
1.0ms	12×	body	160	valid
0.0ms	4×	body	320	nan
0.0ms	5×	body	160	nan

simplify116.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	29	12
3	41	12
4	59	12
5	75	12
6	83	12
7	98	12
8	128	12
9	182	12
10	225	12
done	225	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
3.1b	(- 1.0 (/ (- x y) (- 1.0 y)))
5.2b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
28×	`times-frac`
19×	`difference-of-squares`
18×	`add-cube-cbrt`
17×	`distribute-lft-out--`
12×	`log-prod`
7×	`add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `add-cbrt-cube` `flip--` `associate--r+`
5×	`associate-/r` `associate-/l`
4×	`log-div`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 108

Calls

4 calls:

23.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
10.0ms	(/ (- x y) (- 1.0 y))
21.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
20.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series264.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
37.0ms	(/ (- x y) (- 1.0 y))
53.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
84.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify433.0ms

Counts

120 → 120

Iterations

Useful iterations: done (427.0ms)

Iter	Nodes	Cost
0	205	1894
1	489	1792
2	1361	1680
done	5000	1678

prune291.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- x y))
0.6b	(* (cbrt (- x y)) (cbrt (- x y)))
5.2b	(log (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y)))))
13.8b	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-prod`
32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
14×	`add-cube-cbrt` `cbrt-div`
12×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `flip--`
8×	`associate-r` `associate-l`
7×	`add-exp-log` `pow1/3` `distribute-lft-out--`
6×	`add-log-exp`
5×	`difference-of-squares`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
3×	`log-prod`
2×	`log-div` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 97

Calls

4 calls:

2.0ms	(cbrt (- x y))
20.0ms	(* (cbrt (- x y)) (cbrt (- x y)))
2.0ms	(log (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y)))))
4.0ms	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))

series411.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- x y))
122.0ms	(* (cbrt (- x y)) (cbrt (- x y)))
86.0ms	(log (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y)))))
54.0ms	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))

simplify560.0ms

Counts

109 → 109

Iterations

Useful iterations: done (557.0ms)

Iter	Nodes	Cost
0	197	2049
1	423	1922
2	1471	1452
done	5001	1448

prune303.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
0.0b	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
0.2b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
3.1b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
69×	`times-frac`
37×	`add-cube-cbrt`
28×	`difference-of-squares`
24×	`log-prod`
20×	`distribute-lft-out--`
11×	`associate-/r*`
9×	`add-exp-log`
8×	`add-cbrt-cube` `associate-/l*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
3×	`div-exp` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `div-sub` `rem-log-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `log-div` `diff-log` `log-pow` `associate--r-`

Counts

4 → 144

Calls

4 calls:

10.0ms	(/ (- x y) (- 1.0 y))
22.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
43.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
19.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (- x y) (- 1.0 y))
154.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
132.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
56.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify556.0ms

Counts

156 → 156

Iterations

Useful iterations: 2 (163.0ms)

Iter	Nodes	Cost
0	267	2917
1	627	2789
2	1884	2645
done	5001	2645

prune405.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1.0 (exp 1.0)) (* (* 1.0 (exp 1.0)) (- x y)))
0.0b	(log (+ (* 1.0 (exp 1.0)) (* (* 1.0 (exp 1.0)) (- x y))))
0.3b	(* (* 1.0 (exp 1.0)) (- x y))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt` `*-un-lft-identity`
5×	`add-cube-cbrt` `associate-r` `add-log-exp`
4×	`distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in`
3×	`log-prod` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`log-div` `flip3-+` `associate-*r/` `flip-+`
1×	`+-commutative` `flip3--` `rem-log-exp` `associate-l` `sum-log` `log-pow` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 55

Calls

3 calls:

5.0ms	(+ (* 1.0 (exp 1.0)) (* (* 1.0 (exp 1.0)) (- x y)))
4.0ms	(log (+ (* 1.0 (exp 1.0)) (* (* 1.0 (exp 1.0)) (- x y))))
21.0ms	(* (* 1.0 (exp 1.0)) (- x y))

series373.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(+ (* 1.0 (exp 1.0)) (* (* 1.0 (exp 1.0)) (- x y)))
184.0ms	(log (+ (* 1.0 (exp 1.0)) (* (* 1.0 (exp 1.0)) (- x y))))
92.0ms	(* (* 1.0 (exp 1.0)) (- x y))

simplify595.0ms

Counts

64 → 64

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	122	1113
1	335	1027
2	1388	812
done	5000	812

prune138.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes132.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 17.3b

bsearch135.0ms

Steps

Iters	Range		Point
11	3.382151548740658e-10	12169712469967.395	53143023.87049463
8	-542359391.39979	-925426.909356872	-51178879.93439336

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	29	69
1	35	51
done	35	51

end0.0ms

sample1.0s

Algorithm

intervals

Results

223.0ms	5713×	body	80	valid
163.0ms	825×	body	1280	valid
114.0ms	788×	body	640	valid
100.0ms	3682×	body	80	nan
52.0ms	344×	body	1280	nan
50.0ms	403×	body	640	nan
42.0ms	434×	body	320	valid
18.0ms	213×	body	320	nan
16.0ms	240×	body	160	valid
6.0ms	101×	body	160	nan