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

simplify96.0ms

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	58	12
5	63	12
6	71	12
7	86	12
8	114	12
9	127	12
10	129	12
done	129	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))))

rewrite76.0ms

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:

21.0ms	(- 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)))
19.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series279.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
38.0ms	(/ (- x y) (- 1.0 y))
56.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
87.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify1.4s

Counts

120 → 120

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	205	1894
1	488	1792
2	1198	1680
3	3154	1671
done	5000	1670

prune295.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

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))) (/ (- 1.0 y) (cbrt (- x y))))))
13.0b	(- 1.0 (/ (* (cbrt (- x y)) (cbrt (- x y))) (/ (- 1.0 y) (cbrt (- x y)))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
35×	`cbrt-prod`
34×	`*-un-lft-identity`
14×	`add-cube-cbrt` `cbrt-div`
13×	`difference-of-squares`
12×	`pow1`
10×	`times-frac` `swap-sqr`
9×	`flip3--` `flip--` `distribute-lft-out--`
8×	`log-prod` `associate-r` `associate-l`
7×	`add-exp-log` `pow1/3`
6×	`add-log-exp`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
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 → 107

Calls

4 calls:

2.0ms	(cbrt (- x y))
18.0ms	(* (cbrt (- x y)) (cbrt (- x y)))
32.0ms	(log (- 1.0 (/ (* (cbrt (- x y)) (cbrt (- x y))) (/ (- 1.0 y) (cbrt (- x y))))))
34.0ms	(- 1.0 (/ (* (cbrt (- x y)) (cbrt (- x y))) (/ (- 1.0 y) (cbrt (- x y)))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt (- x y))
127.0ms	(* (cbrt (- x y)) (cbrt (- x y)))
86.0ms	(log (- 1.0 (/ (* (cbrt (- x y)) (cbrt (- x y))) (/ (- 1.0 y) (cbrt (- x y))))))
52.0ms	(- 1.0 (/ (* (cbrt (- x y)) (cbrt (- x y))) (/ (- 1.0 y) (cbrt (- x y)))))

simplify1.9s

Counts

119 → 119

Iterations

Useful iterations: 3 (918.0ms)

Iter	Nodes	Cost
0	222	2400
1	457	2260
2	1190	1742
3	3883	1538
done	5000	1538

prune321.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

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)))

rewrite97.0ms

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))
23.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
39.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
19.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (- x y) (- 1.0 y))
152.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
126.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
55.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify2.0s

Counts

156 → 156

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	267	2917
1	619	2789
2	1542	2645
3	4238	2593
done	5000	2588

prune397.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(log (* 1.0 (* (exp 1.0) (- (+ x 1) y))))
0.2b	(* (exp 1.0) (- (+ x 1) y))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 45

Calls

2 calls:

40.0ms	(log (* 1.0 (* (exp 1.0) (- (+ x 1) y))))
39.0ms	(* (exp 1.0) (- (+ x 1) y))

series171.0ms

Counts

2 → 6

Calls

2 calls:

130.0ms	(log (* 1.0 (* (exp 1.0) (- (+ x 1) y))))
41.0ms	(* (exp 1.0) (- (+ x 1) y))

simplify1.7s

Counts

51 → 51

Iterations

Useful iterations: 3 (631.0ms)

Iter	Nodes	Cost
0	105	632
1	245	616
2	802	541
3	3123	525
done	5000	525

prune97.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes130.0ms

Accuracy

99.3% (0.1b remaining)

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

bsearch125.0ms

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	27	65
1	34	49
done	34	49

end0.0ms

sample992.0ms

Algorithm

intervals

Results

217.0ms	5713×	body	80	valid
162.0ms	825×	body	1280	valid
106.0ms	788×	body	640	valid
102.0ms	3682×	body	80	nan
52.0ms	344×	body	1280	nan
46.0ms	403×	body	640	nan
42.0ms	434×	body	320	valid
18.0ms	213×	body	320	nan
16.0ms	240×	body	160	valid
8.0ms	101×	body	160	nan