Details

sample40.0ms

Algorithm

intervals

Results

8.0ms	187×	body	80	valid
5.0ms	25×	body	1280	valid
3.0ms	107×	body	80	nan
3.0ms	17×	body	640	valid
2.0ms	13×	body	1280	nan
2.0ms	15×	body	320	valid
2.0ms	12×	body	640	nan
1.0ms	12×	body	160	valid
0.0ms	4×	body	320	nan
0.0ms	5×	body	160	nan

simplify91.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize9.0ms

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))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
184×	`*-un-lft-identity`
105×	`prod-diff`
103×	`times-frac`
91×	`add-cube-cbrt`
49×	`difference-of-squares`
47×	`distribute-lft-out--`
12×	`log-prod`
9×	`pow1` `flip3--` `flip--`
8×	`associate-/r/`
7×	`add-exp-log` `add-log-exp`
6×	`fma-neg` `add-cbrt-cube` `associate--r+`
5×	`associate-/r` `log-pow` `associate-/l`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `div-inv`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num`

Counts

4 → 227

Calls

4 calls:

24.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
12.0ms	(/ (- x y) (- 1.0 y))
30.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
29.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
38.0ms	(/ (- x y) (- 1.0 y))
55.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
90.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify1.2s

Counts

239 → 239

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	390	8619
1	974	7647
2	2762	5742
done	5000	5727

prune522.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt (- x y)) 3)
0.7b	(pow (cbrt (- x y)) 3)
5.2b	(log (+ (- 1.0 (/ (pow (cbrt (- x y)) 3) (- 1.0 y))) (- (/ (pow (cbrt (- x y)) 3) (- 1.0 y)) (/ (pow (cbrt (- x y)) 3) (- 1.0 y)))))
12.6b	(- 1.0 (/ (pow (cbrt (- x y)) 3) (- 1.0 y)))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

495×	`add-sqr-sqrt`
490×	`*-un-lft-identity`
348×	`prod-diff`
336×	`times-frac`
276×	`add-cube-cbrt`
172×	`cbrt-prod`
138×	`unpow-prod-down` `cube-prod`
107×	`difference-of-squares`
105×	`distribute-lft-out--`
18×	`sqr-pow`
17×	`cube-mult` `unpow3`
12×	`flip3--` `flip--`
10×	`log-div`
8×	`frac-add`
7×	`pow1` `add-exp-log` `log-prod`
6×	`pow-unpow` `associate-/r/` `add-log-exp`
4×	`cube-div` `expm1-log1p-u` `cbrt-div` `pow-pow` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out`
3×	`fma-neg` `div-inv`
2×	`pow-to-exp` `pow1/3` `pow-exp` `frac-sub` `sub-div` `rem-cube-cbrt`
1×	`sub-neg` `flip3-+` `diff-log` `rem-log-exp` `log-pow` `flip-+`

Counts

4 → 477

Calls

4 calls:

5.0ms	(pow (cbrt (- x y)) 3)
5.0ms	(pow (cbrt (- x y)) 3)
2.1s	(log (+ (- 1.0 (/ (pow (cbrt (- x y)) 3) (- 1.0 y))) (- (/ (pow (cbrt (- x y)) 3) (- 1.0 y)) (/ (pow (cbrt (- x y)) 3) (- 1.0 y)))))
78.0ms	(- 1.0 (/ (pow (cbrt (- x y)) 3) (- 1.0 y)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(pow (cbrt (- x y)) 3)
126.0ms	(pow (cbrt (- x y)) 3)
91.0ms	(log (+ (- 1.0 (/ (pow (cbrt (- x y)) 3) (- 1.0 y))) (- (/ (pow (cbrt (- x y)) 3) (- 1.0 y)) (/ (pow (cbrt (- x y)) 3) (- 1.0 y)))))
62.0ms	(- 1.0 (/ (pow (cbrt (- x y)) 3) (- 1.0 y)))

simplify643.0ms

Counts

489 → 489

Iterations

Useful iterations: done (615.0ms)

Iter	Nodes	Cost
0	733	32095
1	1780	22572
done	5000	16859

prune800.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

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)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-sqr-sqrt`
202×	`*-un-lft-identity`
144×	`times-frac`
102×	`add-cube-cbrt`
93×	`prod-diff`
58×	`difference-of-squares`
50×	`distribute-lft-out--`
24×	`log-prod`
12×	`associate-/r/`
11×	`associate-/r*`
9×	`add-exp-log`
8×	`flip3--` `add-cbrt-cube` `flip--` `associate-/l*`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `div-exp`
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 → 248

Calls

4 calls:

12.0ms	(/ (- x y) (- 1.0 y))
24.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
41.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
31.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (- x y) (- 1.0 y))
160.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
130.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
57.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify1.2s

Counts

260 → 260

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	432	8789
1	1064	8133
2	2990	6363
done	5000	6348

prune612.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`prod-diff`
17×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
5×	`associate-r`
3×	`expm1-log1p-u` `log-prod` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `associate-*r/`
1×	`flip3--` `rem-log-exp` `associate-l` `log-pow` `*-commutative` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 70

Calls

3 calls:

0.0ms	(fma (exp 1.0) 1.0 (* (* 1.0 (exp 1.0)) (- x y)))
1.0ms	(log (fma (exp 1.0) 1.0 (* (* 1.0 (exp 1.0)) (- x y))))
20.0ms	(* (* 1.0 (exp 1.0)) (- x y))

series351.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(fma (exp 1.0) 1.0 (* (* 1.0 (exp 1.0)) (- x y)))
171.0ms	(log (fma (exp 1.0) 1.0 (* (* 1.0 (exp 1.0)) (- x y))))
94.0ms	(* (* 1.0 (exp 1.0)) (- x y))

simplify2.2s

Counts

79 → 79

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	161	1503
1	397	1314
2	1315	1028
3	4656	982
done	5000	982

prune361.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes138.0ms

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	30	81
1	34	64
done	34	64

end0.0ms

sample1.1s

Algorithm

intervals

Results

242.0ms	5713×	body	80	valid
171.0ms	825×	body	1280	valid
122.0ms	788×	body	640	valid
108.0ms	3682×	body	80	nan
57.0ms	344×	body	1280	nan
50.0ms	403×	body	640	nan
46.0ms	434×	body	320	valid
19.0ms	213×	body	320	nan
17.0ms	240×	body	160	valid
6.0ms	101×	body	160	nan