Details

sample33.0ms

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

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	29	6
2	41	6
3	60	6
4	78	6
5	94	6
6	109	6
7	139	6
8	214	6
9	279	6
10	279	6

prune2.0ms

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))))

rewrite80.0ms

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)))))
11.0ms	(/ (- x y) (- 1.0 y))
23.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
20.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series263.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
36.0ms	(/ (- x y) (- 1.0 y))
54.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
85.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify41.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	488	942
1	1388	894
2	5001	876

prune296.0ms

Pruning

4 alts after pruning (4 fresh and 0 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)))

rewrite99.0ms

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:

11.0ms	(/ (- x y) (- 1.0 y))
22.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
42.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
20.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (- x y) (- 1.0 y))
146.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
121.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
52.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify56.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	621	1546
1	1974	1467
2	5001	1448

prune421.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
18×	`log-prod`
15×	`*-un-lft-identity`
8×	`difference-of-squares`
7×	`pow1` `add-exp-log` `add-cube-cbrt`
6×	`log-div` `add-log-exp`
4×	`flip3--` `times-frac` `add-cbrt-cube` `flip--` `distribute-lft-out--`
3×	`rem-log-exp` `log-pow`
1×	`sub-neg` `diff-log` `div-sub` `associate--r-`

Counts

4 → 67

Calls

4 calls:

19.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
20.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
22.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
19.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
83.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
83.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
81.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify57.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	194	742
1	481	673
2	1890	661
3	5002	661

prune314.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

11.0ms	(* (cbrt (log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))) (cbrt (log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))))
21.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
20.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
23.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series1.1s

Counts

4 → 12

Calls

4 calls:

960.0ms	(* (cbrt (log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))) (cbrt (log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))))
50.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
54.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
53.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify104.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	909	2042
1	3667	1869
2	5001	1743

prune427.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes190.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 18.2b

bsearch129.0ms

Steps

Iters	Range		Point
11	3.382151548740658e-10	12169712469967.395	98105251.5900794
8	-542359391.39979	-925426.909356872	-173788009.49411574

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	17
1	34	17

end0.0ms

sample977.0ms

Algorithm

intervals

Results

218.0ms	5713×	body	80	valid
154.0ms	825×	body	1280	valid
109.0ms	788×	body	640	valid
101.0ms	3682×	body	80	nan
50.0ms	344×	body	1280	nan
44.0ms	403×	body	640	nan
41.0ms	434×	body	320	valid
17.0ms	213×	body	320	nan
15.0ms	240×	body	160	valid
5.0ms	101×	body	160	nan