Details

sample36.0ms

Algorithm

intervals

Results

7.0ms	187×	body	80	valid
7.0ms	34×	body	1280	valid
3.0ms	127×	body	80	nan
2.0ms	16×	body	640	valid
2.0ms	15×	body	640	nan
1.0ms	7×	body	1280	nan
1.0ms	11×	body	320	valid
1.0ms	8×	body	160	valid
1.0ms	6×	body	320	nan
0.0ms	6×	body	160	nan

simplify18.0ms

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: 17.2b

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))
2.1b	(- 1.0 (/ (- x y) (- 1.0 y)))
2.8b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite73.0ms

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:

20.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
10.0ms	(/ (- x y) (- 1.0 y))
20.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
18.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series261.0ms

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))
52.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
83.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify49.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (35.0ms)

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

prune283.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
0.2b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
2.1b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite94.0ms

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:

20.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
10.0ms	(/ (- x y) (- 1.0 y))
40.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
18.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
36.0ms	(/ (- x y) (- 1.0 y))
126.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
54.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify64.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (45.0ms)

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

prune372.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp 1.0) (* (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))) (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))))
0.2b	(* (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))) (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
2.1b	(- 1.0 (/ (- x y) (- 1.0 y)))
2.1b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
34×	`sqrt-prod`
32×	`*-un-lft-identity`
24×	`sqrt-div`
19×	`pow1`
14×	`add-cube-cbrt` `flip3--` `flip--`
13×	`swap-sqr`
12×	`difference-of-squares`
11×	`add-cbrt-cube`
9×	`add-exp-log` `times-frac` `associate-r` `associate-l`
8×	`frac-times` `sqrt-pow1` `pow1/2` `associate-/r/` `distribute-lft-out--` `add-log-exp`
5×	`pow-prod-up`
4×	`associate-r/` `associate-l/` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-sub` `div-exp` `prod-exp` `cbrt-unprod` `associate--r-`
1×	`pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `clear-num` `associate-/r` `rem-square-sqrt` `-commutative` `div-inv`

Counts

4 → 129

Calls

4 calls:

44.0ms	(/ (exp 1.0) (* (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))) (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))))
150.0ms	(* (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))) (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
18.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
20.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (exp 1.0) (* (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))) (sqrt (- 1.0 (/ (- x y) (- 1.0 y))))))
51.0ms	(* (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))) (sqrt (- 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)))

simplify50.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	361	1458
1	1331	1278
2	5001	1252

prune317.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (pow (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))) 3))
0.3b	(pow (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))) 3)
2.1b	(- 1.0 (/ (- x y) (- 1.0 y)))
2.8b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
18×	`cbrt-prod`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cube-cbrt`
10×	`pow1` `distribute-lft-out--`
8×	`difference-of-squares`
6×	`add-exp-log` `log-prod` `add-log-exp`
5×	`log-pow` `add-cbrt-cube`
4×	`cube-div` `flip3--` `flip--`
3×	`pow-unpow`
2×	`cube-mult` `log-div` `cbrt-div` `times-frac` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `diff-log` `div-sub` `rem-log-exp` `pow-exp` `rem-cbrt-cube` `associate--r-` `rem-cube-cbrt`

Counts

4 → 93

Calls

4 calls:

5.0ms	(cbrt (pow (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))) 3))
5.0ms	(pow (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))) 3)
20.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
17.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series704.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (pow (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))) 3))
482.0ms	(pow (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))) 3)
48.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
82.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify75.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	805	1310
1	3045	1226
2	5001	1220

prune239.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes174.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 18.3b

bsearch90.0ms

Steps

Iters	Range		Point
10	449.39022747116985	247115898190874.2	146835981.47932932
3	-753118471.6501554	-578421416.8415484	-589339982.7670864

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	23
1	36	23

end0.0ms

sample1.1s

Algorithm

intervals

Results

228.0ms	5698×	body	80	valid
169.0ms	814×	body	1280	valid
118.0ms	792×	body	640	valid
109.0ms	3711×	body	80	nan
54.0ms	333×	body	1280	nan
50.0ms	444×	body	320	valid
43.0ms	354×	body	640	nan
18.0ms	201×	body	320	nan
18.0ms	252×	body	160	valid
7.0ms	127×	body	160	nan