Details

sample40.0ms

Algorithm

intervals

Results

9.0ms	184×	body	80	valid
5.0ms	29×	body	1280	valid
3.0ms	24×	body	640	valid
3.0ms	99×	body	80	nan
2.0ms	13×	body	1280	nan
1.0ms	14×	body	640	nan
1.0ms	9×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	5×	body	320	nan
0.0ms	1×	body	160	nan

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 18.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
2.9b	(- 1.0 (/ (- x y) (- 1.0 y)))
4.5b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite162.0ms

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:

23.0ms	(/ (- x y) (- 1.0 y))
38.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
41.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
44.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series234.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (- x y) (- 1.0 y))
80.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
48.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
74.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify105.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	986	4621
1	3240	3344
2	5001	3134

prune438.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- 1.0 y))
0.3b	(cbrt (- 1.0 y))
4.5b	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
12.8b	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

540×	`times-frac`
485×	`add-sqr-sqrt`
461×	`*-un-lft-identity`
426×	`prod-diff`
303×	`add-cube-cbrt`
298×	`cbrt-div`
269×	`cbrt-prod`
198×	`associate-/r/`
151×	`flip3--` `flip--`
96×	`frac-times`
87×	`difference-of-squares`
79×	`distribute-lft-out--`
48×	`associate-r/` `associate-l/`
27×	`div-inv`
9×	`log-prod`
6×	`add-log-exp`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg`
2×	`log-div` `pow1/3` `div-sub`
1×	`sub-neg` `diff-log` `rem-log-exp` `log-pow` `associate--r-`

Counts

4 → 506

Calls

4 calls:

4.0ms	(cbrt (- 1.0 y))
4.0ms	(cbrt (- 1.0 y))
115.0ms	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
109.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(cbrt (- 1.0 y))
88.0ms	(cbrt (- 1.0 y))
79.0ms	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
48.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

simplify295.0ms

Algorithm

egg-herbie

Counts

518 → 518

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	3148	32097
1	5002	31058

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

4.3b	(log (sqrt (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))))
4.3b	(log (sqrt (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))))
12.8b	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))
12.8b	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

rewrite500.0ms

Algorithm

rewrite-expression-head

Rules

1080×	`times-frac`
956×	`add-sqr-sqrt`
908×	`*-un-lft-identity`
852×	`prod-diff`
600×	`add-cube-cbrt`
588×	`cbrt-div`
518×	`cbrt-prod`
396×	`associate-/r/`
298×	`flip3--` `flip--`
192×	`frac-times`
170×	`difference-of-squares`
154×	`distribute-lft-out--`
96×	`associate-r/` `associate-l/`
54×	`div-inv`
24×	`log-prod`
18×	`sqrt-prod`
8×	`pow1` `add-log-exp`
6×	`add-exp-log` `fma-neg` `log-pow`
4×	`expm1-log1p-u` `log-div` `sqrt-div` `div-sub` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `rem-log-exp` `associate--r-`

Counts

4 → 954

Calls

4 calls:

79.0ms	(log (sqrt (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))))
78.0ms	(log (sqrt (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))))
109.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))
110.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

series345.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(log (sqrt (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))))
124.0ms	(log (sqrt (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))))
45.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))
56.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

simplify542.0ms

Algorithm

egg-herbie

Counts

966 → 966

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	3076	63952
1	5002	61942

prune3.6s

Pruning

4 alts after pruning (4 fresh and 0 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)))))
0.1b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
2.9b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite180.0ms

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:

22.0ms	(/ (- x y) (- 1.0 y))
34.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
65.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
44.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series332.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (- x y) (- 1.0 y))
137.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
112.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
49.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify115.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	1074	4812
1	3721	3718
2	5001	3710

prune545.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes172.0ms

Accuracy

99% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 18.1b

bsearch197.0ms

Steps

Iters	Range		Point
11	0.005224711248419297	3.1001251511911e+29	0.9979648952928983
7	-1455544721.0569484	-41026626.92430381	-78185572.37681165

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	130
1	83	130
2	85	130
3	85	130

end0.0ms

sample1.1s

Algorithm

intervals

Results

220.0ms	5719×	body	80	valid
146.0ms	789×	body	1280	valid
107.0ms	807×	body	640	valid
97.0ms	3800×	body	80	nan
52.0ms	343×	body	1280	nan
46.0ms	409×	body	640	nan
42.0ms	456×	body	320	valid
16.0ms	208×	body	320	nan
15.0ms	229×	body	160	valid
6.0ms	122×	body	160	nan