Details

sample59.0ms

Algorithm

intervals

Results

22.0ms	50×	body	1280	valid
11.0ms	45×	body	640	valid
7.0ms	163×	body	80	valid
3.0ms	21×	body	320	valid
3.0ms	108×	body	80	nan
1.0ms	13×	body	160	valid

simplify120.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (9.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	108	6
4	310	4
5	792	4
6	4192	4
7	5002	4

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x (log (/ x (+ x y)))))
0.0b	(/ (exp (* x (log (/ x (+ x y))))) x)
0.1b	(* x (log (/ x (+ x y))))
9.9b	(log (/ x (+ x y)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac`
234×	`log-prod`
232×	`*-un-lft-identity`
180×	`exp-sum`
156×	`add-sqr-sqrt`
154×	`add-cube-cbrt`
108×	`distribute-rgt-in` `distribute-lft-in`
39×	`distribute-lft-out` `associate-/l*`
26×	`associate-/r/`
14×	`div-inv`
13×	`flip3-+` `flip-+`
10×	`add-exp-log`
8×	`pow1` `add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`associate-l` `associate-/r*`
2×	`div-exp` `rem-log-exp` `log-pow`
1×	`cbrt-undiv` `log-div` `exp-prod` `exp-to-pow` `frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 309

Calls

4 calls:

8.0ms	(exp (* x (log (/ x (+ x y)))))
15.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
9.0ms	(* x (log (/ x (+ x y))))
8.0ms	(log (/ x (+ x y)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(exp (* x (log (/ x (+ x y)))))
129.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
79.0ms	(* x (log (/ x (+ x y))))
54.0ms	(log (/ x (+ x y)))

simplify84.0ms

Algorithm

egg-herbie

Counts

321 → 321

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	843	3316
1	2718	2860
2	5002	2847

prune596.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x y))
0.0b	(/ (pow (exp x) (log (/ x (+ x y)))) x)
0.3b	(pow (exp x) (log (/ x (+ x y))))
9.9b	(log (/ x (+ x y)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
142×	`*-un-lft-identity`
108×	`log-prod`
98×	`add-sqr-sqrt` `add-cube-cbrt`
90×	`unpow-prod-up`
28×	`associate-/l*`
22×	`distribute-lft-out`
15×	`unpow-prod-down`
14×	`associate-/r/`
13×	`add-exp-log`
8×	`add-cbrt-cube` `div-inv`
7×	`pow1` `flip3-+` `associate-/r*` `flip-+`
5×	`div-exp` `sqr-pow`
4×	`expm1-log1p-u` `pow-unpow` `pow-pow` `log1p-expm1-u` `add-log-exp`
3×	`log-div` `exp-prod`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `pow-sub`
1×	`associate-/l/`

Counts

4 → 228

Calls

4 calls:

5.0ms	(/ x (+ x y))
13.0ms	(/ (pow (exp x) (log (/ x (+ x y)))) x)
8.0ms	(pow (exp x) (log (/ x (+ x y))))
5.0ms	(log (/ x (+ x y)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ x (+ x y))
97.0ms	(/ (pow (exp x) (log (/ x (+ x y)))) x)
141.0ms	(pow (exp x) (log (/ x (+ x y))))
47.0ms	(log (/ x (+ x y)))

simplify79.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	686	2318
1	2859	2267
2	5002	2231

prune876.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
4.1b	(log (/ (cbrt x) (cbrt (+ x y))))
6.0b	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

61×	`log-prod`
51×	`cbrt-prod`
46×	`*-un-lft-identity`
43×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
14×	`cbrt-div`
10×	`associate-/r/`
7×	`flip3-+` `rem-log-exp` `flip-+`
6×	`pow1` `distribute-lft-out`
5×	`div-exp`
4×	`expm1-log1p-u` `frac-times` `prod-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `pow1/3` `associate-r/` `associate-l/` `log-pow` `div-inv`

Counts

4 → 116

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
15.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

series511.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt x)
176.0ms	(cbrt x)
72.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
85.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

simplify100.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	449	1200
1	1120	1128
2	3610	1084
3	5002	1070

prune544.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (* -1 y)) x)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`add-exp-log`
1×	`pow1` `cbrt-undiv` `exp-neg` `expm1-log1p-u` `frac-2neg` `mul-1-neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`

Counts

1 → 30

Calls

1 calls:

8.0ms

(/ (exp (* -1 y)) x)

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(/ (exp (* -1 y)) x)

simplify51.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	118	194
1	313	179
2	1512	177
3	5001	177

prune67.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes58.0ms

Accuracy

87.5% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 5.7b

bsearch83.0ms

Steps

Iters	Range		Point
8	1.261082094523378e-16	5.325035394957222e-14	5.2765314246890564e-14
7	-3.6785161962636654e+113	-5.188609141993507e+111	-1.5696397542027947e+112

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	12
1	28	12

end0.0ms

sample1.7s

Algorithm

intervals

Results

667.0ms	1566×	body	1280	valid
362.0ms	1453×	body	640	valid
211.0ms	4881×	body	80	valid
131.0ms	822×	body	320	valid
94.0ms	3030×	body	80	nan
46.0ms	433×	body	160	valid