Details

sample61.0ms

Algorithm

intervals

Results

22.0ms	50×	body	1280	valid
11.0ms	45×	body	640	valid
9.0ms	163×	body	80	valid
3.0ms	108×	body	80	nan
3.0ms	21×	body	320	valid
1.0ms	13×	body	160	valid

simplify110.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (8.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	106	6
4	304	4
5	774	4
6	4142	4
7	5001	4

prune4.0ms

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)))

rewrite61.0ms

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×	`associate-r`
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 → 301

Calls

4 calls:

7.0ms	(exp (* x (log (/ x (+ x y)))))
14.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
8.0ms	(* x (log (/ x (+ x y))))
5.0ms	(log (/ x (+ x y)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(exp (* x (log (/ x (+ x y)))))
126.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
75.0ms	(* x (log (/ x (+ x y))))
46.0ms	(log (/ x (+ x y)))

simplify89.0ms

Algorithm

egg-herbie

Counts

313 → 313

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	825	3278
1	2642	2828
2	5002	2813

prune553.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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)))

rewrite44.0ms

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×	`pow-unpow` `pow-pow` `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 → 220

Calls

4 calls:

5.0ms	(/ x (+ x y))
12.0ms	(/ (pow (exp x) (log (/ x (+ x y)))) x)
8.0ms	(pow (exp x) (log (/ x (+ x y))))
6.0ms	(log (/ x (+ x y)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ x (+ x y))
99.0ms	(/ (pow (exp x) (log (/ x (+ x y)))) x)
133.0ms	(pow (exp x) (log (/ x (+ x y))))
51.0ms	(log (/ x (+ x y)))

simplify77.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	667	2282
1	2777	2231
2	5002	2195

prune633.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

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×	`frac-times` `prod-exp` `add-cbrt-cube` `add-log-exp`
2×	`log-div` `pow1/3` `associate-r/` `associate-l/` `log-pow` `div-inv`

Counts

4 → 108

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
14.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

series514.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt x)
174.0ms	(cbrt x)
73.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
85.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	439	1158
1	1101	1086
2	3533	1043
3	5002	1001

prune430.0ms

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)

rewrite5.0ms

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` `frac-2neg` `mul-1-neg` `div-exp` `clear-num` `div-inv` `associate-/l/` `add-log-exp`

Counts

1 → 28

Calls

1 calls:

4.0ms

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

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

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

simplify51.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	114	186
1	303	172
2	1465	170
3	5003	170

prune58.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes55.0ms

Accuracy

87.5% (0.7b remaining)

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

bsearch88.0ms

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	24	9
1	24	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

674.0ms	1566×	body	1280	valid
368.0ms	1453×	body	640	valid
206.0ms	4881×	body	80	valid
134.0ms	822×	body	320	valid
90.0ms	3030×	body	80	nan
43.0ms	433×	body	160	valid