Details

sample81.0ms

Algorithm

intervals

Results

25.0ms	43×	body	1280	valid
18.0ms	47×	body	640	valid
12.0ms	164×	body	80	valid
8.0ms	30×	body	320	valid
6.0ms	123×	body	80	nan
2.0ms	10×	body	160	valid

simplify115.0ms

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: 7.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x (log (/ x (+ x y)))))
0.0b	(/ x (+ x y))
0.1b	(* x (log (/ x (+ x y))))
6.3b	(log (/ x (+ x y)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

93×	`*-un-lft-identity`
90×	`log-prod`
72×	`times-frac`
57×	`add-sqr-sqrt`
55×	`add-cube-cbrt`
36×	`distribute-rgt-in` `distribute-lft-in` `exp-sum`
19×	`distribute-lft-out`
12×	`associate-/r/`
11×	`add-exp-log`
8×	`pow1` `add-cbrt-cube`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `associate-/r*` `log1p-expm1-u`
3×	`associate-l` `associate-/l*`
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 → 171

Calls

4 calls:

9.0ms	(exp (* x (log (/ x (+ x y)))))
5.0ms	(/ x (+ x y))
12.0ms	(* x (log (/ x (+ x y))))
4.0ms	(log (/ x (+ x y)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(exp (* x (log (/ x (+ x y)))))
40.0ms	(/ x (+ x y))
78.0ms	(* x (log (/ x (+ x y))))
53.0ms	(log (/ x (+ x y)))

simplify62.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	537	1275
1	2087	1187
2	5001	1178

prune356.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
2.8b	(log (/ (cbrt x) (cbrt (+ x y))))
2.9b	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

rewrite23.0ms

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:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
6.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
11.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

series520.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(cbrt x)
178.0ms	(cbrt x)
72.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
82.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 3 (79.0ms)

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

prune514.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

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:

3.0ms

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

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

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

simplify48.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 2 (11.0ms)

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

prune66.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`pow1`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`div-exp` `prod-exp`
3×	`times-frac` `associate-r` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `expm1-log1p-u` `rec-exp` `pow-flip` `1-exp` `pow-prod-down` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`frac-2neg` `clear-num` `associate-/r` `-commutative` `div-inv` `inv-pow` `unswap-sqr`

Counts

2 → 50

Calls

2 calls:

5.0ms	(* x (exp y))
10.0ms	(/ 1 (* x (exp y)))

series42.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(* x (exp y))
20.0ms	(/ 1 (* x (exp y)))

simplify95.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	179	216
1	804	181
2	4323	175
3	5002	175

prune85.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes54.0ms

Accuracy

84.1% (0.9b remaining)

Error of 1.9b against oracle of 1.0b and baseline of 6.5b

bsearch69.0ms

Steps

Iters	Range		Point
8	1.0320989087612647e-20	8.58910903859668e-18	8.457450141620207e-18
2	-8.406169814414707e+115	-7.281669141149857e+115	-7.3893711893619755e+115

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	25
1	37	25

end0.0ms

sample2.5s

Algorithm

intervals

Results

899.0ms	1530×	body	1280	valid
553.0ms	1495×	body	640	valid
348.0ms	4869×	body	80	valid
213.0ms	839×	body	320	valid
156.0ms	3068×	body	80	nan
77.0ms	455×	body	160	valid