Details

sample94.0ms

Algorithm

intervals

Results

35.0ms	57×	body	1280	valid
19.0ms	51×	body	640	valid
11.0ms	154×	body	80	valid
8.0ms	32×	body	320	valid
6.0ms	120×	body	80	nan
2.0ms	15×	body	160	valid

simplify112.0ms

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	108	6
4	310	4
5	792	4
6	4192	4
7	5002	4

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
7.1b	(pow (/ x (+ x y)) x)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
24×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`unpow-prod-down`
7×	`add-exp-log` `distribute-lft-out`
4×	`associate-/r*` `associate-/r/` `add-cbrt-cube`
3×	`pow1` `pow-unpow` `associate-/l*`
2×	`expm1-log1p-u` `flip3-+` `div-exp` `pow-exp` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

2 → 70

Calls

2 calls:

5.0ms	(/ x (+ x y))
7.0ms	(pow (/ x (+ x y)) x)

series280.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ x (+ x y))
235.0ms	(pow (/ x (+ x y)) x)

simplify43.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	320	413
1	1304	399
2	5002	398

prune155.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

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)

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(/ (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

prune75.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

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))
7.0ms	(/ 1 (* x (exp y)))

series47.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(* x (exp y))
21.0ms	(/ 1 (* x (exp y)))

simplify94.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (25.0ms)

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

prune85.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.2b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.7b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
12.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
15.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series1.1s

Counts

4 → 12

Calls

4 calls:

367.0ms	(cbrt x)
180.0ms	(cbrt x)
273.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
279.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify65.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	708	1370
1	2244	1300
2	5002	1271

prune426.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes54.0ms

Accuracy

97.6% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 6.3b

bsearch147.0ms

Steps

Iters	Range		Point
9	1.2774642312839134e-06	1.9435667087631803	1.9234455677719884
10	-1.2865710840676908e+74	-2.585852377202543e+56	-2.4296307746992404e+61

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	18
1	34	18

end0.0ms

sample2.5s

Algorithm

intervals

Results

871.0ms	1479×	body	1280	valid
562.0ms	1488×	body	640	valid
355.0ms	4831×	body	80	valid
223.0ms	869×	body	320	valid
157.0ms	2996×	body	80	nan
71.0ms	445×	body	160	valid