Details

sample79.0ms

Algorithm

intervals

Results

28.0ms	52×	body	1280	valid
16.0ms	47×	body	640	valid
10.0ms	155×	body	80	valid
5.0ms	23×	body	320	valid
4.0ms	14×	body	160	valid
3.0ms	70×	body	80	nan

simplify111.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
6.6b	(pow (/ x (+ x y)) x)

rewrite14.0ms

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)

series36.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/ x (+ x y))
31.0ms	(pow (/ x (+ x y)) x)

simplify39.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (33.0ms)

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

prune366.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.5b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.4b	(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)

series118.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(cbrt x)
10.0ms	(cbrt x)
44.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
55.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify63.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (48.0ms)

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

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.5b	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
1.5b	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
1.5b	(pow (/ (cbrt x) (cbrt (+ x y))) x)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

54×	`unpow-prod-down`
48×	`cbrt-prod`
47×	`*-un-lft-identity`
42×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`add-exp-log`
7×	`pow1`
6×	`distribute-lft-out`
5×	`pow-unpow`
4×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `sqr-pow`
2×	`cbrt-div` `associate-/r/`
1×	`flip3-+` `pow1/3` `div-exp` `flip-+` `div-inv`

Counts

4 → 112

Calls

4 calls:

0.0ms	(cbrt x)
1.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
1.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
14.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)

series88.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(cbrt x)
18.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
16.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
45.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)

simplify54.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	555	1252
1	1982	1220
2	5001	1155

prune1.2s

Pruning

3 alts after pruning (2 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)

series5.0ms

Counts

1 → 3

Calls

1 calls:

5.0ms

(/ (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

prune133.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes103.0ms

Accuracy

98.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 5.7b

bsearch64.0ms

Steps

Iters	Range		Point
9	7.688923129635521e-07	2001.8961909206312	3.973722325568169
6	-1.666976694187906e+42	-1.6462068410071746e+41	-3.035242744540275e+41

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	27
1	34	27

end0.0ms

sample2.3s

Algorithm

intervals

Results

855.0ms	1572×	body	1280	valid
491.0ms	1447×	body	640	valid
308.0ms	4844×	body	80	valid
189.0ms	825×	body	320	valid
150.0ms	2975×	body	80	nan
65.0ms	455×	body	160	valid