Details

sample92.0ms

Algorithm

intervals

Results

30.0ms	50×	body	1280	valid
19.0ms	49×	body	640	valid
14.0ms	140×	body	80	valid
7.0ms	100×	body	80	nan
7.0ms	23×	body	320	valid
4.0ms	22×	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	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: 11.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
5.3b	(pow (/ x (+ x y)) x)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
118×	`*-un-lft-identity`
90×	`unpow-prod-down`
80×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
19×	`distribute-lft-out`
16×	`add-exp-log`
12×	`associate-/r/`
7×	`div-exp` `associate-/r*` `add-cbrt-cube` `div-inv`
6×	`flip3-+` `flip-+`
5×	`sqr-pow`
4×	`pow1` `pow-exp`
3×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 178

Calls

3 calls:

25.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))
7.0ms	(pow (/ x (+ x y)) x)

series386.0ms

Counts

3 → 9

Calls

3 calls:

130.0ms	(/ (pow (/ x (+ x y)) x) x)
38.0ms	(/ x (+ x y))
219.0ms	(pow (/ x (+ x y)) x)

simplify70.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	554	1456
1	2726	1426
2	5002	1426

prune397.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
13×	`unpow-prod-down`
12×	`cbrt-div`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`associate-/r/`
6×	`flip3-+` `flip-+`
5×	`pow1` `pow-exp`
4×	`expm1-log1p-u` `frac-times` `div-exp` `prod-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`associate-r/` `associate-l/`
1×	`pow-to-exp` `pow-pow` `times-frac` `div-inv` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

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

series776.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt x)
169.0ms	(cbrt x)
173.0ms	(cbrt x)
264.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify149.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	378	644
1	1170	603
2	4673	584
3	5001	584

prune273.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.6b	(cbrt x)
0.6b	(cbrt x)
2.5b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

55×	`cbrt-prod`
48×	`log-prod` `*-un-lft-identity`
42×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`add-exp-log` `distribute-lft-out`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`flip3-+` `rem-log-exp` `associate-/r/` `flip-+`
1×	`log-div` `div-exp` `log-pow` `div-inv`

Counts

4 → 103

Calls

4 calls:

2.0ms	(cbrt (+ x y))
0.0ms	(cbrt x)
0.0ms	(cbrt x)
6.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series545.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(cbrt (+ x y))
174.0ms	(cbrt x)
172.0ms	(cbrt x)
72.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify143.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (133.0ms)

Iter	Nodes	Cost
0	370	887
1	1014	855
2	4230	835
3	5002	830

prune472.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x 2) 0)
0.5b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
0.5b	(cbrt (+ x y))
0.6b	(cbrt x)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

52×	`cbrt-prod`
49×	`*-un-lft-identity`
48×	`unpow-prod-down`
42×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`add-exp-log`
10×	`pow1`
9×	`add-cbrt-cube`
7×	`distribute-lft-out`
4×	`expm1-log1p-u` `cbrt-div` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `pow1/3` `pow-exp` `associate-/r/` `flip-+`
1×	`pow-to-exp` `pow-pow` `mul0` `div-exp` `associate-l` `*-commutative` `div-inv` `sqr-pow`

Counts

4 → 115

Calls

4 calls:

7.0ms	(* (* x 2) 0)
12.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.0ms	(cbrt (+ x y))
1.0ms	(cbrt x)

series569.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(* (* x 2) 0)
262.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
128.0ms	(cbrt (+ x y))
177.0ms	(cbrt x)

simplify89.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	606	929
1	2397	908
2	5001	871

prune372.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

98.3% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 5.5b

bsearch157.0ms

Steps

Iters	Range		Point
9	0.000431479263060677	213.0826250665956	7.835280933943446
10	-3.44962383690743e+67	-9.704786708557082e+56	-1.0107557422829784e+57

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	18
1	32	18

end0.0ms

sample2.8s

Algorithm

intervals

Results

944.0ms	1514×	body	1280	valid
588.0ms	1455×	body	640	valid
480.0ms	4856×	body	80	valid
242.0ms	843×	body	320	valid
213.0ms	3064×	body	80	nan
81.0ms	422×	body	160	valid