Details

sample40.0ms

Algorithm

intervals

Results

9.0ms	34×	body	1280	valid
8.0ms	42×	body	640	valid
7.0ms	168×	body	80	valid
3.0ms	21×	body	320	valid
1.0ms	8×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	4
1	24	4
2	48	4
3	71	4
4	79	4
5	79	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (/ (sin y) y))
0.2b	(/ (sin y) y)
3.1b	(/ (* x (/ (sin y) y)) z)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`times-frac`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log` `add-cbrt-cube`
13×	`associate-r`
6×	`cbrt-undiv` `div-exp` `associate-/r*`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `associate-/l*`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-*r/` `clear-num` `unswap-sqr`
1×	`pow-prod-down` `*-commutative` `associate-/l/`

Counts

3 → 89

Calls

3 calls:

14.0ms	(* x (/ (sin y) y))
8.0ms	(/ (sin y) y)
13.0ms	(/ (* x (/ (sin y) y)) z)

series140.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* x (/ (sin y) y))
23.0ms	(/ (sin y) y)
64.0ms	(/ (* x (/ (sin y) y)) z)

simplify47.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	333	511
1	1655	443
2	5001	443

prune209.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt z)
0.5b	(cbrt z)
0.6b	(* (cbrt z) (cbrt z))
2.1b	(* (/ x (* (cbrt z) (cbrt z))) (/ (/ (sin y) y) (cbrt z)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

152×	`times-frac`
125×	`add-sqr-sqrt`
88×	`associate-r`
85×	`add-cube-cbrt` `*-un-lft-identity`
65×	`cbrt-prod`
42×	`add-exp-log`
28×	`add-cbrt-cube`
15×	`cbrt-undiv` `div-exp`
14×	`unswap-sqr`
13×	`pow1` `associate-l` `prod-exp` `cbrt-unprod`
8×	`pow1/3` `div-inv`
6×	`swap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/`

Counts

4 → 199

Calls

4 calls:

1.0ms	(cbrt z)
1.0ms	(cbrt z)
11.0ms	(* (cbrt z) (cbrt z))
70.0ms	(* (/ x (* (cbrt z) (cbrt z))) (/ (/ (sin y) y) (cbrt z)))

series658.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt z)
179.0ms	(cbrt z)
199.0ms	(* (cbrt z) (cbrt z))
104.0ms	(* (/ x (* (cbrt z) (cbrt z))) (/ (/ (sin y) y) (cbrt z)))

simplify52.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1081	1966
1	5002	1612

prune631.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt z) (cbrt z))
0.6b	(* (cbrt z) (cbrt z))
0.6b	(cbrt (* (cbrt z) (cbrt z)))
2.1b	(* (/ x (* (cbrt z) (cbrt z))) (/ (/ (sin y) y) (* (cbrt (* (cbrt z) (cbrt z))) (cbrt (cbrt z)))))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
51×	`add-cbrt-cube`
50×	`add-sqr-sqrt`
33×	`cbrt-prod`
30×	`add-cube-cbrt` `*-un-lft-identity`
29×	`associate-r`
28×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
26×	`times-frac`
20×	`pow1`
19×	`associate-l`
13×	`pow1/3`
12×	`swap-sqr`
10×	`unswap-sqr`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `div-inv`
2×	`pow2` `pow-plus`
1×	`frac-times` `associate-r/` `associate-l/`

Counts

4 → 165

Calls

4 calls:

11.0ms	(* (cbrt z) (cbrt z))
12.0ms	(* (cbrt z) (cbrt z))
5.0ms	(cbrt (* (cbrt z) (cbrt z)))
78.0ms	(* (/ x (* (cbrt z) (cbrt z))) (/ (/ (sin y) y) (* (cbrt (* (cbrt z) (cbrt z))) (cbrt (cbrt z)))))

series778.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(* (cbrt z) (cbrt z))
208.0ms	(* (cbrt z) (cbrt z))
268.0ms	(cbrt (* (cbrt z) (cbrt z)))
102.0ms	(* (/ x (* (cbrt z) (cbrt z))) (/ (/ (sin y) y) (* (cbrt (* (cbrt z) (cbrt z))) (cbrt (cbrt z)))))

simplify96.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	688	1891
1	3858	1462
2	5002	1331

prune442.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (* (sin y) (/ 1 y)))
0.3b	(* (sin y) (/ 1 y))
3.1b	(/ (* x (* (sin y) (/ 1 y))) z)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
31×	`add-cbrt-cube`
22×	`prod-exp`
21×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
14×	`add-cube-cbrt` `times-frac` `associate-r`
12×	`div-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `associate-*r/`
6×	`associate-l`
4×	`pow-prod-down`
3×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-/r*` `un-div-inv` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`*-commutative` `div-inv` `associate-/l/`
1×	`frac-2neg` `clear-num` `associate-/l*`

Counts

3 → 95

Calls

3 calls:

29.0ms	(* x (* (sin y) (/ 1 y)))
20.0ms	(* (sin y) (/ 1 y))
32.0ms	(/ (* x (* (sin y) (/ 1 y))) z)

series140.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* x (* (sin y) (/ 1 y)))
23.0ms	(* (sin y) (/ 1 y))
65.0ms	(/ (* x (* (sin y) (/ 1 y))) z)

simplify56.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	422	595
1	2107	461
2	5002	439

prune184.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes283.0ms

Accuracy

77.8% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 3.1b

bsearch86.0ms

Steps

Iters	Range		Point
9	2.1881140587362268e-26	3.6401178074972383e-19	5.715011145653865e-24
9	-5.8516907299059634e-80	-3.3844226674964425e-87	-4.11794374772535e-81

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	10
1	26	10

end0.0ms

sample1.1s

Algorithm

intervals

Results

268.0ms	988×	body	1280	valid
246.0ms	5798×	body	80	valid
183.0ms	1026×	body	640	valid
93.0ms	591×	body	320	valid
32.0ms	312×	body	160	valid