Details

sample54.0ms

Algorithm

intervals

Results

22.0ms	55×	body	1280	valid
11.0ms	46×	body	640	valid
7.0ms	134×	body	80	valid
2.0ms	11×	body	320	valid
1.0ms	10×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	4
1	15	4
2	15	4

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x (cos y)) (* z (sin y)))
0.1b	(* z (sin y))
0.2b	(* x (cos y))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
7×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+`

Counts

3 → 54

Calls

3 calls:

10.0ms	(+ (* x (cos y)) (* z (sin y)))
9.0ms	(* z (sin y))
9.0ms	(* x (cos y))

series149.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(+ (* x (cos y)) (* z (sin y)))
38.0ms	(* z (sin y))
40.0ms	(* x (cos y))

simplify71.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	195	268
1	748	244
2	2510	244
3	5003	243

prune179.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (cos y)) (cbrt (cos y)))
0.3b	(cbrt (cos y))
0.3b	(cbrt (cos y))
0.3b	(cbrt (cos y))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

14.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
1.0ms	(cbrt (cos y))
1.0ms	(cbrt (cos y))
1.0ms	(cbrt (cos y))

series452.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(* (cbrt (cos y)) (cbrt (cos y)))
99.0ms	(cbrt (cos y))
93.0ms	(cbrt (cos y))
98.0ms	(cbrt (cos y))

simplify110.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	128	471
1	500	419
2	3232	387
3	5002	381

prune316.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (pow (pow (cos y) 2) 1/3))
0.2b	(* (* x (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
0.3b	(pow (cos y) 2)
0.3b	(cbrt (cos y))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
22×	`add-sqr-sqrt`
19×	`unpow-prod-down`
18×	`associate-r`
16×	`prod-exp`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-cbrt-cube`
9×	`pow-exp`
7×	`pow1` `cbrt-unprod`
6×	`cbrt-prod` `unswap-sqr`
5×	`pow-to-exp` `sqr-pow`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `unpow2`
2×	`unpow1/3` `*-commutative`
1×	`pow-pow` `pow1/3` `pow-prod-down`

Counts

4 → 98

Calls

4 calls:

24.0ms	(* x (pow (pow (cos y) 2) 1/3))
43.0ms	(* (* x (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
3.0ms	(pow (cos y) 2)
1.0ms	(cbrt (cos y))

series261.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* x (pow (pow (cos y) 2) 1/3))
37.0ms	(* (* x (pow (pow (cos y) 2) 1/3)) (cbrt (cos y)))
23.0ms	(pow (cos y) 2)
100.0ms	(cbrt (cos y))

simplify46.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	330	610
1	1447	529
2	5001	498

prune359.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow (exp (log (pow (cos y) 2))) 1/3)) (cbrt (cos y)))
0.3b	(pow (cos y) 2)
0.3b	(cbrt (cos y))
2.0b	(log (pow (cos y) 2))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`log-prod` `add-cbrt-cube`
7×	`pow1` `prod-exp`
6×	`cbrt-prod` `unpow-prod-down` `associate-r`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `rem-log-exp` `pow-exp`
2×	`unpow2` `sqr-pow`
1×	`pow-pow` `unpow1/3` `pow1/3` `associate-l` `pow-prod-down` `log-pow` `*-commutative`

Counts

4 → 79

Calls

4 calls:

59.0ms	(* (* x (pow (exp (log (pow (cos y) 2))) 1/3)) (cbrt (cos y)))
3.0ms	(pow (cos y) 2)
1.0ms	(cbrt (cos y))
4.0ms	(log (pow (cos y) 2))

series266.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* x (pow (exp (log (pow (cos y) 2))) 1/3)) (cbrt (cos y)))
25.0ms	(pow (cos y) 2)
101.0ms	(cbrt (cos y))
103.0ms	(log (pow (cos y) 2))

simplify43.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	291	534
1	1259	433
2	5001	392

prune304.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes152.0ms

Accuracy

-5.3% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms

sample1.6s

Algorithm

intervals

Results

588.0ms	1485×	body	1280	valid
334.0ms	1286×	body	640	valid
240.0ms	4272×	body	80	valid
105.0ms	639×	body	320	valid
42.0ms	318×	body	160	valid