Details

sample454.0ms

Algorithm

intervals

Results

144.0ms	34×	body	5120	valid
122.0ms	72×	body	2560	valid
105.0ms	123×	body	1280	valid
41.0ms	80×	body	640	valid
10.0ms	29×	body	320	valid
9.0ms	76×	body	80	valid
2.0ms	11×	body	160	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	44	13
1	149	13
2	869	12
3	5001	11

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
1.0b	(* (pow t 3.0) (tan k))
23.3b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.2b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

337×	`add-exp-log`
220×	`prod-exp`
71×	`div-exp`
65×	`add-cbrt-cube`
51×	`pow-exp`
34×	`pow-to-exp` `cbrt-unprod`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt`
24×	`associate-l`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
12×	`cbrt-undiv`
5×	`pow1` `associate-*r/`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`tan-quot` `pow-unpow` `div-inv` `unswap-sqr`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l*`

Counts

4 → 187

Calls

4 calls:

4.0ms	(pow (/ k t) 2.0)
6.0ms	(* (pow t 3.0) (tan k))
44.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
26.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series913.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(pow (/ k t) 2.0)
240.0ms	(* (pow t 3.0) (tan k))
367.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
245.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify46.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	991	2005
1	5001	1672

prune505.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
6.6b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.7b	(* (pow k 2.0) (pow t 1.0))
18.5b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

1645×	`add-exp-log`
1122×	`prod-exp`
899×	`pow-exp`
688×	`div-exp`
509×	`pow-to-exp`
140×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
29×	`unpow-prod-down`
25×	`add-cbrt-cube`
22×	`times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`associate-r`
18×	`associate-l`
13×	`sqr-pow`
12×	`unswap-sqr`
9×	`associate-/r*`
7×	`cbrt-unprod`
6×	`cbrt-undiv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`unpow2`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `associate-*r/` `inv-pow`

Counts

4 → 608

Calls

4 calls:

8.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
6.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.0ms	(* (pow k 2.0) (pow t 1.0))
38.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.4s

Counts

4 → 12

Calls

4 calls:

338.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
88.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
333.0ms	(* (pow k 2.0) (pow t 1.0))
643.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify147.0ms

Algorithm

egg-herbie

Counts

620 → 620

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	1439	7252
1	4296	7083
2	5003	7076

prune701.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.9b	(pow (cbrt (sin k)) 4)
2.9b	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
6.7b	(* (pow k 2.0) (pow t 1.0))
18.5b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

rewrite3.1s

Algorithm

rewrite-expression-head

Rules

28001×	`times-frac`
11437×	`add-sqr-sqrt`
10972×	`add-cube-cbrt` `*-un-lft-identity`
7741×	`unpow-prod-down`
3843×	`cbrt-prod`
3564×	`associate-r`
3161×	`add-exp-log`
2216×	`div-exp`
1350×	`sqr-pow`
1244×	`pow-exp`
1149×	`prod-exp`
674×	`pow-to-exp`
668×	`unpow2`
323×	`associate-/l*`
302×	`div-inv`
190×	`rec-exp` `1-exp`
117×	`unswap-sqr`
40×	`add-cbrt-cube`
23×	`associate-/r/`
20×	`cbrt-undiv`
18×	`associate-l`
11×	`associate-/r*`
6×	`cbrt-unprod`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow` `*-commutative`
1×	`frac-2neg` `pow1/3` `associate-*r/` `clear-num` `associate-/l/`

Counts

4 → 8307

Calls

4 calls:

2.0ms	(pow (cbrt (sin k)) 4)
177.0ms	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
8.0ms	(* (pow k 2.0) (pow t 1.0))
1.4s	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

125.0ms	(pow (cbrt (sin k)) 4)
86.0ms	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
321.0ms	(* (pow k 2.0) (pow t 1.0))
631.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

simplify1.9s

Algorithm

egg-herbie

Counts

8319 → 8319

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	10549	212822

prune53.4s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 9.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.9b	(pow (cbrt (sin k)) 4)
5.1b	(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ 1 (/ (pow (cbrt (sin k)) 4) l)) (pow (cbrt 1) 2))) (/ (/ (cos k) (/ 1 l)) (pow (cbrt (sin k)) 2)))
5.7b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ 1 (/ (pow (cbrt (sin k)) 4) l)) (pow (cbrt 1) 2)))
6.7b	(* (pow k 2.0) (pow t 1.0))

rewrite7.9s

Algorithm

rewrite-expression-head

Rules

142730×	`add-exp-log`
107683×	`div-exp`
61945×	`prod-exp`
52274×	`pow-exp`
31874×	`pow-to-exp`
17495×	`rec-exp` `1-exp`
5024×	`times-frac`
2543×	`add-sqr-sqrt`
2022×	`*-un-lft-identity`
1899×	`add-cube-cbrt`
1763×	`unpow-prod-down`
1676×	`associate-r`
855×	`cbrt-prod`
396×	`sqr-pow`
210×	`unswap-sqr`
184×	`unpow2`
130×	`add-cbrt-cube`
91×	`div-inv`
60×	`cbrt-undiv`
41×	`cbrt-unprod`
22×	`associate-/r/`
19×	`associate-l`
7×	`pow1`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `*-commutative`
2×	`pow-pow`
1×	`frac-times` `pow1/3` `pow-prod-down` `associate-*l/`

Counts

4 → 24453

Calls

4 calls:

2.0ms	(pow (cbrt (sin k)) 4)
1.0s	(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ 1 (/ (pow (cbrt (sin k)) 4) l)) (pow (cbrt 1) 2))) (/ (/ (cos k) (/ 1 l)) (pow (cbrt (sin k)) 2)))
511.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ 1 (/ (pow (cbrt (sin k)) 4) l)) (pow (cbrt 1) 2)))
13.0ms	(* (pow k 2.0) (pow t 1.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

128.0ms	(pow (cbrt (sin k)) 4)
649.0ms	(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ 1 (/ (pow (cbrt (sin k)) 4) l)) (pow (cbrt 1) 2))) (/ (/ (cos k) (/ 1 l)) (pow (cbrt (sin k)) 2)))
474.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ 1 (/ (pow (cbrt (sin k)) 4) l)) (pow (cbrt 1) 2)))
335.0ms	(* (pow k 2.0) (pow t 1.0))

simplify5.8s

Algorithm

egg-herbie

Counts

24465 → 24465

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	8332	701828

prune53.3s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 5.9b

regimes1.2s

Accuracy

18.2% (4.2b remaining)

Error of 11.1b against oracle of 6.9b and baseline of 12.0b

bsearch322.0ms

Steps

Iters	Range		Point
8	1.2502763784038698e+152	1.3038626640272796e+156	6.696003777935638e+153
8	-8.302663009110035e+173	-7.740116171572404e+170	-7.83518389073447e+170

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	52
1	60	52

end0.0ms

sample13.3s

Algorithm

intervals

Results

4.0s	2287×	body	2560	valid
3.8s	976×	body	5120	valid
3.1s	4055×	body	1280	valid
1.3s	2545×	body	640	valid
337.0ms	1000×	body	320	valid
237.0ms	2084×	body	80	valid
95.0ms	407×	body	160	valid