Details

sample415.0ms

Algorithm

intervals

Results

138.0ms	76×	body	2560	valid
105.0ms	32×	body	5120	valid
93.0ms	145×	body	1280	valid
42.0ms	86×	body	640	valid
8.0ms	24×	body	320	valid
6.0ms	53×	body	80	valid
2.0ms	12×	body	160	valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	44	13
1	147	13
2	857	12
3	5002	11

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.8b	(* (pow t 3.0) (tan k))
20.6b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.0b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite55.0ms

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×	`associate-r` `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 → 179

Calls

4 calls:

4.0ms	(pow (/ k t) 2.0)
6.0ms	(* (pow t 3.0) (tan k))
18.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
15.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series891.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (/ k t) 2.0)
230.0ms	(* (pow t 3.0) (tan k))
362.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
237.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify132.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	974	1954
1	4995	1620
2	5001	1620

prune441.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.9b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.4b	(* (pow k 2.0) (pow t 1.0))
14.3b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite114.0ms

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×	`div-inv` `associate-/l*` `add-log-exp`
3×	`unpow2`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `associate-*r/` `inv-pow`

Counts

4 → 600

Calls

4 calls:

7.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
8.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0ms	(* (pow k 2.0) (pow t 1.0))
26.0ms	(* (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:

327.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
83.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
323.0ms	(* (pow k 2.0) (pow t 1.0))
617.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify162.0ms

Algorithm

egg-herbie

Counts

612 → 612

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	1316	7194
1	4162	7025
2	5002	7018

prune625.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
0.5b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.9b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.3b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite281.0ms

Algorithm

rewrite-expression-head

Rules

5603×	`add-exp-log`
4515×	`prod-exp`
3078×	`pow-exp`
2032×	`div-exp`
1869×	`pow-to-exp`
434×	`rec-exp` `1-exp`
27×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
22×	`times-frac`
20×	`unpow-prod-down`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
11×	`associate-l`
9×	`associate-/r*`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1` `sqr-pow`
4×	`div-inv` `associate-/l*` `unpow2` `add-log-exp`
3×	`pow-unpow` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `associate-r/` `-commutative` `inv-pow`

Counts

4 → 1460

Calls

4 calls:

2.0ms	(pow (sin k) 2)
12.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
8.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
42.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin k) 2)
339.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
82.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
642.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify287.0ms

Algorithm

egg-herbie

Counts

1472 → 1472

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	1742	23543
1	4574	19111
2	5002	17858

prune570.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin k))
0.9b	(pow (cbrt (sin k)) 4)
1.6b	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
14.3b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (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`
11422×	`add-sqr-sqrt`
10969×	`add-cube-cbrt` `*-un-lft-identity`
10259×	`add-exp-log`
7729×	`unpow-prod-down`
6416×	`div-exp`
5073×	`prod-exp`
4256×	`pow-exp`
3846×	`cbrt-prod`
3557×	`associate-r`
2489×	`pow-to-exp`
1342×	`sqr-pow`
668×	`unpow2`
589×	`rec-exp` `1-exp`
323×	`associate-/l*`
302×	`div-inv`
108×	`unswap-sqr`
38×	`add-cbrt-cube`
23×	`associate-/r/`
20×	`cbrt-undiv`
11×	`associate-l` `associate-/r*`
5×	`pow1` `cbrt-unprod`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`pow-pow` `pow1/3`
1×	`frac-2neg` `associate-r/` `clear-num` `-commutative` `associate-/l/`

Counts

4 → 9466

Calls

4 calls:

1.0ms	(cbrt (sin k))
4.0ms	(pow (cbrt (sin k)) 4)
141.0ms	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
1.3s	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

series947.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (sin k))
125.0ms	(pow (cbrt (sin k)) 4)
87.0ms	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
635.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

simplify2.5s

Algorithm

egg-herbie

Counts

9478 → 9478

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	10711	264300

prune55.5s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 4.9b

regimes580.0ms

Accuracy

16.8% (3.9b remaining)

Error of 11.0b against oracle of 7.1b and baseline of 11.8b

bsearch624.0ms

Steps

Iters	Range		Point
8	-2.131125377017844e-152	-1.333102075632568e-156	-7.585502794490059e-156
8	-3.8975250219793675e+142	-5.828232727961281e+138	-3.104316958624234e+141

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	76
1	69	76

end0.0ms

sample13.4s

Algorithm

intervals

Results

4.4s	2306×	body	2560	valid
3.7s	963×	body	5120	valid
2.9s	4084×	body	1280	valid
1.2s	2528×	body	640	valid
350.0ms	1023×	body	320	valid
220.0ms	2032×	body	80	valid
101.0ms	433×	body	160	valid