Details

sample475.0ms

Algorithm

intervals

Results

173.0ms	87×	body	2560	valid
104.0ms	132×	body	1280	valid
98.0ms	21×	body	5120	valid
52.0ms	102×	body	640	valid
10.0ms	28×	body	320	valid
7.0ms	59×	body	80	valid
6.0ms	25×	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: 38.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
1.0b	(* (pow t 3.0) (tan k))
20.1b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.8b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite166.0ms

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:

7.0ms	(pow (/ k t) 2.0)
14.0ms	(* (pow t 3.0) (tan k))
90.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
41.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series870.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (/ k t) 2.0)
224.0ms	(* (pow t 3.0) (tan k))
351.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
232.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify133.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (21.0ms)

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

prune448.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
5.9b	(* (pow k 2.0) (pow t 1.0))
16.0b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite184.0ms

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:

17.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
17.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.0ms	(* (pow k 2.0) (pow t 1.0))
69.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.3s

Counts

4 → 12

Calls

4 calls:

327.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
84.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
315.0ms	(* (pow k 2.0) (pow t 1.0))
618.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify146.0ms

Algorithm

egg-herbie

Counts

612 → 612

Iterations

Useful iterations: 2 (83.0ms)

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

prune605.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin k) 2)
0.5b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.0b	(* (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)))

rewrite425.0ms

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:

3.0ms	(pow (sin k) 2)
45.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
16.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
131.0ms	(* (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)))

series1.0s

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (sin k) 2)
333.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
77.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
621.0ms	(* (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)))

simplify300.0ms

Algorithm

egg-herbie

Counts

1472 → 1472

Iterations

Useful iterations: 2 (85.0ms)

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

prune544.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin k) 2)
3.5b	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
4.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
12.6b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

24975×	`add-exp-log`
19170×	`prod-exp`
16882×	`pow-exp`
11120×	`div-exp`
7942×	`pow-to-exp`
2980×	`rec-exp` `1-exp`
54×	`unpow-prod-down`
40×	`times-frac` `associate-l`
36×	`add-sqr-sqrt`
32×	`add-cbrt-cube`
31×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r` `cbrt-unprod`
10×	`sqr-pow`
8×	`associate-/r*`
6×	`cbrt-undiv`
5×	`pow1`
4×	`div-inv` `unpow2` `add-log-exp`
3×	`pow-unpow` `associate-*r/` `unswap-sqr`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `clear-num` `associate-/l*`

Counts

4 → 5729

Calls

4 calls:

3.0ms	(pow (sin k) 2)
185.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
16.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
74.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.3s

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (sin k) 2)
616.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
82.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
613.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.1s

Algorithm

egg-herbie

Counts

5741 → 5741

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	4266	106117
1	5002	105958

prune771.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.8b

regimes288.0ms

Accuracy

38.1% (3.3b remaining)

Error of 16.0b against oracle of 12.8b and baseline of 18.0b

bsearch544.0ms

Steps

Iters	Range		Point
8	1.048707475731352e-109	1.233250811945564e-106	7.86864403713139e-109
8	-2.803464213148836e-142	-1.382633121979521e-146	-4.767926568016393e-144

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	66
1	66	66

end0.0ms

sample14.3s

Algorithm

intervals

Results

4.1s	921×	body	5120	valid
4.1s	2224×	body	2560	valid
3.4s	4121×	body	1280	valid
1.4s	2573×	body	640	valid
383.0ms	1027×	body	320	valid
246.0ms	1998×	body	80	valid
122.0ms	496×	body	160	valid