Details

sample508.0ms

Algorithm

intervals

Results

141.0ms	129×	body	1280	valid
140.0ms	65×	body	2560	valid
108.0ms	25×	body	5120	valid
61.0ms	67×	body	640	valid
15.0ms	67×	body	80	valid
15.0ms	27×	body	320	valid
5.0ms	14×	body	160	valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (25.0ms)

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: 41.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ k t) 2.0)
0.3b	(* (pow t 3.0) (tan k))
21.1b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.4b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite88.0ms

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:

3.0ms	(pow (/ k t) 2.0)
6.0ms	(* (pow t 3.0) (tan k))
42.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
24.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series905.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (/ k t) 2.0)
236.0ms	(* (pow t 3.0) (tan k))
365.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
244.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify47.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	991	2005
1	5001	1672

prune478.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.9b	(* (pow k 2.0) (pow t 1.0))
6.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.6b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite119.0ms

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)))
8.0ms	(* (pow k 2.0) (pow t 1.0))
6.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
36.0ms	(* (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:

330.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
323.0ms	(* (pow k 2.0) (pow t 1.0))
86.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
628.0ms	(* (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 (83.0ms)

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

prune645.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin k) 2)
0.9b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
6.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.6b	(* (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)))

rewrite297.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 1468

Calls

4 calls:

1.0ms	(pow (sin k) 2)
20.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
6.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
62.0ms	(* (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:

24.0ms	(pow (sin k) 2)
335.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
88.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
647.0ms	(* (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)))

simplify288.0ms

Algorithm

egg-herbie

Counts

1480 → 1480

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	1997	23615
1	4854	19182
2	5002	17933

prune587.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 15.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos k) (sin k))
0.9b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.9b	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
16.6b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

rewrite241.0ms

Algorithm

rewrite-expression-head

Rules

3841×	`add-exp-log`
2622×	`prod-exp`
1370×	`div-exp`
1330×	`pow-exp`
679×	`pow-to-exp`
248×	`rec-exp` `1-exp`
99×	`times-frac`
80×	`add-sqr-sqrt`
65×	`add-cbrt-cube`
59×	`add-cube-cbrt` `*-un-lft-identity`
45×	`associate-r`
24×	`associate-l`
22×	`cbrt-undiv` `cbrt-unprod`
8×	`div-inv`
7×	`pow1` `unpow-prod-down`
6×	`associate-/l*` `unswap-sqr`
5×	`associate-*r/`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`pow-flip` `pow-prod-down` `associate-/r/` `inv-pow` `sqr-pow`

Counts

4 → 939

Calls

4 calls:

4.0ms	(/ (cos k) (sin k))
20.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
28.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
63.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

series1.3s

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (cos k) (sin k))
334.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
89.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
844.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

simplify165.0ms

Algorithm

egg-herbie

Counts

951 → 951

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	2402	15175
1	5001	12337

prune768.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.1b

regimes375.0ms

Accuracy

56.5% (3.2b remaining)

Error of 11.7b against oracle of 8.5b and baseline of 15.9b

bsearch1.6s

Steps

Iters	Range		Point
5	1.3633964723283668e+110	4.321994932968824e+110	2.253243719025402e+110
9	1.234904841362201e-118	3.6659949666767967e-109	1.2653785684425997e-118
8	-1.5421433861803082e-136	-3.2684793898865935e-139	-1.5790227602943146e-138
8	-1.4010399037692342e+171	-1.2627228349167637e+167	-1.3484728286962528e+169

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	84
1	70	84

end0.0ms

sample17.8s

Algorithm

intervals

Results

4.9s	2192×	body	2560	valid
4.6s	4095×	body	1280	valid
4.6s	954×	body	5120	valid
2.0s	2575×	body	640	valid
592.0ms	1019×	body	320	valid
481.0ms	2032×	body	80	valid
167.0ms	421×	body	160	valid