Details

sample507.0ms

Algorithm

intervals

Results

145.0ms	65×	body	2560	valid
141.0ms	129×	body	1280	valid
110.0ms	25×	body	5120	valid
52.0ms	67×	body	640	valid
19.0ms	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	147	13
2	857	12
3	5002	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)))

rewrite85.0ms

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:

3.0ms	(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)))
21.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series869.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow (/ k t) 2.0)
225.0ms	(* (pow t 3.0) (tan k))
350.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
235.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify136.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (21.0ms)

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

prune430.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.4b

localize23.0ms

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)))

rewrite115.0ms

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	(* (pow k 2.0) (pow t 1.0))
6.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
35.0ms	(* (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:

325.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
321.0ms	(* (pow k 2.0) (pow t 1.0))
85.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
622.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify153.0ms

Algorithm

egg-herbie

Counts

612 → 612

Iterations

Useful iterations: 2 (82.0ms)

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

prune591.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.2b

localize24.0ms

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)))

rewrite295.0ms

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:

1.0ms	(pow (sin k) 2)
21.0ms	(/ 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))
61.0ms	(* (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)
325.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
85.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
634.0ms	(* (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)))

simplify279.0ms

Algorithm

egg-herbie

Counts

1472 → 1472

Iterations

Useful iterations: 2 (86.0ms)

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

prune531.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 15.0b

localize24.0ms

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))))

rewrite431.0ms

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×	`associate-/r*` `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 → 931

Calls

4 calls:

3.0ms	(/ (cos k) (sin k))
21.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
30.0ms	(* (/ (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))))

series1.1s

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (cos k) (sin k))
327.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
83.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
623.0ms	(* (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))))

simplify163.0ms

Algorithm

egg-herbie

Counts

943 → 943

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	2147	15097
1	5002	12259

prune700.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.1b

regimes360.0ms

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	71	86
1	71	86

end0.0ms

sample18.0s

Algorithm

intervals

Results

5.0s	2192×	body	2560	valid
4.6s	4095×	body	1280	valid
4.6s	954×	body	5120	valid
2.0s	2575×	body	640	valid
585.0ms	1019×	body	320	valid
483.0ms	2032×	body	80	valid
168.0ms	421×	body	160	valid