Details

sample463.0ms

Algorithm

intervals

Results

138.0ms	76×	body	2560	valid
122.0ms	144×	body	1280	valid
105.0ms	28×	body	5120	valid
42.0ms	80×	body	640	valid
14.0ms	82×	body	80	valid
12.0ms	35×	body	320	valid
3.0ms	13×	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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
1.0b	(* (pow t 3.0) (tan k))
21.4b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
30.0b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite165.0ms

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:

6.0ms	(pow (/ k t) 2.0)
16.0ms	(* (pow t 3.0) (tan k))
89.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
44.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series836.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(pow (/ k t) 2.0)
218.0ms	(* (pow t 3.0) (tan k))
338.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
224.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify40.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	991	2005
1	5001	1672

prune498.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.6b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.8b	(* (pow k 2.0) (pow t 1.0))
17.1b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite178.0ms

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:

17.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
16.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
18.0ms	(* (pow k 2.0) (pow t 1.0))
70.0ms	(* (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:

317.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
80.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
309.0ms	(* (pow k 2.0) (pow t 1.0))
606.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify152.0ms

Algorithm

egg-herbie

Counts

620 → 620

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1439	7260
1	4421	7083
2	5002	7083

prune670.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 17.6b

localize26.0ms

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))))
4.6b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.1b	(* (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)))

rewrite398.0ms

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:

3.0ms	(pow (sin k) 2)
44.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
17.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
133.0ms	(* (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)
315.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
81.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
614.0ms	(* (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)))

simplify277.0ms

Algorithm

egg-herbie

Counts

1480 → 1480

Iterations

Useful iterations: 2 (86.0ms)

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

prune805.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
0.6b	(/ (cos k) (/ (/ (sin k) l) l))
2.2b	(/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k))
17.1b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k)))

rewrite636.0ms

Algorithm

rewrite-expression-head

Rules

3522×	`times-frac`
2743×	`add-exp-log`
1561×	`add-sqr-sqrt`
1506×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp`
1348×	`div-exp`
974×	`pow-exp`
509×	`pow-to-exp`
406×	`associate-r`
186×	`rec-exp` `1-exp`
140×	`associate-/l*`
112×	`div-inv`
56×	`add-cbrt-cube`
47×	`associate-/r*`
29×	`cbrt-undiv`
15×	`unswap-sqr`
12×	`unpow-prod-down`
11×	`associate-l`
8×	`associate-/r/` `cbrt-unprod`
6×	`sqr-pow`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`pow-flip` `associate-r/` `-commutative` `associate-/l/` `inv-pow`

Counts

4 → 1799

Calls

4 calls:

47.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
21.0ms	(/ (cos k) (/ (/ (sin k) l) l))
57.0ms	(/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k))
298.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k)))

series1.1s

Counts

4 → 12

Calls

4 calls:

318.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
67.0ms	(/ (cos k) (/ (/ (sin k) l) l))
79.0ms	(/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k))
587.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k)))

simplify308.0ms

Algorithm

egg-herbie

Counts

1811 → 1811

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5001	33648

prune7.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.7b

regimes263.0ms

Accuracy

0% (3.5b remaining)

Error of 11.1b against oracle of 7.5b and baseline of 11.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	18
1	29	18

end0.0ms

sample14.5s

Algorithm

intervals

Results

4.1s	968×	body	5120	valid
4.0s	2164×	body	2560	valid
3.6s	4153×	body	1280	valid
1.3s	2414×	body	640	valid
391.0ms	1039×	body	320	valid
257.0ms	2018×	body	80	valid
119.0ms	439×	body	160	valid