Details

sample451.0ms

Algorithm

intervals

Results

160.0ms	78×	body	2560	valid
125.0ms	27×	body	5120	valid
78.0ms	111×	body	1280	valid
45.0ms	88×	body	640	valid
12.0ms	26×	body	320	valid
8.0ms	74×	body	80	valid
3.0ms	12×	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

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 40.6b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.6b	(* (pow t 3.0) (tan k))
20.7b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
30.8b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite432.0ms

Algorithm

rewrite-expression-head

Rules

5057×	`add-sqr-sqrt`
2843×	`associate-l`
2812×	`unswap-sqr`
2783×	`times-frac`
2196×	`associate-r`
1235×	`unpow-prod-down`
1036×	`add-cube-cbrt` `*-un-lft-identity`
565×	`sqr-pow`
337×	`add-exp-log`
336×	`*-commutative`
328×	`swap-sqr`
220×	`prod-exp`
81×	`associate-/r*`
71×	`div-exp`
65×	`add-cbrt-cube`
51×	`pow-exp`
34×	`pow-to-exp` `cbrt-unprod`
32×	`div-inv`
28×	`associate-/l*`
12×	`pow1` `cbrt-undiv`
5×	`associate-*r/`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`tan-quot` `pow-unpow`
1×	`pow-pow` `frac-2neg` `associate-*l/` `clear-num` `associate-/r/`

Counts

4 → 2597

Calls

4 calls:

4.0ms	(pow (/ k t) 2.0)
6.0ms	(* (pow t 3.0) (tan k))
97.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
19.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series927.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (/ k t) 2.0)
239.0ms	(* (pow t 3.0) (tan k))
370.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
250.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify550.0ms

Algorithm

egg-herbie

Counts

2609 → 2609

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5002	53914

prune7.9s

Filtered

2609 candidates to 1671 candidates (36.0%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	2587	22	2609
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	2589	22	2611

Merged error: 14.0b

Counts

2611 → 22

localize22.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.9b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.2b	(* (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)))

rewrite452.0ms

Algorithm

rewrite-expression-head

Rules

2158×	`add-sqr-sqrt`
1645×	`add-exp-log`
1373×	`unswap-sqr`
1368×	`times-frac`
1282×	`unpow-prod-down`
1122×	`prod-exp`
899×	`pow-exp`
688×	`div-exp`
623×	`sqr-pow`
509×	`pow-to-exp`
471×	`*-un-lft-identity`
364×	`associate-r`
285×	`unpow2`
259×	`add-cube-cbrt`
203×	`associate-l`
140×	`rec-exp` `1-exp`
45×	`associate-/l*`
44×	`associate-/r*`
31×	`associate-*r/`
27×	`*-commutative`
25×	`add-cbrt-cube`
11×	`pow1`
7×	`cbrt-unprod`
6×	`cbrt-undiv`
4×	`expm1-log1p-u` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `un-div-inv`
2×	`pow-flip`
1×	`inv-pow`

Counts

4 → 1636

Calls

4 calls:

15.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
19.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
9.0ms	(* (pow k 2.0) (pow t 1.0))
219.0ms	(* (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:

336.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
89.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
336.0ms	(* (pow k 2.0) (pow t 1.0))
655.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify352.0ms

Algorithm

egg-herbie

Counts

1648 → 1648

Iterations

Useful iterations: 1 (93.0ms)

Iter	Nodes	Cost
0	4829	29271
1	5002	26595

prune2.7s

Filtered

1648 candidates to 561 candidates (66.0%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	1633	15	1648
Fresh	12	9	21
Picked	1	0	1
Done	0	0	0
Total	1646	24	1670

Merged error: 5.9b

Counts

1670 → 24

localize26.0ms

Local error

Found 4 expressions with local error:

1.3b	(sqrt (pow (sin k) 2))
4.1b	(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (sqrt (pow (sin k) 2)))) (/ (pow l (/ 2 2)) (sqrt (pow (sin k) 2))))
6.2b	(* (pow k 2.0) (pow t 1.0))
6.6b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (sqrt (pow (sin k) 2))))

rewrite2.5s

Algorithm

rewrite-expression-head

Rules

22478×	`add-sqr-sqrt`
14360×	`unswap-sqr`
12419×	`times-frac`
10033×	`unpow-prod-down`
7040×	`sqrt-prod`
5619×	`sqr-pow`
2601×	`*-un-lft-identity`
2375×	`add-exp-log`
1676×	`unpow2`
1474×	`prod-exp`
930×	`div-exp`
877×	`associate-l`
841×	`pow-exp`
619×	`associate-*r/`
609×	`frac-times`
583×	`associate-/r*`
574×	`add-cube-cbrt`
537×	`associate-r`
533×	`associate-/l*`
391×	`pow-to-exp`
150×	`rec-exp` `1-exp`
77×	`clear-num`
71×	`un-div-inv`
55×	`*-commutative`
53×	`frac-2neg`
47×	`add-cbrt-cube`
29×	`associate-*l/`
21×	`cbrt-unprod`
15×	`pow1`
10×	`cbrt-undiv`
6×	`sqrt-pow1`
5×	`pow-prod-down` `div-inv`
4×	`expm1-log1p-u` `rem-sqrt-square` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
1×	`pow-pow` `pow1/2`

Counts

4 → 6407

Calls

4 calls:

3.0ms	(sqrt (pow (sin k) 2))
660.0ms	(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (sqrt (pow (sin k) 2)))) (/ (pow l (/ 2 2)) (sqrt (pow (sin k) 2))))
9.0ms	(* (pow k 2.0) (pow t 1.0))
183.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (sqrt (pow (sin k) 2))))

series1.5s

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (pow (sin k) 2))
674.0ms	(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (sqrt (pow (sin k) 2)))) (/ (pow l (/ 2 2)) (sqrt (pow (sin k) 2))))
342.0ms	(* (pow k 2.0) (pow t 1.0))
475.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (sqrt (pow (sin k) 2))))

simplify2.1s

Algorithm

egg-herbie

Counts

6419 → 6419

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5301	238299

prune27.9s

Filtered

6419 candidates to 4333 candidates (32.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	6407	12	6419
Fresh	14	9	23
Picked	1	0	1
Done	0	0	0
Total	6422	21	6443

Merged error: 1.9b

Counts

6443 → 21

localize36.0ms

Local error

Found 4 expressions with local error:

1.3b	(sqrt (pow (sin k) 2))
1.3b	(sqrt (pow (sin k) 2))
4.1b	(* (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (sqrt (pow (sin k) 2))))) (/ (pow l (/ 2 2)) (sqrt (pow (sin k) 2))))
6.1b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (sqrt (pow (sin k) 2))))

rewrite18.5s

Algorithm

rewrite-expression-head

Rules

228746×	`add-sqr-sqrt`
163283×	`unswap-sqr`
130493×	`times-frac`
121218×	`unpow-prod-down`
60728×	`sqr-pow`
56652×	`sqrt-prod`
30640×	`*-un-lft-identity`
28861×	`add-exp-log`
20041×	`prod-exp`
14079×	`unpow2`
13604×	`pow-exp`
12177×	`div-exp`
5594×	`pow-to-exp`
3219×	`associate-l`
2670×	`rec-exp` `1-exp`
1257×	`associate-*r/`
1016×	`associate-r`
609×	`frac-times`
589×	`add-cube-cbrt`
583×	`associate-/r*`
533×	`associate-/l*`
77×	`clear-num`
71×	`un-div-inv`
58×	`add-cbrt-cube`
55×	`*-commutative`
53×	`frac-2neg`
30×	`cbrt-unprod`
29×	`associate-*l/`
19×	`pow1`
12×	`sqrt-pow1`
11×	`cbrt-undiv`
8×	`rem-sqrt-square`
7×	`pow-prod-down`
6×	`pow-unpow` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-pow` `pow1/2`

Counts

4 → 45646

Calls

4 calls:

3.0ms	(sqrt (pow (sin k) 2))
3.0ms	(sqrt (pow (sin k) 2))
3.3s	(* (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (sqrt (pow (sin k) 2))))) (/ (pow l (/ 2 2)) (sqrt (pow (sin k) 2))))
184.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (sqrt (pow (sin k) 2))))

series1.2s

Counts

4 → 12

Calls

4 calls:

8.0ms	(sqrt (pow (sin k) 2))
8.0ms	(sqrt (pow (sin k) 2))
692.0ms	(* (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (sqrt (pow (sin k) 2))))) (/ (pow l (/ 2 2)) (sqrt (pow (sin k) 2))))
490.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (sqrt (pow (sin k) 2))))

simplify25.1s

Algorithm

egg-herbie

Counts

45658 → 45658

Iterations

Useful iterations: 0 (852.0ms)

Iter	Nodes	Cost
0	32272	2490285

prune4.2m

Filtered

45658 candidates to 28966 candidates (36.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	45649	9	45658
Fresh	12	8	20
Picked	1	0	1
Done	0	0	0
Total	45662	17	45679

Merged error: 1.7b

Counts

45679 → 17

regimes374.0ms

Accuracy

12.9% (4.2b remaining)

Error of 6.0b against oracle of 1.8b and baseline of 6.7b

bsearch411.0ms

Steps

Iters	Range		Point
7	1.1331523325576258e+113	2.8373063757459126e+114	1.8244525873006635e+113
8	3.8817349418585827e-94	1.780122232043068e-91	1.8015154766176852e-93

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	98
1	84	98
2	84	98

end0.0ms

sample13.5s

Algorithm

intervals

Results

4.5s	2275×	body	2560	valid
3.8s	914×	body	5120	valid
2.9s	4076×	body	1280	valid
1.2s	2554×	body	640	valid
334.0ms	972×	body	320	valid
237.0ms	2113×	body	80	valid
100.0ms	410×	body	160	valid