Details

sample431.0ms

Algorithm

intervals

Results

169.0ms	82×	body	2560	valid
91.0ms	30×	body	5120	valid
88.0ms	123×	body	1280	valid
38.0ms	83×	body	640	valid
8.0ms	73×	body	80	valid
6.0ms	18×	body	320	valid
4.0ms	19×	body	160	valid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (27.0ms)

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: 39.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.8b	(* (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)))
28.6b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite55.0ms

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:

5.0ms	(pow (/ k t) 2.0)
6.0ms	(* (pow t 3.0) (tan k))
19.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
12.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series907.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (/ k t) 2.0)
243.0ms	(* (pow t 3.0) (tan k))
362.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
236.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify42.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	991	2005
1	5001	1672

prune494.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
6.6b	(* (pow k 2.0) (pow t 1.0))
7.1b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.4b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

1597×	`add-exp-log`
1095×	`prod-exp`
882×	`pow-exp`
668×	`div-exp`
492×	`pow-to-exp`
130×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
32×	`unpow-prod-down`
20×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
19×	`times-frac` `associate-r`
18×	`associate-l`
14×	`sqr-pow`
12×	`unswap-sqr`
8×	`associate-/r*`
6×	`cbrt-unprod`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp`
3×	`pow-unpow` `div-inv`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-r/` `clear-num` `associate-/l`

Counts

4 → 575

Calls

4 calls:

3.0ms	(pow (sin k) 2)
7.0ms	(* (pow k 2.0) (pow t 1.0))
8.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
27.0ms	(* (pow (/ 1 (* (pow k 2.0) (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)
335.0ms	(* (pow k 2.0) (pow t 1.0))
88.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
648.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify151.0ms

Algorithm

egg-herbie

Counts

587 → 587

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	1304	6971
1	3873	6815
2	5003	6814

prune642.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.2b	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
6.6b	(* (pow k 2.0) (pow t 1.0))
16.4b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

1169×	`add-exp-log`
660×	`prod-exp`
466×	`div-exp`
367×	`pow-exp`
157×	`pow-to-exp`
90×	`times-frac`
88×	`add-sqr-sqrt`
80×	`rec-exp` `1-exp`
61×	`add-cbrt-cube`
55×	`add-cube-cbrt` `*-un-lft-identity`
52×	`associate-r`
31×	`associate-l`
21×	`cbrt-unprod`
20×	`cbrt-undiv`
19×	`unpow-prod-down`
15×	`unswap-sqr`
9×	`sqr-pow`
7×	`pow1` `div-inv`
5×	`associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`frac-times` `associate-*l/`
1×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `associate-/r/` `inv-pow`

Counts

4 → 448

Calls

4 calls:

7.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
23.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
8.0ms	(* (pow k 2.0) (pow t 1.0))
26.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

series1.4s

Counts

4 → 12

Calls

4 calls:

333.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
89.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
338.0ms	(* (pow k 2.0) (pow t 1.0))
650.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

simplify91.0ms

Algorithm

egg-herbie

Counts

460 → 460

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1868	5492
1	5001	5177

prune813.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.4b	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) l)) (/ (sin k) l))
6.5b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) l))
6.6b	(* (pow k 2.0) (pow t 1.0))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

1420×	`add-exp-log`
774×	`prod-exp`
599×	`div-exp`
465×	`pow-exp`
195×	`pow-to-exp`
100×	`rec-exp` `1-exp`
52×	`add-cbrt-cube`
39×	`add-sqr-sqrt`
37×	`times-frac`
27×	`add-cube-cbrt` `*-un-lft-identity`
19×	`unpow-prod-down`
18×	`associate-l`
17×	`cbrt-undiv` `cbrt-unprod`
14×	`associate-/r*`
9×	`unswap-sqr` `sqr-pow`
8×	`associate-r`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `associate-r/` `associate-l/` `clear-num` `*-commutative`
1×	`pow-flip` `associate-/r/` `associate-/l/` `inv-pow`

Counts

4 → 470

Calls

4 calls:

7.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
27.0ms	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) l)) (/ (sin k) l))
15.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) l))
7.0ms	(* (pow k 2.0) (pow t 1.0))

series2.0s

Counts

4 → 12

Calls

4 calls:

333.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
644.0ms	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) l)) (/ (sin k) l))
468.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) l))
533.0ms	(* (pow k 2.0) (pow t 1.0))

simplify89.0ms

Algorithm

egg-herbie

Counts

482 → 482

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1747	5905
1	5001	5586

prune570.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.2b

regimes516.0ms

Accuracy

54.3% (2.1b remaining)

Error of 8.9b against oracle of 6.8b and baseline of 11.4b

bsearch2.1s

Steps

Iters	Range		Point
7	4.235658600533781e+130	1.942270646392544e+132	1.1512157854309419e+132
10	2.5314598921169833e-163	7.07945799005041e-151	7.600193379940175e-155
9	-1.436137459727321e-134	-1.3993923063577276e-140	-2.705728249136002e-140
7	-4.617021828322126e+139	-2.474160229639802e+138	-4.5772359455565565e+139

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 2 (1.0ms)

Iter	Nodes	Cost
0	57	88
1	60	88
2	66	35
3	69	35
4	75	35
5	86	35
6	93	35
7	94	35
8	94	35

end0.0ms

sample13.5s

Algorithm

intervals

Results

4.5s	2279×	body	2560	valid
3.9s	963×	body	5120	valid
2.9s	4045×	body	1280	valid
1.2s	2516×	body	640	valid
312.0ms	929×	body	320	valid
233.0ms	2109×	body	80	valid
101.0ms	457×	body	160	valid