Details

sample0.0hr

Algorithm

intervals

Results

0.0hr	30×	body	5120	valid
0.0hr	65×	body	2560	valid
0.0hr	132×	body	1280	valid
0.0hr	76×	body	640	valid
0.0hr	42×	body	320	valid
0.0hr	65×	body	80	valid
0.0hr	13×	body	160	valid

simplify0.0hr

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0hr)

Iter	Nodes	Cost
0	44	13
1	147	13
2	857	12
3	5002	11

prune0.0hr

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: 41.4b

Counts

2 → 2

localize0.0hr

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.8b	(* (pow t 3.0) (tan k))
19.7b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.2b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite0.0hr

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:

0.0hr	(pow (/ k t) 2.0)
0.0hr	(* (pow t 3.0) (tan k))
0.0hr	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
0.0hr	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(pow (/ k t) 2.0)
0.0hr	(* (pow t 3.0) (tan k))
0.0hr	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
0.0hr	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify0.0hr

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (0.0hr)

Iter	Nodes	Cost
0	1123	2068
1	5002	1738

prune0.0hr

Filtered

191 candidates to 93 candidates (51.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	180	11	191
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	181	12	193

Merged error: 28.4b

Counts

193 → 12

localize0.0hr

Local error

Found 4 expressions with local error:

0.8b	(* (pow t 3.0) (tan k))
13.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
19.7b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))
20.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

1610×	`add-exp-log`
1168×	`prod-exp`
346×	`div-exp`
341×	`pow-exp`
205×	`pow-to-exp`
95×	`add-cbrt-cube`
55×	`cbrt-unprod`
41×	`associate-l`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
15×	`cbrt-undiv`
9×	`associate-*r/`
5×	`associate-r`
4×	`tan-quot` `pow1` `add-log-exp` `sqr-pow`
3×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l*`

Counts

4 → 408

Calls

4 calls:

0.0hr	(* (pow t 3.0) (tan k))
0.0hr	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
0.0hr	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))
0.0hr	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(* (pow t 3.0) (tan k))
0.0hr	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
0.0hr	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))
0.0hr	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify0.0hr

Algorithm

egg-herbie

Counts

420 → 420

Iterations

Useful iterations: 1 (0.0hr)

Iter	Nodes	Cost
0	1771	6487
1	5002	5612

prune0.0hr

Filtered

420 candidates to 110 candidates (73.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	414	6	420
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	417	15	432

Merged error: 28.4b

Counts

432 → 15

localize0.0hr

Local error

Found 4 expressions with local error:

1.9b	(/ (* l l) (sin k))
13.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
18.7b	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))
20.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

1610×	`add-exp-log`
1029×	`prod-exp`
485×	`div-exp`
340×	`pow-exp`
204×	`pow-to-exp`
98×	`add-cbrt-cube`
48×	`cbrt-unprod`
42×	`associate-l`
30×	`add-sqr-sqrt`
28×	`times-frac`
26×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
24×	`cbrt-undiv`
9×	`associate-r/` `associate-r*`
6×	`pow1`
5×	`div-inv`
4×	`add-log-exp`
3×	`tan-quot` `associate-/r` `-commutative`
2×	`unswap-sqr` `sqr-pow`
1×	`frac-times` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `associate-/r/` `associate-/l`

Counts

4 → 418

Calls

4 calls:

0.0hr	(/ (* l l) (sin k))
0.0hr	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
0.0hr	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))
0.0hr	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(/ (* l l) (sin k))
0.0hr	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
0.0hr	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))
0.0hr	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify0.0hr

Algorithm

egg-herbie

Counts

430 → 430

Iterations

Useful iterations: 1 (0.0hr)

Iter	Nodes	Cost
0	1730	6648
1	5001	5458

prune0.0hr

Filtered

430 candidates to 107 candidates (75.1%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	420	10	430
Fresh	7	7	14
Picked	0	1	1
Done	0	0	0
Total	427	18	445

Merged error: 23.9b

Counts

445 → 18

localize0.0hr

Local error

Found 4 expressions with local error:

1.9b	(/ (* l l) (sin k))
14.5b	(* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
15.2b	(* (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k))))
20.5b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite0.0hr

Algorithm

rewrite-expression-head

Rules

2259×	`add-exp-log`
1240×	`prod-exp`
875×	`div-exp`
338×	`pow-exp`
217×	`add-cbrt-cube`
207×	`pow-to-exp`
178×	`times-frac`
134×	`associate-l`
106×	`add-sqr-sqrt`
105×	`cbrt-unprod`
102×	`add-cube-cbrt` `*-un-lft-identity`
91×	`unpow-prod-down`
66×	`cbrt-undiv`
54×	`sqrt-prod`
11×	`pow1` `div-inv`
10×	`associate-*r/`
9×	`associate-r`
7×	`sqr-pow`
6×	`frac-times`
4×	`pow-prod-down` `associate-*l/` `add-log-exp`
3×	`associate-/r` `-commutative`
2×	`tan-quot` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r/` `associate-/l*`

Counts

4 → 589

Calls

4 calls:

0.0hr	(/ (* l l) (sin k))
0.0hr	(* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
0.0hr	(* (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k))))
0.0hr	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(/ (* l l) (sin k))
0.0hr	(* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
0.0hr	(* (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k))))
0.0hr	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify0.0hr

Algorithm

egg-herbie

Counts

601 → 601

Iterations

Useful iterations: 1 (0.0hr)

Iter	Nodes	Cost
0	2394	11773
1	5001	10742

prune0.0hr

Filtered

601 candidates to 194 candidates (67.7%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	594	7	601
Fresh	4	12	16
Picked	1	0	1
Done	0	1	1
Total	599	20	619

Merged error: 22.0b

Counts

619 → 20

regimes0.0hr

Accuracy

42.1% (5.9b remaining)

Error of 28.4b against oracle of 22.5b and baseline of 32.7b

bsearch0.0hr

Steps

Iters	Range	Point
10	2.146598932358039e-112	9.794742891101381e-98	1.60231479643995e-108
10	-1.2128248765666837e-307	1.3459246724270578e-298	-7.30602271957343e-309
10	-3.722248476023086e-102	-4.3018125905191136e-113	-2.7119492113822656e-108

Iters

Range

Point

2.146598932358039e-112

9.794742891101381e-98

1.60231479643995e-108

-1.2128248765666837e-307

1.3459246724270578e-298

-7.30602271957343e-309

-3.722248476023086e-102

-4.3018125905191136e-113

-2.7119492113822656e-108

simplify0.0hr

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0hr)

Iter	Nodes	Cost
0	85	80
1	91	80
2	91	80

end0.0hr

sample0.0hr

Algorithm

intervals

Results

0.0hr	2254×	body	2560	valid
0.0hr	990×	body	5120	valid
0.0hr	4099×	body	1280	valid
0.0hr	2480×	body	640	valid
0.0hr	994×	body	320	valid
0.0hr	2028×	body	80	valid
0.0hr	458×	body	160	valid

Details

sample0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

regimes0.0hr

bsearch0.0hr

simplify0.0hr

end0.0hr

sample0.0hr

Profiling