Details

sample296.0ms

Algorithm

intervals

Results

13.0ms	52×	body	1280	valid
6.0ms	145×	body	80	valid
4.0ms	27×	body	640	valid
2.0ms	20×	body	320	valid
1.0ms	12×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	22	9
2	29	9
3	37	9
4	43	9
5	45	9
6	45	9

prune3.0ms

Filtered

1 candidates to 0 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: 0.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `prod-diff` `associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 119

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series223.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- 1.0 (* (tan x) (tan x)))
99.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(* (tan x) (tan x))
57.0ms	(* (tan x) (tan x))

simplify51.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	917
2	5001	882

prune301.0ms

Filtered

131 candidates to 91 candidates (69.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	122	9	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	9	132

Merged error: 0.0b

Counts

132 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
0.1b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(* (tan x) (sin x))
0.2b	(* (tan x) (tan x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
13×	`pow1`
6×	`tan-quot` `associate-r` `associate-l` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`cbrt-undiv` `swap-sqr` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `*-commutative` `div-inv` `unswap-sqr`
1×	`pow2` `frac-times` `flip3--` `flip3-+` `pow-plus` `div-sub` `associate-*r/` `pow-sqr` `pow-prod-up` `flip--` `flip-+`

Counts

4 → 117

Calls

4 calls:

10.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(/ (* (tan x) (sin x)) (cos x))
5.0ms	(* (tan x) (sin x))
5.0ms	(* (tan x) (tan x))

series258.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
63.0ms	(/ (* (tan x) (sin x)) (cos x))
44.0ms	(* (tan x) (sin x))
37.0ms	(* (tan x) (tan x))

simplify63.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	455	1207
1	1904	1097
2	5001	1088

prune365.0ms

Filtered

129 candidates to 92 candidates (71.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	129	9	138

Merged error: 0.0b

Counts

138 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1.0 1) (fma (tan x) (tan x) 1.0))
0.2b	(* (/ (tan x) (fma (tan x) (tan x) 1.0)) (/ (sin x) (cos x)))
0.2b	(/ (tan x) (fma (tan x) (tan x) 1.0))
0.3b	(- (/ (/ 1.0 1) (fma (tan x) (tan x) 1.0)) (* (/ (tan x) (fma (tan x) (tan x) 1.0)) (/ (sin x) (cos x))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

238×	`times-frac`
150×	`add-sqr-sqrt`
138×	`add-cube-cbrt` `*-un-lft-identity`
43×	`fma-neg` `prod-diff`
25×	`add-exp-log`
23×	`add-cbrt-cube`
16×	`div-inv` `associate-/l*`
13×	`associate-r` `associate-l`
10×	`div-exp`
8×	`cbrt-undiv`
6×	`pow1` `associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`associate-*l/` `frac-sub`
2×	`frac-times` `frac-2neg` `associate-*r/` `clear-num` `associate-/l/`
1×	`tan-quot` `sub-neg` `flip3--` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `flip--` `sub-div`

Counts

4 → 259

Calls

4 calls:

6.0ms	(/ (/ 1.0 1) (fma (tan x) (tan x) 1.0))
10.0ms	(* (/ (tan x) (fma (tan x) (tan x) 1.0)) (/ (sin x) (cos x)))
4.0ms	(/ (tan x) (fma (tan x) (tan x) 1.0))
18.0ms	(- (/ (/ 1.0 1) (fma (tan x) (tan x) 1.0)) (* (/ (tan x) (fma (tan x) (tan x) 1.0)) (/ (sin x) (cos x))))

series513.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (/ 1.0 1) (fma (tan x) (tan x) 1.0))
142.0ms	(* (/ (tan x) (fma (tan x) (tan x) 1.0)) (/ (sin x) (cos x)))
90.0ms	(/ (tan x) (fma (tan x) (tan x) 1.0))
210.0ms	(- (/ (/ 1.0 1) (fma (tan x) (tan x) 1.0)) (* (/ (tan x) (fma (tan x) (tan x) 1.0)) (/ (sin x) (cos x))))

simplify142.0ms

Algorithm

egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	998	4547
1	4349	4028
2	5002	4013

prune847.0ms

Filtered

271 candidates to 201 candidates (74.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	268	3	271
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	272	8	280

Merged error: 0.0b

Counts

280 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1.0 1) (fma (tan x) (tan x) 1.0))
0.2b	(* (/ 1 (/ (fma (tan x) (tan x) 1.0) (tan x))) (/ (sin x) (cos x)))
0.2b	(/ 1 (/ (fma (tan x) (tan x) 1.0) (tan x)))
0.3b	(- (/ (/ 1.0 1) (fma (tan x) (tan x) 1.0)) (* (/ 1 (/ (fma (tan x) (tan x) 1.0) (tan x))) (/ (sin x) (cos x))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

380×	`times-frac`
235×	`add-sqr-sqrt`
206×	`*-un-lft-identity`
202×	`add-cube-cbrt`
67×	`add-exp-log`
47×	`associate-l`
43×	`fma-neg` `prod-diff`
35×	`add-cbrt-cube`
33×	`div-exp`
23×	`div-inv`
17×	`associate-/r*`
16×	`associate-/l*`
15×	`cbrt-undiv`
14×	`prod-exp`
13×	`associate-r`
10×	`unswap-sqr`
9×	`associate-/r/`
7×	`tan-quot` `pow1` `1-exp`
6×	`rec-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`frac-sub`
2×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `pow-prod-down` `*-commutative` `flip--` `associate-/l/` `inv-pow`

Counts

4 → 362

Calls

4 calls:

6.0ms	(/ (/ 1.0 1) (fma (tan x) (tan x) 1.0))
21.0ms	(* (/ 1 (/ (fma (tan x) (tan x) 1.0) (tan x))) (/ (sin x) (cos x)))
7.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (tan x)))
19.0ms	(- (/ (/ 1.0 1) (fma (tan x) (tan x) 1.0)) (* (/ 1 (/ (fma (tan x) (tan x) 1.0) (tan x))) (/ (sin x) (cos x))))

series509.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (/ 1.0 1) (fma (tan x) (tan x) 1.0))
140.0ms	(* (/ 1 (/ (fma (tan x) (tan x) 1.0) (tan x))) (/ (sin x) (cos x)))
91.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (tan x)))
207.0ms	(- (/ (/ 1.0 1) (fma (tan x) (tan x) 1.0)) (* (/ 1 (/ (fma (tan x) (tan x) 1.0) (tan x))) (/ (sin x) (cos x))))

simplify81.0ms

Algorithm

egg-herbie

Counts

374 → 374

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1438	6173
1	5002	5397

prune1.1s

Filtered

374 candidates to 263 candidates (70.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	373	1	374
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	374	8	382

Merged error: 0.0b

Counts

382 → 8

regimes135.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	16
1	17	16

end0.0ms

sample942.0ms

Algorithm

intervals

Results

378.0ms	1534×	body	1280	valid
202.0ms	1236×	body	640	valid
150.0ms	4308×	body	80	valid
72.0ms	613×	body	320	valid
25.0ms	309×	body	160	valid