Details

sample288.0ms

Algorithm

intervals

Results

12.0ms	46×	body	1280	valid
8.0ms	47×	body	640	valid
6.0ms	135×	body	80	valid
2.0ms	14×	body	320	valid
1.0ms	14×	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)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 213

Calls

4 calls:

23.0ms	(- 1.0 (* (tan x) (tan x)))
20.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series218.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- 1.0 (* (tan x) (tan x)))
104.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(* (tan x) (tan x))
46.0ms	(* (tan x) (tan x))

simplify76.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	556	2609
1	1850	2160
2	5001	2010

prune257.0ms

Filtered

225 candidates to 97 candidates (43.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	211	14	225
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	212	14	226

Merged error: 0.0b

Counts

226 → 14

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

84×	`*-un-lft-identity`
59×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
32×	`times-frac`
27×	`associate-r` `associate-l`
24×	`frac-times`
21×	`pow1` `add-exp-log`
20×	`associate-/r*` `distribute-lft-out`
15×	`add-cbrt-cube`
13×	`associate-r/` `associate-/l`
12×	`flip3--` `flip--`
8×	`tan-quot`
7×	`swap-sqr`
6×	`prod-exp` `unswap-sqr`
5×	`clear-num` `difference-of-squares`
4×	`expm1-log1p-u` `frac-2neg` `div-exp` `associate-l/` `associate-/r/` `-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `un-div-inv`
2×	`cbrt-undiv` `pow2` `rec-exp` `flip3-+` `pow-plus` `1-exp` `pow-sqr` `pow-prod-up` `flip-+` `div-inv` `distribute-lft-out--`
1×	`pow-flip` `inv-pow`

Counts

4 → 192

Calls

4 calls:

9.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
24.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series213.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
93.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
32.0ms	(* (tan x) (tan x))
35.0ms	(* (tan x) (tan x))

simplify75.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	490	1835
1	2380	1602
2	5001	1511

prune280.0ms

Filtered

204 candidates to 108 candidates (52.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	199	5	204
Fresh	6	7	13
Picked	0	1	1
Done	0	0	0
Total	205	13	218

Merged error: 0.0b

Counts

218 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin x) 2)
0.2b	(pow (sin x) 2)
0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

2.0ms	(pow (sin x) 2)
2.0ms	(pow (sin x) 2)
2.0ms	(pow (cos x) 2)
2.0ms	(pow (cos x) 2)

series76.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin x) 2)
19.0ms	(pow (sin x) 2)
20.0ms	(pow (cos x) 2)
17.0ms	(pow (cos x) 2)

simplify60.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	146	308
1	487	260
2	1640	260
3	5002	256

prune206.0ms

Filtered

92 candidates to 56 candidates (60.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	92	13	105

Merged error: 0.0b

Counts

105 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (fma 1.0 1.0 (* (- (pow (tan x) 3)) (tan x))) (fma (tan x) (tan x) 1.0)) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (- (pow (tan x) 3)) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(pow (tan x) 3)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

130×	`*-un-lft-identity`
119×	`times-frac`
78×	`add-sqr-sqrt`
74×	`add-cube-cbrt`
37×	`associate-l`
28×	`distribute-lft-out`
16×	`associate-/l*`
14×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`unpow-prod-down` `associate-/l/`
8×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-/r*`
7×	`div-inv`
6×	`associate-r`
5×	`tan-quot`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `unpow3` `swap-sqr` `div-exp` `sqr-pow`
2×	`frac-2neg` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `associate-/r/` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-lft-neg-out` `pow2` `frac-times` `pow-to-exp` `neg-mul-1` `pow-pow` `flip3-+` `pow-plus` `associate-*l/` `pow-exp` `pow-sqr` `pow-prod-up` `flip-+` `rem-cube-cbrt`

Counts

4 → 200

Calls

4 calls:

12.0ms	(/ (/ (fma 1.0 1.0 (* (- (pow (tan x) 3)) (tan x))) (fma (tan x) (tan x) 1.0)) (+ 1.0 (* (tan x) (tan x))))
10.0ms	(* (- (pow (tan x) 3)) (tan x))
5.0ms	(* (tan x) (tan x))
2.0ms	(pow (tan x) 3)

series338.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ (/ (fma 1.0 1.0 (* (- (pow (tan x) 3)) (tan x))) (fma (tan x) (tan x) 1.0)) (+ 1.0 (* (tan x) (tan x))))
66.0ms	(* (- (pow (tan x) 3)) (tan x))
35.0ms	(* (tan x) (tan x))
46.0ms	(pow (tan x) 3)

simplify115.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	740	3204
1	3788	2928
2	5001	2902

prune430.0ms

Filtered

212 candidates to 134 candidates (63.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	209	3	212
Fresh	2	8	10
Picked	1	0	1
Done	0	2	2
Total	212	13	225

Merged error: 0b

Counts

225 → 13

regimes135.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	10
1	13	10

end0.0ms

sample930.0ms

Algorithm

intervals

Results

370.0ms	1478×	body	1280	valid
198.0ms	1180×	body	640	valid
158.0ms	4439×	body	80	valid
70.0ms	608×	body	320	valid
23.0ms	295×	body	160	valid