Details

sample462.0ms

Algorithm

intervals

Results

131.0ms	53×	body	2560	valid
59.0ms	94×	body	1280	valid
14.0ms	58×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	14×	body	160	valid
1.0ms	12×	body	80	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.5b	(- x (tan x))
1.6b	(- x (sin x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 110

Calls

3 calls:

9.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series181.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (- x (sin x)) (- x (tan x)))
60.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify56.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	472	1059
1	1737	854
2	5001	854

prune240.0ms

Filtered

119 candidates to 79 candidates (66.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
0.2b	(/ (sin x) (cos x))
1.5b	(- x (/ (sin x) (cos x)))
1.6b	(- x (sin x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
73×	`times-frac`
67×	`add-cube-cbrt`
48×	`prod-diff`
22×	`difference-of-squares`
15×	`distribute-lft-out--`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
6×	`fma-neg`
5×	`div-inv`
4×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `associate-/r/` `associate-/l/`
1×	`quot-tan` `div-sub`

Counts

4 → 177

Calls

4 calls:

12.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
4.0ms	(/ (sin x) (cos x))
8.0ms	(- x (/ (sin x) (cos x)))
4.0ms	(- x (sin x))

series183.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
21.0ms	(/ (sin x) (cos x))
50.0ms	(- x (/ (sin x) (cos x)))
35.0ms	(- x (sin x))

simplify93.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	759	2708
1	2962	1984
2	5001	1876

prune336.0ms

Filtered

189 candidates to 111 candidates (58.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos x))
0.3b	(cbrt (cos x))
1.5b	(- x (/ (/ (sin x) (* (cbrt (cos x)) (cbrt (cos x)))) (cbrt (cos x))))
1.6b	(- x (sin x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
157×	`add-sqr-sqrt`
147×	`prod-diff`
145×	`*-un-lft-identity`
141×	`add-cube-cbrt`
71×	`cbrt-prod`
21×	`div-inv`
8×	`add-log-exp`
6×	`fma-neg` `difference-of-squares`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 215

Calls

4 calls:

1.0ms	(cbrt (cos x))
1.0ms	(cbrt (cos x))
21.0ms	(- x (/ (/ (sin x) (* (cbrt (cos x)) (cbrt (cos x)))) (cbrt (cos x))))
4.0ms	(- x (sin x))

series301.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (cos x))
104.0ms	(cbrt (cos x))
52.0ms	(- x (/ (/ (sin x) (* (cbrt (cos x)) (cbrt (cos x)))) (cbrt (cos x))))
37.0ms	(- x (sin x))

simplify157.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1288	10081
1	4966	6337
2	5001	6337

prune419.0ms

Filtered

227 candidates to 104 candidates (45.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

1.5b	(- x (/ (sin x) (cos x)))
1.6b	(- x (sin x))
1.6b	(- x (sin x))
1.6b	(- x (sin x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt`
68×	`*-un-lft-identity`
66×	`prod-diff`
60×	`add-cube-cbrt`
28×	`times-frac`
12×	`fma-neg` `add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--`
3×	`div-inv`

Counts

4 → 143

Calls

4 calls:

8.0ms	(- x (/ (sin x) (cos x)))
4.0ms	(- x (sin x))
5.0ms	(- x (sin x))
4.0ms	(- x (sin x))

series157.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- x (/ (sin x) (cos x)))
38.0ms	(- x (sin x))
31.0ms	(- x (sin x))
37.0ms	(- x (sin x))

simplify62.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	491	2159
1	1658	1289
2	5002	1286

prune303.0ms

Filtered

155 candidates to 81 candidates (52.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch76.0ms

Steps

Iters	Range		Point
7	0.007472435306926121	0.16151685480387348	0.03498891734086663
9	-0.10280128843953673	-1.4570494276460042e-08	-0.03348886015006478

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	19
1	29	19

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.8s	1555×	body	2560	valid
1.6s	2787×	body	1280	valid
477.0ms	1933×	body	640	valid
146.0ms	917×	body	320	valid
50.0ms	444×	body	160	valid
25.0ms	364×	body	80	valid