Details

sample463.0ms

Algorithm

intervals

Results

115.0ms	56×	body	2560	valid
62.0ms	92×	body	1280	valid
18.0ms	55×	body	640	valid
6.0ms	27×	body	320	valid
2.0ms	12×	body	160	valid
1.0ms	14×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.1b	(- x (sin x))
1.1b	(- x (tan x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 80

Calls

3 calls:

11.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (sin x))
5.0ms	(- x (tan x))

series176.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
37.0ms	(- x (sin x))
62.0ms	(- x (tan x))

simplify150.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685

prune202.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (- x (tan x)) (- x (sin x))))
0.0b	(/ (- x (tan x)) (- x (sin x)))
1.1b	(- x (sin x))
1.1b	(- x (tan x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
200×	`add-sqr-sqrt` `*-un-lft-identity`
92×	`add-cube-cbrt`
54×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3--` `div-exp` `flip--` `associate-/l*` `add-log-exp`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv`
2×	`sub-neg` `rec-exp` `frac-2neg` `diff-log` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `inv-pow`

Counts

4 → 228

Calls

4 calls:

14.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
10.0ms	(/ (- x (tan x)) (- x (sin x)))
3.0ms	(- x (sin x))
2.0ms	(- x (tan x))

series235.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
75.0ms	(/ (- x (tan x)) (- x (sin x)))
30.0ms	(- x (sin x))
55.0ms	(- x (tan x))

simplify84.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	744	2647
1	3445	2441
2	5001	2278

prune355.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x (sin x)))
0.0b	(/ (/ 1 (- x (tan x))) (/ 1 (- x (sin x))))
1.1b	(- x (sin x))
1.1b	(- x (tan x))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

1116×	`times-frac`
686×	`add-sqr-sqrt` `*-un-lft-identity`
410×	`add-cube-cbrt`
138×	`distribute-lft-out--` `difference-of-squares`
91×	`associate-/r/`
48×	`add-exp-log`
47×	`flip3--` `flip--`
46×	`div-inv`
34×	`div-exp`
26×	`associate-/r*`
24×	`associate-/l*`
18×	`add-cbrt-cube`
9×	`cbrt-undiv` `rec-exp` `1-exp`
8×	`add-log-exp`
5×	`pow1`
2×	`sub-neg` `frac-2neg` `diff-log` `clear-num`
1×	`pow-flip` `associate-/l/` `inv-pow`

Counts

4 → 584

Calls

4 calls:

6.0ms	(/ 1 (- x (sin x)))
29.0ms	(/ (/ 1 (- x (tan x))) (/ 1 (- x (sin x))))
3.0ms	(- x (sin x))
2.0ms	(- x (tan x))

series197.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ 1 (- x (sin x)))
79.0ms	(/ (/ 1 (- x (tan x))) (/ 1 (- x (sin x))))
37.0ms	(- x (sin x))
50.0ms	(- x (tan x))

simplify120.0ms

Algorithm

egg-herbie

Counts

596 → 596

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	2281	9456
1	5003	8545

prune806.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 9/40 (pow x 2))
0.1b	(* 27/2800 (pow x 4))
17.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

5.0ms	(* 9/40 (pow x 2))
5.0ms	(* 27/2800 (pow x 4))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series116.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(* 9/40 (pow x 2))
37.0ms	(* 27/2800 (pow x 4))
50.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify42.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	273	364
1	1191	319
2	5002	315

prune137.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes29.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.6b

bsearch82.0ms

Steps

Iters	Range		Point
9	0.006665254470786589	7065.8830381017015	0.027484538016213013
9	-14674.600957416102	-0.00012459925560949148	-0.02707742369240808

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	19
1	33	19

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.4s	1548×	body	2560	valid
1.9s	2797×	body	1280	valid
642.0ms	1881×	body	640	valid
236.0ms	929×	body	320	valid
75.0ms	473×	body	160	valid
33.0ms	372×	body	80	valid