Details

sample444.0ms

Algorithm

intervals

Results

115.0ms	59×	body	2560	valid
41.0ms	68×	body	1280	valid
20.0ms	61×	body	640	valid
11.0ms	42×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	10×	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: 32.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.3b	(- x (sin x))
2.3b	(- x (tan x))

rewrite33.0ms

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))

series177.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (- x (sin x)) (- x (tan x)))
37.0ms	(- x (sin x))
62.0ms	(- x (tan x))

simplify149.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

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

prune199.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
14.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite21.0ms

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	(* 27/2800 (pow x 4))
6.0ms	(* 9/40 (pow x 2))
8.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series108.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* 27/2800 (pow x 4))
28.0ms	(* 9/40 (pow x 2))
45.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify42.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	318
2	5001	315

prune142.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2)
0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
14.6b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
15×	`associate-r`
14×	`add-exp-log`
12×	`*-un-lft-identity`
11×	`add-log-exp`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `diff-log` `sqr-pow`
3×	`sub-neg`
2×	`pow-to-exp` `flip3--` `pow-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `unpow2`
1×	`associate--l-` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 82

Calls

4 calls:

19.0ms	(- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2)
5.0ms	(* 27/2800 (pow x 4))
5.0ms	(* 9/40 (pow x 2))
3.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2)
38.0ms	(* 27/2800 (pow x 4))
24.0ms	(* 9/40 (pow x 2))
108.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify45.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	308	480
1	1219	449
2	5001	437

prune176.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- x (sin x)) (- (sqrt x) (sqrt (tan x))))
0.1b	(/ 1 (+ (sqrt x) (sqrt (tan x))))
1.5b	(- (sqrt x) (sqrt (tan x)))
2.3b	(- x (sin x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
60×	`times-frac`
50×	`sqrt-prod`
39×	`difference-of-squares`
30×	`add-cube-cbrt`
25×	`distribute-lft-out--`
14×	`associate-/r*`
10×	`add-exp-log`
8×	`add-cbrt-cube` `distribute-lft-out` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`flip3--` `associate-/r/` `flip--`
3×	`div-exp`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `clear-num` `div-inv` `associate-/l/`
1×	`rec-exp` `pow-flip` `flip3-+` `1-exp` `div-sub` `flip-+` `inv-pow`

Counts

4 → 149

Calls

4 calls:

17.0ms	(/ (- x (sin x)) (- (sqrt x) (sqrt (tan x))))
10.0ms	(/ 1 (+ (sqrt x) (sqrt (tan x))))
6.0ms	(- (sqrt x) (sqrt (tan x)))
3.0ms	(- x (sin x))

series244.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- x (sin x)) (- (sqrt x) (sqrt (tan x))))
61.0ms	(/ 1 (+ (sqrt x) (sqrt (tan x))))
51.0ms	(- (sqrt x) (sqrt (tan x)))
36.0ms	(- x (sin x))

simplify62.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	594	1849
1	2280	1717
2	5001	1694

prune306.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes49.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch76.0ms

Steps

Iters	Range		Point
7	0.003064448021395057	0.16998237910242062	0.028890275250899152
10	-4.508778152722845	-1.8057709034692785e-13	-0.030137210439935006

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	11
1	28	11

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.4s	1609×	body	2560	valid
1.8s	2735×	body	1280	valid
631.0ms	1888×	body	640	valid
208.0ms	933×	body	320	valid
67.0ms	448×	body	160	valid
34.0ms	387×	body	80	valid