Details

sample470.0ms

Algorithm

intervals

Results

116.0ms	50×	body	2560	valid
57.0ms	85×	body	1280	valid
18.0ms	53×	body	640	valid
8.0ms	37×	body	320	valid
3.0ms	19×	body	160	valid
1.0ms	12×	body	80	valid

simplify11.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.0b	(- x (tan x))
2.0b	(- x (sin x))

rewrite34.0ms

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)))
2.0ms	(- x (tan x))
5.0ms	(- x (sin x))

series173.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
57.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify153.0ms

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

prune209.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 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))
12.0b	(- (* 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	(* 27/2800 (pow x 4))
5.0ms	(* 9/40 (pow x 2))
8.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series107.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* 27/2800 (pow x 4))
27.0ms	(* 9/40 (pow x 2))
45.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify41.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (35.0ms)

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

prune146.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

2.0b	(- x (tan x))
2.0b	(- x (sin x))
2.0b	(- x (sin x))
2.0b	(- x (sin x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

2.0ms	(- x (tan x))
3.0ms	(- x (sin x))
3.0ms	(- x (sin x))
3.0ms	(- x (sin x))

series147.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- x (tan x))
31.0ms	(- x (sin x))
31.0ms	(- x (sin x))
34.0ms	(- x (sin x))

simplify68.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	150	309
1	342	289
2	774	289
3	2023	289
4	5001	289

prune181.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 3)
2.0b	(- x (tan x))
2.0b	(- (pow x 3) (pow (sin x) 3))
16.8b	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (- x (tan x))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
49×	`difference-of-squares`
41×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
16×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`associate-/r/` `add-log-exp`
6×	`flip3--` `flip--`
5×	`pow1`
4×	`frac-times`
3×	`difference-cubes` `pow-unpow` `flip3-+` `flip-+`
2×	`cbrt-undiv` `sub-neg` `diff-log` `associate-r/` `div-exp` `associate-l/` `associate-/l/`
1×	`cube-mult` `pow-to-exp` `pow-pow` `frac-2neg` `unpow3` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `rem-cube-cbrt`

Counts

4 → 147

Calls

4 calls:

2.0ms	(pow (sin x) 3)
3.0ms	(- x (tan x))
15.0ms	(- (pow x 3) (pow (sin x) 3))
55.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (- x (tan x))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (sin x) 3)
55.0ms	(- x (tan x))
102.0ms	(- (pow x 3) (pow (sin x) 3))
254.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (* (+ (* (sin x) (+ (sin x) x)) (pow x 2)) (- x (tan x))))

simplify97.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	630	1900
1	3022	1778
2	5002	1734

prune404.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes57.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.6b

bsearch89.0ms

Steps

Iters	Range		Point
10	7.712829756242493e-08	8770343.893451896	0.028954196312268393
9	-1827977.1926269082	-0.00043085380315138777	-0.028975567409347768

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	11
1	29	11

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.6s	1621×	body	2560	valid
1.8s	2664×	body	1280	valid
659.0ms	1932×	body	640	valid
221.0ms	938×	body	320	valid
75.0ms	472×	body	160	valid
35.0ms	373×	body	80	valid