Details

sample486.0ms

Algorithm

intervals

Results

127.0ms	53×	body	2560	valid
61.0ms	76×	body	1280	valid
28.0ms	68×	body	640	valid
9.0ms	31×	body	320	valid
3.0ms	16×	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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite23.0ms

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))
6.0ms	(- x (sin x))

series171.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(/ (- x (sin x)) (- x (tan x)))
57.0ms	(- x (tan x))
39.0ms	(- x (sin x))

simplify148.0ms

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

prune212.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
15.6b	(- (* 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))

series107.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* 27/2800 (pow x 4))
24.0ms	(* 9/40 (pow x 2))
48.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify45.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (35.0ms)

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

prune144.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (tan x)) (- x (sin x)))
0.0b	(/ 1 (/ (- x (tan x)) (- x (sin x))))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite46.0ms

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:

11.0ms	(/ (- x (tan x)) (- x (sin x)))
19.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
3.0ms	(- x (tan x))
3.0ms	(- x (sin x))

series236.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ (- x (tan x)) (- x (sin x)))
76.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
53.0ms	(- x (tan x))
31.0ms	(- x (sin x))

simplify82.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	744	2647
1	3445	2441
2	5001	2279

prune354.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

1.7b	(- x (tan x))
1.7b	(- x (tan x))
1.7b	(- x (sin x))
1.7b	(- 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 (tan x))
3.0ms	(- x (sin x))
3.0ms	(- x (sin x))

series168.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- x (tan x))
53.0ms	(- x (tan x))
30.0ms	(- x (sin x))
35.0ms	(- x (sin x))

simplify67.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	150	314
1	342	294
2	774	294
3	2023	294
4	5001	294

prune189.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.1b

bsearch88.0ms

Steps

Iters	Range		Point
10	2.1112891761060846e-05	363928.4733812492	0.02907288472896622
8	-0.10438916540540782	-0.00034188071245303247	-0.027819204802016273

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	12
1	33	12

end0.0ms

sample7.0s

Algorithm

intervals

Results

3.7s	1602×	body	2560	valid
2.1s	2770×	body	1280	valid
768.0ms	1859×	body	640	valid
264.0ms	919×	body	320	valid
100.0ms	495×	body	160	valid
40.0ms	355×	body	80	valid