Details

sample490.0ms

Algorithm

intervals

Results

139.0ms	61×	body	2560	valid
63.0ms	88×	body	1280	valid
17.0ms	48×	body	640	valid
6.0ms	25×	body	320	valid
4.0ms	21×	body	160	valid
1.0ms	13×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 36.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.8b	(- x (sin x))
2.0b	(- x (tan x))

rewrite39.0ms

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:

13.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (sin x))
6.0ms	(- x (tan x))

series178.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (- x (sin x)) (- x (tan x)))
36.0ms	(- x (sin x))
64.0ms	(- x (tan x))

simplify54.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (11.0ms)

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

prune248.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
12.8b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma 27/2800 (pow x 4) 1/2)
0.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series129.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(fma 27/2800 (pow x 4) 1/2)
45.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify144.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	51	133
1	162	117
2	626	117
3	3552	117
4	5001	117

prune82.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin x) 2)
0.2b	(pow (sin x) 2)
20.1b	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))
20.1b	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
42×	`div-exp`
37×	`pow-to-exp` `pow-exp`
36×	`prod-exp`
18×	`unpow-prod-down`
16×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
14×	`add-cbrt-cube`
6×	`pow1` `pow-unpow` `unpow2` `sqr-pow`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-pow` `frac-2neg` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 144

Calls

4 calls:

1.0ms	(pow (sin x) 2)
2.0ms	(pow (sin x) 2)
6.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))
8.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin x) 2)
19.0ms	(pow (sin x) 2)
60.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))
76.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))

simplify46.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	395	1062
1	1696	952
2	5002	952

prune393.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

1.8b	(- x (sin x))
1.8b	(- x (sin x))
1.8b	(- x (sin x))
2.0b	(- x (tan x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

3.0ms	(- x (sin x))
4.0ms	(- x (sin x))
3.0ms	(- x (sin x))
3.0ms	(- x (tan x))

series154.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- x (sin x))
31.0ms	(- x (sin x))
31.0ms	(- x (sin x))
55.0ms	(- x (tan x))

simplify92.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	258	969
1	749	605
2	3295	569
3	5001	401

prune255.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.8b

bsearch84.0ms

Steps

Iters	Range		Point
10	2.30341956868392e-10	214.50772926448735	0.03182738450357233
8	-0.12347723982223391	-6.246474786567043e-06	-0.03610505077074316

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	24
1	31	24

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.5s	1598×	body	2560	valid
1.8s	2662×	body	1280	valid
650.0ms	1874×	body	640	valid
222.0ms	982×	body	320	valid
85.0ms	513×	body	160	valid
33.0ms	371×	body	80	valid