Details

sample294.0ms

Algorithm

intervals

Results

20.0ms	47×	body	1280	valid
13.0ms	51×	body	640	valid
8.0ms	126×	body	80	valid
4.0ms	22×	body	320	valid
1.0ms	10×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	22	9
2	29	9
3	37	9
4	43	9
5	45	9
6	45	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `prod-diff` `associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 119

Calls

4 calls:

8.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
3.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series211.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(- 1.0 (* (tan x) (tan x)))
31.0ms	(* (tan x) (tan x))
53.0ms	(* (tan x) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	918
2	5001	882

prune288.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

1.0ms	(pow (cos x) 2)
1.0ms	(pow (cos x) 2)
1.0ms	(pow (sin x) 2)
2.0ms	(pow (sin x) 2)

series73.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (cos x) 2)
16.0ms	(pow (cos x) 2)
21.0ms	(pow (sin x) 2)
19.0ms	(pow (sin x) 2)

simplify61.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	146	308
1	487	260
2	1671	260
3	5001	256

prune249.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (tan x) (tan x) 1.0)
0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
76×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
13×	`difference-of-squares`
12×	`pow1`
11×	`add-cbrt-cube`
9×	`associate-/r/`
7×	`div-exp`
6×	`add-log-exp`
5×	`flip3--` `flip--` `div-inv`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-neg` `swap-sqr` `associate-r` `associate-l` `prod-diff` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`pow2` `frac-times` `sub-neg` `pow-flip` `frac-2neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `inv-pow` `unswap-sqr`

Counts

4 → 159

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
2.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))

series211.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(fma (tan x) (tan x) 1.0)
34.0ms	(- 1.0 (* (tan x) (tan x)))
104.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
32.0ms	(* (tan x) (tan x))

simplify75.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	570	2046
1	2617	1859
2	5002	1752

prune330.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
0.2b	(- (sqrt 1.0) (tan x))
0.2b	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
44×	`add-cube-cbrt`
37×	`times-frac`
27×	`associate-r`
20×	`sqrt-prod`
18×	`prod-diff`
16×	`difference-of-squares`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out--`
7×	`associate-l`
6×	`fma-neg` `associate-/l*` `add-log-exp`
4×	`tan-quot` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`frac-times` `swap-sqr` `associate-l/` `prod-exp` `associate-/r` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip--` `div-inv` `associate-/l/`
1×	`pow2` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `clear-num` `pow-sqr` `pow-prod-up` `distribute-lft-out`

Counts

4 → 167

Calls

4 calls:

41.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
6.0ms	(- (sqrt 1.0) (tan x))
16.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))

series351.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
39.0ms	(- (sqrt 1.0) (tan x))
91.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))

simplify88.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	644	2081
1	3042	1700
2	5002	1661

prune380.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes160.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	17
1	14	17

end0.0ms

sample1.5s

Algorithm

intervals

Results

653.0ms	1521×	body	1280	valid
342.0ms	1285×	body	640	valid
241.0ms	4286×	body	80	valid
108.0ms	606×	body	320	valid
37.0ms	302×	body	160	valid