Details

sample299.0ms

Algorithm

intervals

Results

20.0ms	45×	body	1280	valid
12.0ms	44×	body	640	valid
9.0ms	135×	body	80	valid
4.0ms	19×	body	320	valid
2.0ms	13×	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: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(* (tan x) (tan x))
0.2b	(* (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))))
2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series221.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
39.0ms	(- 1.0 (* (tan x) (tan x)))
31.0ms	(* (tan x) (tan x))
60.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (36.0ms)

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

prune299.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 184

Calls

4 calls:

4.0ms	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
10.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))

series271.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
106.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
32.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(* (tan x) (tan x))

simplify77.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	593	2482
1	2691	2268
2	5001	2158

prune397.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (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 (- 1.0 (* (tan x) (tan x)))))
0.2b	(* (tan x) (tan x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

582×	`times-frac`
308×	`add-sqr-sqrt`
263×	`add-cube-cbrt` `*-un-lft-identity`
50×	`add-exp-log`
43×	`difference-of-squares`
35×	`div-inv`
34×	`div-exp`
29×	`associate-/r/`
21×	`associate-/r*`
20×	`add-cbrt-cube`
16×	`associate-/l*`
15×	`flip3--` `flip--`
12×	`pow1`
9×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`add-log-exp`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `swap-sqr` `associate-r` `associate-l` `prod-diff`
2×	`frac-2neg` `clear-num`
1×	`pow2` `frac-times` `sub-neg` `pow-flip` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate-/l/` `inv-pow` `unswap-sqr`

Counts

4 → 383

Calls

4 calls:

2.0ms	(/ 1 (fma (tan x) (tan x) 1.0))
2.0ms	(- 1.0 (* (tan x) (tan x)))
16.0ms	(/ (/ 1 (fma (tan x) (tan x) 1.0)) (/ 1 (- 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))

series238.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ 1 (fma (tan x) (tan x) 1.0))
32.0ms	(- 1.0 (* (tan x) (tan x)))
109.0ms	(/ (/ 1 (fma (tan x) (tan x) 1.0)) (/ 1 (- 1.0 (* (tan x) (tan x)))))
32.0ms	(* (tan x) (tan x))

simplify88.0ms

Algorithm

egg-herbie

Counts

395 → 395

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1698	7107
1	5001	6501

prune706.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (fma (tan x) (tan x) 1.0))
0.2b	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(/ (/ 1 (fma (tan x) (tan x) 1.0)) (/ 1 (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

390×	`times-frac`
186×	`add-sqr-sqrt` `*-un-lft-identity`
180×	`add-cube-cbrt`
113×	`associate-/r/`
93×	`add-exp-log`
60×	`frac-times` `div-exp`
46×	`flip3-+` `flip-+`
45×	`flip3--` `flip--`
36×	`prod-diff`
32×	`div-inv`
30×	`associate-r/` `associate-l/`
29×	`add-cbrt-cube`
22×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
18×	`associate-/r*`
16×	`rec-exp` `1-exp` `associate-/l*`
14×	`cbrt-undiv`
13×	`prod-exp`
7×	`pow1`
6×	`fma-def` `associate-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u`
3×	`cbrt-unprod`
2×	`sub-neg` `frac-2neg` `clear-num` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `pow-flip` `pow-prod-down` `sum-log` `*-commutative` `associate-/l/` `distribute-lft-out--` `inv-pow` `unswap-sqr`

Counts

4 → 396

Calls

4 calls:

2.0ms	(/ 1 (fma (tan x) (tan x) 1.0))
30.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
7.0ms	(+ (sqrt 1.0) (tan x))
28.0ms	(/ (/ 1 (fma (tan x) (tan x) 1.0)) (/ 1 (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))))

series412.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ 1 (fma (tan x) (tan x) 1.0))
103.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
32.0ms	(+ (sqrt 1.0) (tan x))
210.0ms	(/ (/ 1 (fma (tan x) (tan x) 1.0)) (/ 1 (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))))

simplify102.0ms

Algorithm

egg-herbie

Counts

408 → 408

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1896	8770
1	5001	7513

prune856.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes108.0ms

Accuracy

0% (0.4b 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	16	12
1	16	12

end0.0ms

sample1.6s

Algorithm

intervals

Results

687.0ms	1522×	body	1280	valid
363.0ms	1267×	body	640	valid
254.0ms	4244×	body	80	valid
119.0ms	628×	body	320	valid
44.0ms	339×	body	160	valid