Details

sample279.0ms

Algorithm

intervals

Results

12.0ms	51×	body	1280	valid
7.0ms	44×	body	640	valid
5.0ms	130×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	13×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	21	9
2	26	9
3	34	9
4	37	9
5	37	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)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`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×	`associate-/l*`
3×	`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 → 105

Calls

4 calls:

6.0ms	(/ (- 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))

series209.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(* (tan x) (tan x))
52.0ms	(* (tan x) (tan x))

simplify43.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5001	824

prune250.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
0.2b	(- (sqrt 1.0) (tan x))
0.2b	(* (tan x) (tan x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`pow1`
10×	`add-cube-cbrt`
9×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
5×	`frac-times`
4×	`tan-quot` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`
3×	`sub-neg` `associate-r/` `swap-sqr` `associate-l/`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `pow2` `pow-plus` `diff-log` `sum-log` `pow-sqr` `pow-prod-up`

Counts

4 → 89

Calls

4 calls:

4.0ms	(+ (sqrt 1.0) (tan x))
11.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
4.0ms	(- (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))

series203.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (sqrt 1.0) (tan x))
99.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
36.0ms	(- (sqrt 1.0) (tan x))
34.0ms	(* (tan x) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	328	693
1	1582	618
2	5001	607

prune247.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
80×	`add-sqr-sqrt`
63×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1` `add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube` `difference-of-squares`
9×	`associate-/r/`
8×	`tan-quot`
7×	`div-exp`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`flip3--` `flip--` `div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow2` `frac-times` `rec-exp` `pow-plus` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `clear-num` `inv-pow`

Counts

4 → 165

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series187.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- 1.0 (* (tan x) (tan x)))
90.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
34.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))

simplify73.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	545	2150
1	2567	1968
2	5001	1866

prune280.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.2b	(* (* (tan x) (tan x)) (+ (* (tan x) (tan x)) 1.0))
0.4b	(pow (* (tan x) (tan x)) 3)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
24×	`tan-quot`
19×	`add-sqr-sqrt`
16×	`add-exp-log` `add-cbrt-cube`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`frac-times`
9×	`associate-r` `associate-*l/`
8×	`associate-*r/`
7×	`associate-l`
6×	`pow-pow` `swap-sqr` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`cube-div` `pow2` `pow-unpow` `pow-plus` `pow-sqr` `*-commutative` `pow-prod-up` `unswap-sqr`
2×	`pow-exp` `rem-cube-cbrt`
1×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `unpow-prod-down` `distribute-lft-in` `unpow3` `cube-prod` `sqr-pow`

Counts

4 → 117

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
12.0ms	(* (* (tan x) (tan x)) (+ (* (tan x) (tan x)) 1.0))
6.0ms	(pow (* (tan x) (tan x)) 3)

series206.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
79.0ms	(* (* (tan x) (tan x)) (+ (* (tan x) (tan x)) 1.0))
65.0ms	(pow (* (tan x) (tan x)) 3)

simplify76.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	449	752
1	2389	662
2	5001	651

prune304.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes123.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	39
1	26	39

end0.0ms

sample901.0ms

Algorithm

intervals

Results

354.0ms	1454×	body	1280	valid
202.0ms	1288×	body	640	valid
143.0ms	4291×	body	80	valid
70.0ms	648×	body	320	valid
24.0ms	319×	body	160	valid