Details

sample298.0ms

Algorithm

intervals

Results

17.0ms	52×	body	1280	valid
7.0ms	35×	body	640	valid
7.0ms	140×	body	80	valid
3.0ms	23×	body	320	valid
1.0ms	6×	body	160	valid

simplify14.0ms

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: 0.4b

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)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite26.0ms

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:

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))

series208.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (- 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))
52.0ms	(* (tan x) (tan x))

simplify45.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

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

prune247.0ms

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

rewrite47.0ms

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:

31.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
4.0ms	(+ (sqrt 1.0) (tan x))
5.0ms	(- (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))

series200.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
31.0ms	(+ (sqrt 1.0) (tan x))
38.0ms	(- (sqrt 1.0) (tan x))
31.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (39.0ms)

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

prune255.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`pow1` `add-log-exp`
9×	`add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
4×	`tan-quot` `exp-prod`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`sum-log` `rem-exp-log` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `pow2` `frac-times` `sub-neg` `flip3--` `flip3-+` `pow-plus` `diff-log` `associate-r/` `exp-sum` `pow-prod-down` `associate-l/` `prod-exp` `sqrt-prod` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

4.0ms	(+ (sqrt 1.0) (tan x))
5.0ms	(- (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))
14.0ms	(exp (+ (sqrt 1.0) (tan x)))

series164.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (sqrt 1.0) (tan x))
36.0ms	(- (sqrt 1.0) (tan x))
35.0ms	(* (tan x) (tan x))
61.0ms	(exp (+ (sqrt 1.0) (tan x)))

simplify125.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (117.0ms)

Iter	Nodes	Cost
0	239	389
1	858	352
2	3906	344
3	5001	338

prune241.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-log-exp`
12×	`add-sqr-sqrt` `flip3-+` `flip-+`
11×	`pow1`
10×	`tan-quot` `*-un-lft-identity` `frac-add`
8×	`add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube` `distribute-neg-frac`
5×	`frac-times` `associate-*r/` `sum-log`
3×	`+-commutative` `swap-sqr` `associate-r` `associate-l` `associate-*l/` `distribute-lft-out`
2×	`distribute-lft-neg-out` `associate-+r+`
1×	`pow2` `distribute-rgt-in` `associate-+l+` `distribute-rgt-out` `distribute-lft-in` `pow-plus` `unsub-neg` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

2.0ms	(+ 1.0 (* (sqrt 1.0) (tan x)))
4.0ms	(+ (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))
13.0ms	(+ (+ 1.0 (* (sqrt 1.0) (tan x))) (* (- (tan x)) (+ (sqrt 1.0) (tan x))))

series147.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ 1.0 (* (sqrt 1.0) (tan x)))
32.0ms	(+ (sqrt 1.0) (tan x))
31.0ms	(* (tan x) (tan x))
37.0ms	(+ (+ 1.0 (* (sqrt 1.0) (tan x))) (* (- (tan x)) (+ (sqrt 1.0) (tan x))))

simplify77.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	537	1007
1	2728	950
2	5002	918

prune261.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes182.0ms

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	12	12
1	12	12

end0.0ms

sample1.1s

Algorithm

intervals

Results

434.0ms	1478×	body	1280	valid
255.0ms	1255×	body	640	valid
205.0ms	4332×	body	80	valid
93.0ms	629×	body	320	valid
31.0ms	306×	body	160	valid