Details

sample278.0ms

Algorithm

intervals

Results

12.0ms	50×	body	1280	valid
7.0ms	44×	body	640	valid
6.0ms	139×	body	80	valid
2.0ms	14×	body	320	valid
1.0ms	9×	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))

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:

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))
8.0ms	(* (tan x) (tan x))

series217.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
35.0ms	(- 1.0 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))
53.0ms	(* (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

prune252.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
37×	`times-frac`
30×	`add-cube-cbrt`
27×	`associate-r`
14×	`difference-of-squares`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`associate-l` `sqrt-prod` `distribute-lft-out--`
6×	`associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`tan-quot` `associate-/r/`
3×	`frac-times` `swap-sqr` `associate-l/` `prod-exp` `associate-/r` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `associate-/l/` `distribute-lft-out`
1×	`+-commutative` `pow2` `flip3--` `frac-2neg` `pow-plus` `div-sub` `clear-num` `sum-log` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 132

Calls

4 calls:

7.0ms	(+ (sqrt 1.0) (tan x))
8.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
17.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))

series354.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (sqrt 1.0) (tan x))
93.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
195.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
33.0ms	(* (tan x) (tan x))

simplify83.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	558	1651
1	2781	1488
2	5002	1472

prune343.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.3b	(cbrt (/ (pow (- 1.0 (* (tan x) (tan x))) 3) (pow (+ 1.0 (* (tan x) (tan x))) 3)))
0.4b	(pow (- 1.0 (* (tan x) (tan x))) 3)
0.4b	(pow (+ 1.0 (* (tan x) (tan x))) 3)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

174×	`cbrt-prod`
168×	`times-frac`
121×	`add-sqr-sqrt`
97×	`unpow-prod-down` `cube-prod`
93×	`add-cube-cbrt` `*-un-lft-identity`
28×	`cube-mult` `unpow3` `sqr-pow`
26×	`difference-of-squares`
13×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`cube-div` `pow-unpow`
4×	`tan-quot` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `rem-cube-cbrt`
1×	`pow2` `frac-times` `cbrt-div` `flip3--` `pow-plus` `pow1/3` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 263

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
16.0ms	(cbrt (/ (pow (- 1.0 (* (tan x) (tan x))) 3) (pow (+ 1.0 (* (tan x) (tan x))) 3)))
4.0ms	(pow (- 1.0 (* (tan x) (tan x))) 3)
4.0ms	(pow (+ 1.0 (* (tan x) (tan x))) 3)

series284.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (tan x) (tan x))
95.0ms	(cbrt (/ (pow (- 1.0 (* (tan x) (tan x))) 3) (pow (+ 1.0 (* (tan x) (tan x))) 3)))
82.0ms	(pow (- 1.0 (* (tan x) (tan x))) 3)
72.0ms	(pow (+ 1.0 (* (tan x) (tan x))) 3)

simplify134.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	774	5005
1	3884	4865
2	5003	4746

prune372.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(- 1.0 (/ (pow (sin x) 2) (pow (cos x) 2)))
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
17×	`unpow-prod-down` `difference-of-squares`
16×	`times-frac`
12×	`*-un-lft-identity`
11×	`unpow2` `sqr-pow`
10×	`add-cube-cbrt`
9×	`pow-unpow`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-pow` `pow-exp`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 84

Calls

4 calls:

2.0ms	(pow (cos x) 2)
20.0ms	(- 1.0 (/ (pow (sin x) 2) (pow (cos x) 2)))
3.0ms	(pow (sin x) 2)
3.0ms	(pow (sin x) 2)

series103.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (cos x) 2)
45.0ms	(- 1.0 (/ (pow (sin x) 2) (pow (cos x) 2)))
19.0ms	(pow (sin x) 2)
22.0ms	(pow (sin x) 2)

simplify98.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	313	607
1	856	528
2	3075	524
3	5001	524

prune200.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes197.0ms

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	13	12
1	13	12

end0.0ms

sample921.0ms

Algorithm

intervals

Results

374.0ms	1528×	body	1280	valid
193.0ms	1219×	body	640	valid
153.0ms	4360×	body	80	valid
61.0ms	558×	body	320	valid
26.0ms	335×	body	160	valid