Details

sample276.0ms

Algorithm

intervals

Results

11.0ms	46×	body	1280	valid
6.0ms	37×	body	640	valid
6.0ms	133×	body	80	valid
3.0ms	24×	body	320	valid
1.0ms	16×	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: 0.4b

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))

series214.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(- 1.0 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))
53.0ms	(* (tan x) (tan x))

simplify44.0ms

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

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
184×	`*-un-lft-identity`
176×	`add-sqr-sqrt`
94×	`add-cube-cbrt`
40×	`difference-of-squares`
30×	`associate-/r*`
25×	`distribute-lft-out`
20×	`sqrt-prod` `distribute-lft-out--`
13×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
11×	`pow1`
7×	`flip3--` `flip--` `div-inv` `associate-/l*`
6×	`add-log-exp`
4×	`tan-quot` `cbrt-undiv` `div-exp` `associate-/l/`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 227

Calls

4 calls:

8.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
4.0ms	(- (sqrt 1.0) (tan x))
15.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
5.0ms	(* (tan x) (tan x))

series377.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
39.0ms	(- (sqrt 1.0) (tan x))
194.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
33.0ms	(* (tan x) (tan x))

simplify117.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	733	4179
1	3738	3943
2	5001	3925

prune522.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

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)

rewrite12.0ms

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×	`pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

2.0ms	(pow (cos x) 2)
2.0ms	(pow (cos x) 2)
2.0ms	(pow (sin x) 2)
3.0ms	(pow (sin x) 2)

series74.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (cos x) 2)
17.0ms	(pow (cos x) 2)
18.0ms	(pow (sin x) 2)
19.0ms	(pow (sin x) 2)

simplify59.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	141	284
1	469	240
2	1590	240
3	5001	236

prune229.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

286×	`times-frac`
235×	`*-un-lft-identity`
201×	`add-sqr-sqrt`
131×	`add-cube-cbrt`
112×	`log-pow`
102×	`exp-prod`
35×	`distribute-lft-out`
34×	`associate-/r*` `difference-of-squares`
27×	`pow1`
17×	`sqrt-prod` `distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`div-inv`
5×	`log-prod`
4×	`tan-quot` `exp-sum` `associate-/l*`
3×	`cbrt-undiv` `swap-sqr` `div-exp` `associate-r` `associate-l`
2×	`sub-neg` `exp-diff` `rem-exp-log` `associate-/l/`
1×	`pow2` `frac-times` `log-div` `frac-2neg` `flip3-+` `pow-plus` `diff-log` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 258

Calls

4 calls:

17.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (log (exp (- (sqrt 1.0) (tan x))))))
6.0ms	(log (exp (- (sqrt 1.0) (tan x))))
5.0ms	(* (tan x) (tan x))
6.0ms	(exp (- (sqrt 1.0) (tan x)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (log (exp (- (sqrt 1.0) (tan x))))))
37.0ms	(log (exp (- (sqrt 1.0) (tan x))))
35.0ms	(* (tan x) (tan x))
72.0ms	(exp (- (sqrt 1.0) (tan x)))

simplify118.0ms

Algorithm

egg-herbie

Counts

270 → 270

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	837	5036
1	3743	4779
2	5001	4774

prune535.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes239.0ms

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

sample922.0ms

Algorithm

intervals

Results

373.0ms	1511×	body	1280	valid
200.0ms	1267×	body	640	valid
148.0ms	4317×	body	80	valid
63.0ms	571×	body	320	valid
26.0ms	334×	body	160	valid