Details

sample310.0ms

Algorithm

intervals

Results

19.0ms	42×	body	1280	valid
14.0ms	52×	body	640	valid
9.0ms	140×	body	80	valid
3.0ms	15×	body	320	valid
1.0ms	7×	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)))
0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 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:

2.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series211.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- 1.0 (* (tan x) (tan x)))
94.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))
53.0ms	(* (tan x) (tan x))

simplify45.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (32.0ms)

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

prune238.0ms

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

38.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
16.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(- (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))

series345.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
89.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
36.0ms	(- (sqrt 1.0) (tan x))
34.0ms	(* (tan x) (tan x))

simplify79.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	561	1675
1	2802	1512
2	5001	1496

prune325.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
0.1b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(* (tan x) (sin x))
0.3b	(* (tan x) (tan x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

15.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
4.0ms	(/ (* (tan x) (sin x)) (cos x))
4.0ms	(* (tan x) (sin x))
5.0ms	(* (tan x) (tan x))

series241.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
58.0ms	(/ (* (tan x) (sin x)) (cos x))
45.0ms	(* (tan x) (sin x))
31.0ms	(* (tan x) (tan x))

simplify57.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	441	1158
1	1849	1060
2	5001	1054

prune302.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.4b	(pow (* (tan x) (tan x)) 3)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

137×	`pow1`
44×	`tan-quot`
39×	`pow-prod-up`
26×	`pow-prod-down`
25×	`pow-sqr`
23×	`add-exp-log` `add-cbrt-cube`
21×	`pow-plus`
20×	`frac-times`
17×	`add-sqr-sqrt`
16×	`pow2`
14×	`associate-r/` `associate-l/`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`prod-exp` `cbrt-unprod`
7×	`swap-sqr` `associate-r` `associate-l`
6×	`pow-pow`
4×	`add-log-exp`
3×	`cube-div` `pow-unpow` `*-commutative` `unswap-sqr`
2×	`pow-exp` `rem-cube-cbrt`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `sqr-pow`

Counts

4 → 163

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
23.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
4.0ms	(pow (* (tan x) (tan x)) 3)

series175.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))
45.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
66.0ms	(pow (* (tan x) (tan x)) 3)

simplify53.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	375	585
1	1557	516
2	5001	505

prune285.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes154.0ms

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	11
1	13	11

end0.0ms

sample1.6s

Algorithm

intervals

Results

687.0ms	1515×	body	1280	valid
346.0ms	1230×	body	640	valid
254.0ms	4337×	body	80	valid
128.0ms	624×	body	320	valid
39.0ms	294×	body	160	valid