Details

sample349.0ms

Algorithm

intervals

Results

20.0ms	44×	body	1280	valid
11.0ms	38×	body	640	valid
9.0ms	135×	body	80	valid
5.0ms	23×	body	320	valid
2.0ms	16×	body	160	valid

simplify33.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	9
1	21	9
2	26	9
3	34	9
4	37	9
5	37	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

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)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite68.0ms

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:

24.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(- 1.0 (* (tan x) (tan x)))
14.0ms	(* (tan x) (tan x))
21.0ms	(* (tan x) (tan x))

series198.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
36.0ms	(- 1.0 (* (tan x) (tan x)))
30.0ms	(* (tan x) (tan x))
42.0ms	(* (tan x) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

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

prune243.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
21×	`-un-lft-identity` `associate-r*`
20×	`pow1` `add-cube-cbrt`
17×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`times-frac`
10×	`associate-l`
8×	`tan-quot`
6×	`swap-sqr` `prod-exp` `add-log-exp`
5×	`unswap-sqr`
4×	`frac-times` `associate-*l/` `cbrt-unprod`
3×	`flip3--` `associate-r/` `pow-prod-down` `-commutative` `flip--`
2×	`pow2` `pow-plus` `div-exp` `associate-/r/` `pow-sqr` `pow-prod-up` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `flip3-+` `diff-log` `1-exp` `un-div-inv` `flip-+` `div-inv`

Counts

4 → 112

Calls

4 calls:

34.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(- 1.0 (* (tan x) (tan x)))
14.0ms	(* (tan x) (tan x))
17.0ms	(* (tan x) (tan x))

series181.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
33.0ms	(- 1.0 (* (tan x) (tan x)))
30.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))

simplify55.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	382	946
1	1727	838
2	5001	797

prune231.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

33×	`pow1`
23×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
16×	`tan-quot`
13×	`add-exp-log` `add-cbrt-cube`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`pow-pow`
4×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `pow-prod-up` `cbrt-unprod` `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 → 113

Calls

4 calls:

15.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))
17.0ms	(* (tan x) (tan x))
12.0ms	(pow (* (tan x) (tan x)) 3)

series159.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
63.0ms	(pow (* (tan x) (tan x)) 3)

simplify41.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	211	452
1	971	401
2	5001	384

prune295.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin x) 2)
0.2b	(pow (sin x) 2)
0.3b	(pow (cos x) 2)
0.3b	(pow (cos x) 2)

rewrite16.0ms

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:

3.0ms	(pow (sin x) 2)
4.0ms	(pow (sin x) 2)
3.0ms	(pow (cos x) 2)
4.0ms	(pow (cos x) 2)

series69.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (sin x) 2)
18.0ms	(pow (sin x) 2)
16.0ms	(pow (cos x) 2)
19.0ms	(pow (cos x) 2)

simplify60.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	141	284
1	469	240
2	1588	240
3	5001	236

prune190.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes185.0ms

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	9	14
1	9	14

end0.0ms

sample1.7s

Algorithm

intervals

Results

696.0ms	1524×	body	1280	valid
380.0ms	1277×	body	640	valid
262.0ms	4255×	body	80	valid
138.0ms	611×	body	320	valid
46.0ms	333×	body	160	valid