Details

sample304.0ms

Algorithm

intervals

Results

23.0ms	48×	body	1280	valid
13.0ms	36×	body	640	valid
10.0ms	139×	body	80	valid
5.0ms	23×	body	320	valid
2.0ms	10×	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)))
0.2b	(/ (- 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))

series210.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- 1.0 (* (tan x) (tan x)))
93.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
31.0ms	(* (tan x) (tan x))
51.0ms	(* (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

prune255.0ms

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

rewrite10.0ms

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:

1.0ms	(pow (cos x) 2)
4.0ms	(pow (cos x) 2)
1.0ms	(pow (sin x) 2)
2.0ms	(pow (sin x) 2)

series69.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify61.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (56.0ms)

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

prune227.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
92×	`add-sqr-sqrt`
72×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-/r*`
21×	`add-exp-log`
19×	`pow1`
16×	`difference-of-squares`
15×	`add-cbrt-cube`
11×	`associate-/r/`
8×	`tan-quot` `div-exp`
6×	`swap-sqr` `associate-r` `associate-l` `div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `add-log-exp`
2×	`pow2` `frac-times` `rec-exp` `frac-2neg` `pow-plus` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`pow-flip` `flip3-+` `flip-+` `inv-pow`

Counts

4 → 187

Calls

4 calls:

10.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x))))
13.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series246.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x))))
90.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
35.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))

simplify78.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	579	2595
1	2779	2386
2	5001	2281

prune357.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin x))
0.2b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (/ (* (tan x) (sin x)) (cos x)))))
0.3b	(* (tan x) (tan x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
98×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
70×	`add-cube-cbrt`
24×	`add-exp-log` `associate-/r*`
18×	`add-cbrt-cube`
14×	`pow1`
12×	`distribute-lft-out--` `difference-of-squares`
9×	`div-exp` `associate-/r/`
6×	`tan-quot` `associate-r` `associate-l` `div-inv`
5×	`cbrt-undiv`
4×	`flip3--` `flip--` `associate-/l*` `add-log-exp`
3×	`swap-sqr` `associate-*l/` `prod-exp` `cbrt-unprod`
2×	`rec-exp` `frac-2neg` `1-exp` `pow-prod-down` `clear-num` `*-commutative` `unswap-sqr`
1×	`pow2` `frac-times` `pow-flip` `pow-plus` `associate-*r/` `pow-sqr` `pow-prod-up` `associate-/l/` `inv-pow`

Counts

4 → 177

Calls

4 calls:

5.0ms	(* (tan x) (sin x))
5.0ms	(/ (* (tan x) (sin x)) (cos x))
16.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (/ (* (tan x) (sin x)) (cos x)))))
5.0ms	(* (tan x) (tan x))

series244.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (tan x) (sin x))
56.0ms	(/ (* (tan x) (sin x)) (cos x))
111.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (/ (* (tan x) (sin x)) (cos x)))))
32.0ms	(* (tan x) (tan x))

simplify92.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	671	2798
1	3284	2578
2	5001	2463

prune351.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes216.0ms

Accuracy

0% (0.4b 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	17	12
1	17	12

end0.0ms

sample1.8s

Algorithm

intervals

Results

765.0ms	1569×	body	1280	valid
387.0ms	1221×	body	640	valid
316.0ms	4324×	body	80	valid
126.0ms	566×	body	320	valid
53.0ms	320×	body	160	valid