Details

sample500.0ms

Algorithm

intervals

Results

289.0ms	46×	body	1280	valid
29.0ms	34×	body	640	valid
23.0ms	139×	body	80	valid
13.0ms	21×	body	320	valid
6.0ms	16×	body	160	valid

simplify63.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	21	15
3	26	15
4	34	15
5	36	15
done	36	15

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

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:

31.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(- 1.0 (* (tan x) (tan x)))
18.0ms	(* (tan x) (tan x))
35.0ms	(* (tan x) (tan x))

series300.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
63.0ms	(- 1.0 (* (tan x) (tan x)))
47.0ms	(* (tan x) (tan x))
58.0ms	(* (tan x) (tan x))

simplify2.1s

Counts

117 → 117

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	138	1632
1	315	1486
2	861	1368
3	2678	1346
done	5001	1342

prune348.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

11.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
41.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
22.0ms	(* (tan x) (tan x))
16.0ms	(* (tan x) (tan x))

series367.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
147.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
45.0ms	(* (tan x) (tan x))
62.0ms	(* (tan x) (tan x))

simplify3.0s

Counts

144 → 144

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	169	2062
1	386	1786
2	1126	1585
3	3773	1543
done	5001	1539

prune446.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

10.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
27.0ms	(* (tan x) (sin x))
17.0ms	(/ (* (tan x) (sin x)) (cos x))
19.0ms	(* (tan x) (tan x))

series269.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
68.0ms	(* (tan x) (sin x))
87.0ms	(/ (* (tan x) (sin x)) (cos x))
38.0ms	(* (tan x) (tan x))

simplify1.5s

Counts

95 → 95

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	134	997
1	289	912
2	951	816
done	5000	807

prune433.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin x))
0.2b	(* (tan x) (sin x))
0.2b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(/ (* (tan x) (sin x)) (cos x))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`times-frac` `associate-r` `associate-l` `associate-/r*`
4×	`tan-quot` `cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l/` `associate-/l` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

25.0ms	(* (tan x) (sin x))
20.0ms	(* (tan x) (sin x))
26.0ms	(/ (* (tan x) (sin x)) (cos x))
31.0ms	(/ (* (tan x) (sin x)) (cos x))

series312.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (tan x) (sin x))
53.0ms	(* (tan x) (sin x))
98.0ms	(/ (* (tan x) (sin x)) (cos x))
102.0ms	(/ (* (tan x) (sin x)) (cos x))

simplify2.6s

Counts

94 → 94

Iterations

Useful iterations: 2 (110.0ms)

Iter	Nodes	Cost
0	86	934
1	185	898
2	639	774
3	3087	774
done	5000	774

prune415.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes326.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	12	21
done	12	21

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.8s	1546×	body	1280	valid
1.7s	1198×	body	640	valid
745.0ms	4315×	body	80	valid
315.0ms	647×	body	320	valid
130.0ms	294×	body	160	valid