Details

sample276.0ms

Algorithm

intervals

Results

43.0ms	46×	body	1280	valid
19.0ms	141×	body	80	valid
16.0ms	28×	body	640	valid
10.0ms	26×	body	320	valid
5.0ms	15×	body	160	valid

simplify104.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	15
1	17	15
2	34	15
3	37	15
done	37	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

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

rewrite74.0ms

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:

29.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(- 1.0 (* (tan x) (tan x)))
16.0ms	(* (tan x) (tan x))
19.0ms	(* (tan x) (tan x))

series341.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
65.0ms	(- 1.0 (* (tan x) (tan x)))
72.0ms	(* (tan x) (tan x))
66.0ms	(* (tan x) (tan x))

simplify9.5s

Counts

117 → 117

Iterations

Useful iterations: done (9.5s)

Iter	Nodes	Cost
0	138	1632
1	2418	1480
done	5000	1376

prune351.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 165

Calls

4 calls:

5.0ms	(- 1.0 (* (tan x) (tan x)))
26.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
39.0ms	(* (tan x) (tan x))
26.0ms	(* (tan x) (tan x))

series375.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- 1.0 (* (tan x) (tan x)))
181.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
63.0ms	(* (tan x) (tan x))
67.0ms	(* (tan x) (tan x))

simplify5.8s

Counts

177 → 177

Iterations

Useful iterations: done (5.8s)

Iter	Nodes	Cost
0	249	3696
1	3219	3280
done	5000	3134

prune380.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

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)

rewrite81.0ms

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:

31.0ms	(* (tan x) (tan x))
16.0ms	(* (tan x) (tan x))
16.0ms	(* (tan x) (tan x))
13.0ms	(pow (* (tan x) (tan x)) 3)

series257.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (tan x) (tan x))
42.0ms	(* (tan x) (tan x))
61.0ms	(* (tan x) (tan x))
89.0ms	(pow (* (tan x) (tan x)) 3)

simplify2.4s

Counts

125 → 125

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	90	1018
1	805	733
done	5001	691

prune409.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

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

rewrite192.0ms

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:

103.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
24.0ms	(- (sqrt 1.0) (tan x))
39.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
17.0ms	(* (tan x) (tan x))

series560.0ms

Counts

4 → 12

Calls

4 calls:

299.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
55.0ms	(- (sqrt 1.0) (tan x))
150.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
56.0ms	(* (tan x) (tan x))

simplify4.4s

Counts

147 → 147

Iterations

Useful iterations: done (4.4s)

Iter	Nodes	Cost
0	216	2757
1	3734	2524
done	5000	2335

prune540.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes186.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	17
1	12	17
done	12	17

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.2s	1546×	body	1280	valid
891.0ms	1258×	body	640	valid
586.0ms	4253×	body	80	valid
288.0ms	634×	body	320	valid
128.0ms	309×	body	160	valid