Details

sample353.0ms

Algorithm

intervals

Results

27.0ms	61×	body	1280	valid
10.0ms	36×	body	640	valid
9.0ms	135×	body	80	valid
3.0ms	18×	body	320	valid
1.0ms	6×	body	160	valid

simplify40.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	13	9
1	22	9
2	29	9
3	37	9
4	43	9
5	45	9
6	45	9
done	45	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 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))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`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×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `prod-diff` `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 → 119

Calls

4 calls:

10.0ms	(- 1.0 (* (tan x) (tan x)))
18.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
14.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

series212.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- 1.0 (* (tan x) (tan x)))
98.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))
46.0ms	(* (tan x) (tan x))

simplify45.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	917
2	5001	882
done	5001	882

prune278.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
34×	`add-cube-cbrt`
24×	`times-frac`
21×	`prod-diff`
13×	`pow1`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`tan-quot` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `swap-sqr` `associate-/r*`
2×	`flip3--` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `-commutative` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `frac-times` `sub-neg` `frac-2neg` `flip3-+` `pow-plus` `diff-log` `div-sub` `associate-*r/` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `flip-+`

Counts

4 → 133

Calls

4 calls:

15.0ms	(* (tan x) (sin x))
11.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
37.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
15.0ms	(* (tan x) (tan x))

series239.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (tan x) (sin x))
53.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
110.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(* (tan x) (tan x))

simplify80.0ms

Counts

145 → 145

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	560	1909
1	2268	1535
2	5002	1475
done	5002	1475

prune349.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
19×	`pow1` `log-pow`
18×	`exp-prod`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
7×	`difference-of-squares`
6×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`log-prod` `associate-/r*`
2×	`pow2` `frac-times` `flip3-+` `pow-plus` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp` `clear-num` `flip--`

Counts

4 → 131

Calls

4 calls:

18.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
17.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))
25.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

series256.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
35.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))
96.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify43.0ms

Counts

143 → 143

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	373	1261
1	1240	1156
2	5001	1132
done	5001	1132

prune342.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
37×	`times-frac`
32×	`add-cube-cbrt`
27×	`associate-l`
14×	`difference-of-squares`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`sqrt-prod`
7×	`associate-r` `distribute-lft-out--`
6×	`fma-def` `associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`tan-quot` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`frac-times` `associate-r/` `swap-sqr` `prod-exp` `associate-/r` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `associate-/l/` `distribute-lft-out`
1×	`+-commutative` `pow2` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `pow-plus` `div-sub` `clear-num` `sum-log` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 148

Calls

4 calls:

29.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
67.0ms	(* (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))) (+ (sqrt 1.0) (tan x)))
9.0ms	(+ (sqrt 1.0) (tan x))
17.0ms	(* (tan x) (tan x))

series351.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
191.0ms	(* (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))) (+ (sqrt 1.0) (tan x)))
34.0ms	(+ (sqrt 1.0) (tan x))
33.0ms	(* (tan x) (tan x))

simplify86.0ms

Counts

160 → 160

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	712	1742
1	3440	1513
2	5001	1495
done	5001	1495

prune350.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes166.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	11
1	13	11
done	13	11

end0.0ms

sample1.6s

Algorithm

intervals

Results

707.0ms	1556×	body	1280	valid
362.0ms	1285×	body	640	valid
235.0ms	4264×	body	80	valid
122.0ms	623×	body	320	valid
39.0ms	272×	body	160	valid