Details

sample310.0ms

Algorithm

intervals

Results

23.0ms	50×	body	1280	valid
12.0ms	42×	body	640	valid
9.0ms	131×	body	80	valid
4.0ms	19×	body	320	valid
2.0ms	14×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	22	14
3	29	14
4	37	14
5	42	14
6	44	14
done	44	14

prune17.0ms

Pruning

2 alts after pruning (2 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)))
0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite30.0ms

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:

3.0ms	(- 1.0 (* (tan x) (tan x)))
9.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series217.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1.0 (* (tan x) (tan x)))
100.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
40.0ms	(* (tan x) (tan x))
43.0ms	(* (tan x) (tan x))

simplify1.9s

Counts

131 → 131

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	151	1789
1	336	1638
2	909	1453
3	3217	1419
done	5000	1418

prune314.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
40×	`add-cube-cbrt`
37×	`times-frac`
22×	`associate-r`
20×	`sqrt-prod`
18×	`prod-diff`
16×	`difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out--`
6×	`pow1` `fma-neg` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u`
3×	`associate-/r*`
2×	`cbrt-undiv` `frac-times` `flip3--` `flip3-+` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `fma-udef` `distribute-lft-out`

Counts

4 → 143

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
19.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))
36.0ms	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
7.0ms	(- (sqrt 1.0) (tan x))

series413.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(fma (tan x) (tan x) 1.0)
109.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))
221.0ms	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
39.0ms	(- (sqrt 1.0) (tan x))

simplify1.0s

Counts

155 → 155

Iterations

Useful iterations: 2 (371.0ms)

Iter	Nodes	Cost
0	224	3085
1	545	2688
2	1845	2370
done	5000	2370

prune382.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

20.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(/ (* (tan x) (sin x)) (cos x))
5.0ms	(* (tan x) (sin x))
6.0ms	(* (tan x) (tan x))

series259.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
64.0ms	(/ (* (tan x) (sin x)) (cos x))
43.0ms	(* (tan x) (sin x))
37.0ms	(* (tan x) (tan x))

simplify712.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (215.0ms)

Iter	Nodes	Cost
0	198	2029
1	452	1923
2	1468	1712
done	5000	1712

prune370.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
108×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
70×	`add-cube-cbrt`
19×	`associate-/r*`
15×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/l*`
12×	`difference-of-squares`
11×	`pow1`
7×	`div-inv`
5×	`tan-quot` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`frac-2neg` `swap-sqr` `associate-r` `associate-l` `clear-num` `associate-/r/` `associate-/l/`
1×	`pow2` `frac-times` `flip3--` `flip3-+` `pow-plus` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 182

Calls

4 calls:

76.0ms	(/ (- 1.0 (/ (tan x) (/ (cos x) (sin x)))) (+ 1.0 (* (tan x) (tan x))))
4.0ms	(/ (cos x) (sin x))
6.0ms	(/ (tan x) (/ (cos x) (sin x)))
6.0ms	(* (tan x) (tan x))

series239.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (- 1.0 (/ (tan x) (/ (cos x) (sin x)))) (+ 1.0 (* (tan x) (tan x))))
19.0ms	(/ (cos x) (sin x))
59.0ms	(/ (tan x) (/ (cos x) (sin x)))
38.0ms	(* (tan x) (tan x))

simplify1.0s

Counts

194 → 194

Iterations

Useful iterations: 2 (429.0ms)

Iter	Nodes	Cost
0	311	3413
1	695	3238
2	2165	2997
done	5001	2997

prune555.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes111.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	12	23
done	12	23

end0.0ms

sample1.6s

Algorithm

intervals

Results

685.0ms	1515×	body	1280	valid
362.0ms	1249×	body	640	valid
257.0ms	4274×	body	80	valid
129.0ms	640×	body	320	valid
49.0ms	322×	body	160	valid