Details

sample261.0ms

Algorithm

intervals

Results

61.0ms	38×	body	640	valid
57.0ms	46×	body	1280	valid
22.0ms	144×	body	80	valid
9.0ms	19×	body	320	valid
3.0ms	9×	body	160	valid

simplify41.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	36
5	36
4	34
3	26
2	21
1	13
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`pow1`
15×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`associate-/l*`
4×	`insert-posit16`
3×	`associate-/r*`
2×	`pow2` `frac-times` `pow-plus` `flip3--` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 114

Calls

4 calls:

28.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
9.0ms	(- 1 (* (tan x) (tan x)))
29.0ms	(* (tan x) (tan x))
52.0ms	(* (tan x) (tan x))

series273.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
58.0ms	(- 1 (* (tan x) (tan x)))
37.0ms	(* (tan x) (tan x))
83.0ms	(* (tan x) (tan x))

simplify2.8s

Counts

126 → 126

Iterations

Iter	Nodes
3	2613
2	939
1	356
0	144

prune755.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
21×	`times-frac` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
11×	`pow1`
10×	`difference-of-squares`
7×	`associate-/l*`
6×	`associate-/r*` `add-log-exp`
5×	`tan-quot` `distribute-lft-out--`
4×	`insert-posit16`
3×	`cbrt-undiv` `swap-sqr` `div-exp` `associate-r` `associate-l` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `prod-exp` `associate-*r/` `associate-/r/` `cbrt-unprod` `div-inv` `flip--`
1×	`pow2` `frac-times` `sub-neg` `flip3-+` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `pow-sqr` `-commutative` `pow-prod-up` `flip-+` `unswap-sqr`

Counts

4 → 113

Calls

4 calls:

29.0ms	(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (* (tan x) (tan x))))
8.0ms	(- 1 (/ (* (sin x) (tan x)) (cos x)))
14.0ms	(/ (* (sin x) (tan x)) (cos x))
14.0ms	(* (tan x) (tan x))

series300.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (* (tan x) (tan x))))
70.0ms	(- 1 (/ (* (sin x) (tan x)) (cos x)))
62.0ms	(/ (* (sin x) (tan x)) (cos x))
53.0ms	(* (tan x) (tan x))

simplify15.8s

Counts

125 → 125

Iterations

Iter	Nodes
3	5954
2	1556
1	476
0	187

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

240×	`pow1`
74×	`pow-prod-up`
72×	`tan-quot`
48×	`pow-prod-down`
46×	`pow-sqr`
38×	`pow-plus`
36×	`frac-times`
32×	`add-cbrt-cube` `add-exp-log`
28×	`pow2`
24×	`associate-l/` `associate-r/`
18×	`prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`swap-sqr` `associate-r` `associate-l`
4×	`*-commutative` `insert-posit16` `add-log-exp` `unswap-sqr`

Counts

4 → 216

Calls

4 calls:

23.0ms	(* (tan x) (tan x))
13.0ms	(* (tan x) (tan x))
78.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
85.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (tan x) (tan x))
52.0ms	(* (tan x) (tan x))
59.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
84.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify2.8s

Counts

228 → 228

Iterations

Iter	Nodes
4	4413
3	1927
2	870
1	287
0	108

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

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

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
25×	`pow1`
24×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`tan-quot`
10×	`add-cbrt-cube` `add-exp-log`
9×	`swap-sqr` `associate-r` `associate-l`
8×	`times-frac`
6×	`add-log-exp` `difference-of-squares`
5×	`distribute-rgt-out--` `div-inv`
4×	`associate-/r/` `insert-posit16`
3×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `flip-+` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

4 → 115

Calls

4 calls:

28.0ms	(* (tan x) (tan x))
26.0ms	(* (tan x) (tan x))
16.0ms	(* (tan x) (tan x))
39.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

series291.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (tan x) (tan x))
35.0ms	(* (tan x) (tan x))
35.0ms	(* (tan x) (tan x))
161.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

simplify1.8s

Counts

127 → 127

Iterations

Iter	Nodes
3	2697
2	796
1	293
0	121

prune847.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes329.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	8
1	8
0	7

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.8s	1552×	body	1280	valid
1.7s	1239×	body	640	valid
965.0ms	4318×	body	80	valid
459.0ms	588×	body	320	valid
123.0ms	303×	body	160	valid