Details

sample325.0ms

Algorithm

intervals

Results

129.0ms	56×	body	1280	valid
45.0ms	37×	body	640	valid
35.0ms	136×	body	80	valid
20.0ms	23×	body	320	valid
2.0ms	4×	body	160	valid

simplify81.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan x)))
0.1b	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite165.0ms

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:

9.0ms	(- 1 (* (tan x) (tan x)))
20.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
51.0ms	(* (tan x) (tan x))
80.0ms	(* (tan x) (tan x))

series351.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- 1 (* (tan x) (tan x)))
150.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
58.0ms	(* (tan x) (tan x))
86.0ms	(* (tan x) (tan x))

simplify4.4s

Counts

126 → 126

Iterations

Iter	Nodes
3	2955
2	941
1	358
0	144

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
0.2b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(* (tan x) (sin x))
0.3b	(* (tan x) (tan x))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

34.0ms	(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
25.0ms	(/ (* (tan x) (sin x)) (cos x))
17.0ms	(* (tan x) (sin x))
16.0ms	(* (tan x) (tan x))

series303.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
73.0ms	(/ (* (tan x) (sin x)) (cos x))
57.0ms	(* (tan x) (sin x))
46.0ms	(* (tan x) (tan x))

simplify25.9s

Counts

129 → 129

Iterations

Iter	Nodes
3	5519
2	1447
1	478
0	197

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1 (/ (tan x) (/ (cos x) (sin x)))) (+ 1 (* (tan x) (tan x))))
0.2b	(/ (cos x) (sin x))
0.3b	(/ (tan x) (/ (cos x) (sin x)))
0.3b	(* (tan x) (tan x))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
135×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
73×	`add-cube-cbrt`
24×	`difference-of-squares`
19×	`associate-/r*`
16×	`associate-/l*`
15×	`add-cbrt-cube` `add-exp-log`
11×	`pow1`
7×	`div-inv`
5×	`cbrt-undiv` `div-exp` `tan-quot`
4×	`insert-posit16` `distribute-lft-out--` `add-log-exp`
3×	`clear-num` `frac-2neg` `swap-sqr` `associate-r` `associate-l` `associate-/r/` `associate-/l/`
1×	`pow2` `frac-times` `flip3-+` `pow-plus` `flip3--` `div-sub` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `flip--` `unswap-sqr`

Counts

4 → 190

Calls

4 calls:

67.0ms	(/ (- 1 (/ (tan x) (/ (cos x) (sin x)))) (+ 1 (* (tan x) (tan x))))
15.0ms	(/ (cos x) (sin x))
13.0ms	(/ (tan x) (/ (cos x) (sin x)))
18.0ms	(* (tan x) (tan x))

series295.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- 1 (/ (tan x) (/ (cos x) (sin x)))) (+ 1 (* (tan x) (tan x))))
31.0ms	(/ (cos x) (sin x))
83.0ms	(/ (tan x) (/ (cos x) (sin x)))
43.0ms	(* (tan x) (tan x))

simplify1.3s

Counts

202 → 202

Iterations

Iter	Nodes
2	2373
1	797
0	328

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

7.0ms	(- 1 (tan x))
7.0ms	(+ 1 (tan x))
49.0ms	(/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x)))
20.0ms	(* (tan x) (tan x))

series440.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- 1 (tan x))
18.0ms	(+ 1 (tan x))
338.0ms	(/ (+ 1 (* (tan x) (tan x))) (- 1 (tan x)))
52.0ms	(* (tan x) (tan x))

simplify2.7s

Counts

114 → 114

Iterations

Iter	Nodes
3	2726
2	1002
1	389
0	168

prune908.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes319.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	15
1	15
0	12

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.7s	1518×	body	1280	valid
1.3s	1247×	body	640	valid
1.0s	4361×	body	80	valid
911.0ms	576×	body	320	valid
161.0ms	298×	body	160	valid