Details

sample228.0ms

Algorithm

intervals

Results

44.0ms	46×	body	1280	valid
18.0ms	34×	body	640	valid
15.0ms	139×	body	80	valid
7.0ms	21×	body	320	valid
4.0ms	16×	body	160	valid

simplify44.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

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

rewrite120.0ms

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:

39.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
11.0ms	(- 1.0 (* (tan x) (tan x)))
30.0ms	(* (tan x) (tan x))
35.0ms	(* (tan x) (tan x))

series389.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
64.0ms	(- 1.0 (* (tan x) (tan x)))
77.0ms	(* (tan x) (tan x))
77.0ms	(* (tan x) (tan x))

simplify673.0ms

Counts: 117 → 117

prune363.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
28×	`add-cube-cbrt`
21×	`pow1` `add-exp-log` `associate-r`
20×	`times-frac`
15×	`add-cbrt-cube`
10×	`associate-l`
8×	`tan-quot`
6×	`swap-sqr` `prod-exp`
5×	`unswap-sqr`
4×	`frac-times` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`associate-r/` `pow-prod-down` `associate-/r` `-commutative` `associate-/l`
2×	`cbrt-undiv` `pow2` `rec-exp` `flip3--` `flip3-+` `pow-plus` `1-exp` `pow-sqr` `pow-prod-up` `flip--` `flip-+` `div-inv`
1×	`pow-flip` `frac-2neg` `clear-num` `un-div-inv` `inv-pow` `difference-of-squares`

Counts

4 → 132

Calls

4 calls:

10.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
65.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
15.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

series330.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
133.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
69.0ms	(* (tan x) (tan x))
56.0ms	(* (tan x) (tan x))

simplify909.0ms

Counts: 144 → 144

prune361.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

24.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
28.0ms	(* (tan x) (sin x))
31.0ms	(/ (* (tan x) (sin x)) (cos x))
21.0ms	(* (tan x) (tan x))

series321.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
63.0ms	(* (tan x) (sin x))
125.0ms	(/ (* (tan x) (sin x)) (cos x))
43.0ms	(* (tan x) (tan x))

simplify723.0ms

Counts: 95 → 95

prune391.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin x))
0.2b	(* (tan x) (sin x))
0.2b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(/ (* (tan x) (sin x)) (cos x))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`times-frac` `associate-r` `associate-l` `associate-/r*`
4×	`tan-quot` `cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l/` `associate-/l` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

15.0ms	(* (tan x) (sin x))
21.0ms	(* (tan x) (sin x))
32.0ms	(/ (* (tan x) (sin x)) (cos x))
33.0ms	(/ (* (tan x) (sin x)) (cos x))

series315.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (tan x) (sin x))
58.0ms	(* (tan x) (sin x))
89.0ms	(/ (* (tan x) (sin x)) (cos x))
107.0ms	(/ (* (tan x) (sin x)) (cos x))

simplify566.0ms

Counts: 94 → 94

prune425.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes382.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0s

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.7s	1198×	body	640	valid
1.6s	1546×	body	1280	valid
654.0ms	4315×	body	80	valid
307.0ms	647×	body	320	valid
81.0ms	294×	body	160	valid