Details

sample253.0ms

Algorithm

intervals

Results

53.0ms	52×	body	1280	valid
25.0ms	35×	body	640	valid
18.0ms	25×	body	320	valid
18.0ms	132×	body	80	valid
4.0ms	12×	body	160	valid

simplify59.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	42
5	42
4	37
3	29
2	22
1	13
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize76.0ms

Local error

Found 4 expressions with local error:

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

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
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×	`associate-/r*` `fma-neg` `prod-diff`
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 → 119

Calls

4 calls:

62.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
9.0ms	(- 1.0 (* (tan x) (tan x)))
24.0ms	(* (tan x) (tan x))
28.0ms	(* (tan x) (tan x))

series375.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
46.0ms	(- 1.0 (* (tan x) (tan x)))
53.0ms	(* (tan x) (tan x))
166.0ms	(* (tan x) (tan x))

simplify2.6s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
3	4089
2	1071
1	374
0	151

prune715.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 176

Calls

4 calls:

51.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
9.0ms	(- (sqrt 1.0) (tan x))
70.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
12.0ms	(* (tan x) (tan x))

series591.0ms

Counts

4 → 12

Calls

4 calls:

320.0ms	(/ (* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x))) (+ 1.0 (* (tan x) (tan x))))
51.0ms	(- (sqrt 1.0) (tan x))
175.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
45.0ms	(* (tan x) (tan x))

simplify2.9s

Counts

188 → 188

Iterations

Iter	Nodes
done	5001
2	2752
1	832
0	266

prune870.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

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-cbrt-cube` `add-exp-log`
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×	`associate-/r*` `fma-neg` `swap-sqr`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate-r/` `associate-/r/` `-commutative` `cbrt-unprod` `flip--` `unswap-sqr` `associate-/l/`
1×	`pow2` `frac-times` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `pow-plus` `diff-log` `div-sub` `div-exp` `associate-*l/` `pow-sqr` `pow-prod-up` `flip-+`

Counts

4 → 133

Calls

4 calls:

33.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
9.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
11.0ms	(* (sin x) (tan x))
12.0ms	(* (tan x) (tan x))

series360.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
75.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
64.0ms	(* (sin x) (tan x))
58.0ms	(* (tan x) (tan x))

simplify2.0s

Counts

145 → 145

Iterations

Iter	Nodes
done	5000
2	1797
1	610
0	242

prune961.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

15.0ms	(+ (sqrt 1.0) (tan x))
40.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))
67.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
18.0ms	(- (sqrt 1.0) (tan x))

series529.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+ (sqrt 1.0) (tan x))
132.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))
259.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
73.0ms	(- (sqrt 1.0) (tan x))

simplify2.0s

Counts

165 → 165

Iterations

Iter	Nodes
done	5002
2	1779
1	560
0	217

prune811.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

regimes336.0ms

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
done	11
1	11
0	9

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.5s	1554×	body	1280	valid
1.4s	1207×	body	640	valid
611.0ms	4285×	body	80	valid
235.0ms	637×	body	320	valid
86.0ms	317×	body	160	valid