Details

sample203.0ms

Algorithm

intervals

Results

40.0ms	45×	body	1280	valid
18.0ms	144×	body	80	valid
16.0ms	29×	body	640	valid
10.0ms	26×	body	320	valid
3.0ms	12×	body	160	valid

simplify62.0ms

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

localize25.0ms

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))

rewrite378.0ms

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:

29.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
315.0ms	(- 1.0 (* (tan x) (tan x)))
13.0ms	(* (tan x) (tan x))
14.0ms	(* (tan x) (tan x))

series337.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
54.0ms	(- 1.0 (* (tan x) (tan x)))
74.0ms	(* (tan x) (tan x))
78.0ms	(* (tan x) (tan x))

simplify3.0s

Counts

131 → 131

Iterations

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

prune737.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `tan-quot` `add-exp-log`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`log1p-udef` `sub-neg` `flip3--` `diff-log` `log1p-expm1` `flip--` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

9.0ms	(- 1.0 (* (tan x) (tan x)))
15.0ms	(* (tan x) (tan x))
12.0ms	(* (tan x) (tan x))
0.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))

series518.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- 1.0 (* (tan x) (tan x)))
62.0ms	(* (tan x) (tan x))
36.0ms	(* (tan x) (tan x))
369.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))

simplify2.2s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
3	1894
2	706
1	285
0	119

prune594.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite159.0ms

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:

17.0ms	(- (sqrt 1.0) (tan x))
95.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
30.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))
7.0ms	(+ (sqrt 1.0) (tan x))

series496.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (sqrt 1.0) (tan x))
247.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
149.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))
62.0ms	(+ (sqrt 1.0) (tan x))

simplify1.9s

Counts

165 → 165

Iterations

Iter	Nodes
done	5001
2	1777
1	561
0	217

prune921.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

294×	`times-frac`
252×	`add-sqr-sqrt`
194×	`*-un-lft-identity`
138×	`add-cube-cbrt`
77×	`associate-r`
50×	`difference-of-squares`
36×	`add-exp-log`
30×	`associate-/r*`
28×	`sqrt-prod`
25×	`distribute-lft-out--`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
10×	`div-inv`
8×	`flip3--` `flip--`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`fma-def` `associate-/l*` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-l` `log1p-expm1-u`
3×	`flip3-+` `cbrt-unprod` `flip-+`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*l/` `distribute-lft-out`
1×	`+-commutative` `sum-log` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 298

Calls

4 calls:

36.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))))
117.0ms	(* (+ (sqrt 1.0) (tan x)) (/ 1 (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x)))))
15.0ms	(+ (sqrt 1.0) (tan x))
25.0ms	(/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x)))

series709.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x))))
339.0ms	(* (+ (sqrt 1.0) (tan x)) (/ 1 (/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x)))))
61.0ms	(+ (sqrt 1.0) (tan x))
183.0ms	(/ (fma (tan x) (tan x) 1.0) (- (sqrt 1.0) (tan x)))

simplify2.8s

Counts

310 → 310

Iterations

Iter	Nodes
done	5001
2	2853
1	1004
0	364

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes479.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	16
1	16
0	12

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.4s	1530×	body	1280	valid
1.3s	1195×	body	640	valid
1.1s	4291×	body	80	valid
288.0ms	655×	body	320	valid
159.0ms	329×	body	160	valid