Details

sample231.0ms

Algorithm

intervals

Results

50.0ms	49×	body	1280	valid
31.0ms	44×	body	640	valid
20.0ms	124×	body	80	valid
12.0ms	26×	body	320	valid
4.0ms	13×	body	160	valid

simplify406.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	45
6	45
5	43
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

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 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))

rewrite118.0ms

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))))
26.0ms	(- 1.0 (* (tan x) (tan x)))
24.0ms	(* (tan x) (tan x))
29.0ms	(* (tan x) (tan x))

series310.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
54.0ms	(- 1.0 (* (tan x) (tan x)))
49.0ms	(* (tan x) (tan x))
71.0ms	(* (tan x) (tan x))

simplify1.9s

Counts

131 → 131

Iterations

Iter	Nodes
done	5001
2	1700
1	376
0	151

prune832.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
45.1b	(fma (- (tan x)) (tan x) (* (tan x) (tan x)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
22×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
12×	`tan-quot`
10×	`add-cbrt-cube` `add-exp-log`
9×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
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`
1×	`fma-udef`

Counts

4 → 100

Calls

4 calls:

16.0ms	(* (tan x) (tan x))
14.0ms	(* (tan x) (tan x))
17.0ms	(* (tan x) (tan x))
0.0ms	(fma (- (tan x)) (tan x) (* (tan x) (tan x)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (tan x) (tan x))
45.0ms	(* (tan x) (tan x))
60.0ms	(* (tan x) (tan x))
178.0ms	(fma (- (tan x)) (tan x) (* (tan x) (tan x)))

simplify6.4s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
3	4739
2	635
1	144
0	64

prune655.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`prod-diff`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`times-frac`
6×	`associate-r` `associate-l` `tan-quot` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/r` `fma-neg` `swap-sqr` `associate-l/` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`pow2` `frac-times` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `flip3--` `diff-log` `associate-r/` `pow-sqr` `pow-prod-up` `flip--` `associate-/l` `distribute-lft-out--` `difference-of-squares` `associate-/l/`

Counts

4 → 115

Calls

4 calls:

24.0ms	(/ (* (tan x) (sin x)) (cos x))
12.0ms	(* (tan x) (sin x))
10.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
21.0ms	(* (tan x) (tan x))

series282.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (* (tan x) (sin x)) (cos x))
60.0ms	(* (tan x) (sin x))
69.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
65.0ms	(* (tan x) (tan x))

simplify2.0s

Counts

127 → 127

Iterations

Iter	Nodes
done	5000
2	2750
1	482
0	192

prune825.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

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))
0.3b	(+ (sqrt 1.0) (tan x))

rewrite108.0ms

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:

12.0ms	(- (sqrt 1.0) (tan x))
52.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
24.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))
14.0ms	(+ (sqrt 1.0) (tan x))

series529.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (sqrt 1.0) (tan x))
287.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0)))
150.0ms	(/ (- (sqrt 1.0) (tan x)) (fma (tan x) (tan x) 1.0))
38.0ms	(+ (sqrt 1.0) (tan x))

simplify2.5s

Counts

165 → 165

Iterations

Iter	Nodes
done	5001
2	3331
1	564
0	217

prune680.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes288.0ms

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	13
1	13
0	11

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.8s	1455×	body	1280	valid
767.0ms	1236×	body	640	valid
642.0ms	4389×	body	80	valid
477.0ms	312×	body	160	valid
267.0ms	608×	body	320	valid