Details

sample302.0ms

Algorithm

intervals

Results

23.0ms	51×	body	1280	valid
10.0ms	36×	body	640	valid
7.0ms	128×	body	80	valid
4.0ms	21×	body	160	valid
4.0ms	20×	body	320	valid

simplify31.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	22	14
3	29	14
4	37	14
5	42	14
6	44	14
done	44	14

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

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))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`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×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `prod-diff` `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 → 119

Calls

4 calls:

8.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series210.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(- 1.0 (* (tan x) (tan x)))
39.0ms	(* (tan x) (tan x))
43.0ms	(* (tan x) (tan x))

simplify1.7s

Counts

131 → 131

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	151	1789
1	336	1638
2	918	1453
3	3278	1419
done	5000	1418

prune319.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (sqrt 1.0) (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))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

5.0ms	(+ (sqrt 1.0) (tan x))
6.0ms	(- (sqrt 1.0) (tan x))
34.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
5.0ms	(* (tan x) (tan x))

series217.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (sqrt 1.0) (tan x))
38.0ms	(- (sqrt 1.0) (tan x))
111.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
33.0ms	(* (tan x) (tan x))

simplify838.0ms

Counts

175 → 175

Iterations

Useful iterations: 2 (335.0ms)

Iter	Nodes	Cost
0	210	3440
1	539	2534
2	1724	1952
done	5001	1952

prune356.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (tan x) (tan x) 1.0)
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
3.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
1.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(fma (tan x) (tan x) 1.0)
35.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(* (tan x) (tan x))
235.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0)))

simplify1.1s

Counts

84 → 84

Iterations

Useful iterations: 3 (474.0ms)

Iter	Nodes	Cost
0	131	993
1	262	914
2	715	820
3	2535	793
done	5000	793

prune266.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
72×	`*-un-lft-identity` `prod-diff`
64×	`add-cube-cbrt`
60×	`exp-sum`
46×	`log-prod`
42×	`sqrt-prod`
23×	`distribute-rgt-in` `distribute-lft-in`
14×	`pow1`
13×	`associate-r`
12×	`exp-prod`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-l` `log-pow`
6×	`fma-neg` `difference-of-squares`
4×	`tan-quot` `expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`swap-sqr` `associate-*l/` `distribute-lft-out--`
2×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`pow2` `frac-times` `flip3--` `flip3-+` `pow-plus` `exp-diff` `associate-*r/` `pow-sqr` `pow-prod-up` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 185

Calls

4 calls:

6.0ms	(- (sqrt 1.0) (tan x))
66.0ms	(* (+ (sqrt 1.0) (tan x)) (log (exp (- (sqrt 1.0) (tan x)))))
5.0ms	(* (tan x) (tan x))
14.0ms	(exp (- (sqrt 1.0) (tan x)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (sqrt 1.0) (tan x))
105.0ms	(* (+ (sqrt 1.0) (tan x)) (log (exp (- (sqrt 1.0) (tan x)))))
37.0ms	(* (tan x) (tan x))
73.0ms	(exp (- (sqrt 1.0) (tan x)))

simplify906.0ms

Counts

197 → 197

Iterations

Useful iterations: done (900.0ms)

Iter	Nodes	Cost
0	272	4294
1	613	2989
2	1721	1800
done	5000	1797

prune355.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes131.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	15	21
done	15	21

end0.0ms

sample1.6s

Algorithm

intervals

Results

648.0ms	1450×	body	1280	valid
377.0ms	1309×	body	640	valid
243.0ms	4314×	body	80	valid
118.0ms	598×	body	320	valid
51.0ms	329×	body	160	valid