Details

sample372.0ms

Algorithm

intervals

Results

75.0ms	47×	body	1280	valid
63.0ms	40×	body	640	valid
17.0ms	138×	body	80	valid
9.0ms	19×	body	320	valid
4.0ms	12×	body	160	valid

simplify291.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	7	257
1	13	257
2	22	257
3	29	257
4	37	257
5	43	257
6	45	257
done	45	257

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize77.0ms

Local error

Found 4 expressions with local error:

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

rewrite99.0ms

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:

6.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
28.0ms	(* (tan x) (tan x))
28.0ms	(* (tan x) (tan x))

series271.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- 1.0 (* (tan x) (tan x)))
111.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
46.0ms	(* (tan x) (tan x))
78.0ms	(* (tan x) (tan x))

simplify1.9s

Counts

131 → 131

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	151	42422
1	376	35971
2	1697	34713
done	5001	34586

prune737.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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))
46.3b	(fma (- (tan x)) (tan x) (* (tan x) (tan x)))

rewrite53.0ms

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:

15.0ms	(* (tan x) (tan x))
12.0ms	(* (tan x) (tan x))
22.0ms	(* (tan x) (tan x))
1.0ms	(fma (- (tan x)) (tan x) (* (tan x) (tan x)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (tan x) (tan x))
45.0ms	(* (tan x) (tan x))
54.0ms	(* (tan x) (tan x))
155.0ms	(fma (- (tan x)) (tan x) (* (tan x) (tan x)))

simplify6.9s

Counts

112 → 112

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	64	25628
1	144	20675
2	635	19907
3	4739	19352
done	5000	19352

prune622.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

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))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
28×	`add-cube-cbrt`
21×	`pow1` `associate-r` `add-exp-log`
20×	`times-frac`
15×	`add-cbrt-cube`
10×	`associate-l`
8×	`tan-quot`
6×	`swap-sqr` `prod-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `pow-prod-down` `associate-r/` `-commutative` `associate-/l`
2×	`pow2` `cbrt-undiv` `rec-exp` `flip3-+` `pow-plus` `flip3--` `1-exp` `pow-sqr` `pow-prod-up` `flip-+` `div-inv` `flip--`
1×	`clear-num` `frac-2neg` `un-div-inv` `pow-flip` `inv-pow` `difference-of-squares`

Counts

4 → 140

Calls

4 calls:

18.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
56.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
23.0ms	(* (tan x) (tan x))
24.0ms	(* (tan x) (tan x))

series334.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ 1 (+ 1.0 (* (tan x) (tan x))))
118.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
62.0ms	(* (tan x) (tan x))
63.0ms	(* (tan x) (tan x))

simplify3.5s

Counts

152 → 152

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	175	49988
1	453	40444
2	3188	37664
done	5001	37419

prune649.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
0.3b	(* (tan x) (tan x))
0.3b	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

5.0ms	(- 1.0 (* (tan x) (tan x)))
16.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
28.0ms	(* (tan x) (tan x))
23.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))))

series431.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- 1.0 (* (tan x) (tan x)))
173.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
44.0ms	(* (tan x) (tan x))
149.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))))

simplify2.1s

Counts

130 → 130

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	202	50939
1	425	40928
2	1778	40146
done	5000	40009

prune682.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes301.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	392
1	12	392
done	12	392

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.3s	1465×	body	1280	valid
1.2s	4287×	body	80	valid
851.0ms	1308×	body	640	valid
570.0ms	342×	body	160	valid
223.0ms	598×	body	320	valid