Details

sample384.0ms

Algorithm

intervals

Results

123.0ms	64×	body	1280	valid
35.0ms	38×	body	640	valid
27.0ms	128×	body	80	valid
9.0ms	16×	body	320	valid
5.0ms	10×	body	160	valid

simplify35.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	44
5	44
4	39
3	31
2	24
1	15
0	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.2b	(- 1 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
24×	`add-cube-cbrt`
18×	`pow1`
15×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
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 → 128

Calls

4 calls:

15.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
7.0ms	(- 1 (* (tan x) (tan x)))
14.0ms	(* (tan x) (tan x))
16.0ms	(* (tan x) (tan x))

series210.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
44.0ms	(- 1 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))
47.0ms	(* (tan x) (tan x))

simplify774.0ms

Counts

140 → 140

Iterations

Iter	Nodes
3	2763
2	985
1	382
0	157

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1 (* (tan x) (tan x)))
0.3b	(log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`pow1`
15×	`*-un-lft-identity`
14×	`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×	`insert-posit16` `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` `difference-of-squares` `unswap-sqr`
1×	`log1p-udef` `sub-neg` `flip3--` `diff-log` `log1p-expm1` `flip--`

Counts

4 → 97

Calls

4 calls:

14.0ms	(- 1 (* (tan x) (tan x)))
1.0ms	(log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))
30.0ms	(* (tan x) (tan x))
26.0ms	(* (tan x) (tan x))

series368.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- 1 (* (tan x) (tan x)))
227.0ms	(log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))
37.0ms	(* (tan x) (tan x))
59.0ms	(* (tan x) (tan x))

simplify3.2s

Counts

109 → 109

Iterations

Iter	Nodes
4	4469
3	1457
2	589
1	261
0	115

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(log (exp (log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1`
18×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `tan-quot` `add-exp-log`
6×	`swap-sqr` `associate-r` `associate-l`
5×	`expm1-log1p-u`
4×	`log-pow` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-prod`
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` `rem-log-exp` `log1p-expm1`

Counts

4 → 92

Calls

4 calls:

0.0ms	(log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))
15.0ms	(* (tan x) (tan x))
17.0ms	(* (tan x) (tan x))
3.0ms	(log (exp (log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))))

series586.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))
56.0ms	(* (tan x) (tan x))
42.0ms	(* (tan x) (tan x))
254.0ms	(log (exp (log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))))

simplify1.5s

Counts

104 → 104

Iterations

Iter	Nodes
4	3133
3	1057
2	461
1	204
0	103

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

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))
0.4b	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

143×	`times-frac`
136×	`add-sqr-sqrt`
135×	`prod-diff`
124×	`*-un-lft-identity`
116×	`add-cube-cbrt`
54×	`associate-/r/`
30×	`div-inv`
27×	`flip3-+` `flip-+`
25×	`pow1`
15×	`fma-neg`
12×	`tan-quot`
10×	`add-cbrt-cube` `add-exp-log`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`add-log-exp` `difference-of-squares`
5×	`distribute-rgt-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
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`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

4 → 273

Calls

4 calls:

30.0ms	(* (tan x) (tan x))
29.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))
54.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

series375.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (tan x) (tan x))
62.0ms	(* (tan x) (tan x))
59.0ms	(* (tan x) (tan x))
191.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

simplify4.0s

Counts

285 → 285

Iterations

Iter	Nodes
3	6239
2	1976
1	749
0	313

prune3.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes377.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	14
1	14
0	11

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.5s	1526×	body	1280	valid
1.5s	4322×	body	80	valid
1.1s	1238×	body	640	valid
417.0ms	615×	body	320	valid
118.0ms	299×	body	160	valid