Details

sample304.0ms

Algorithm

intervals

Results

134.0ms	45×	body	1280	valid
49.0ms	44×	body	640	valid
33.0ms	138×	body	80	valid
15.0ms	20×	body	320	valid
5.0ms	9×	body	160	valid

simplify111.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.1b	(- 1 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

192×	`*-un-lft-identity`
180×	`add-sqr-sqrt`
75×	`times-frac`
70×	`difference-of-squares`
65×	`add-cube-cbrt`
45×	`prod-diff`
38×	`associate-l`
32×	`distribute-lft-out`
29×	`swap-sqr`
19×	`*-commutative` `unswap-sqr`
18×	`pow1`
15×	`associate-r` `associate-/l*`
14×	`distribute-lft-out--`
10×	`add-cbrt-cube` `add-exp-log`
8×	`tan-quot`
6×	`add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg`
2×	`pow2` `frac-times` `pow-plus` `flip3--` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `associate-/r/` `pow-sqr` `pow-prod-up` `cbrt-unprod` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 252

Calls

4 calls:

119.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
59.0ms	(- 1 (* (tan x) (tan x)))
32.0ms	(* (tan x) (tan x))
34.0ms	(* (tan x) (tan x))

series375.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
128.0ms	(- 1 (* (tan x) (tan x)))
78.0ms	(* (tan x) (tan x))
69.0ms	(* (tan x) (tan x))

simplify2.1s

Counts

264 → 264

Iterations

Iter	Nodes
done	5000
2	1564
1	612
0	267

prune646.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 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))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
45×	`prod-diff`
43×	`add-cube-cbrt`
18×	`pow1`
17×	`swap-sqr`
16×	`associate-l`
15×	`associate-r`
10×	`difference-of-squares`
8×	`add-cbrt-cube` `tan-quot` `add-exp-log`
7×	`*-commutative` `unswap-sqr`
6×	`add-log-exp`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u`
3×	`fma-neg`
2×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `pow-prod-up` `cbrt-unprod` `distribute-lft-out--`
1×	`log1p-udef` `sub-neg` `flip3--` `diff-log` `log1p-expm1` `flip--`

Counts

4 → 149

Calls

4 calls:

24.0ms	(- 1 (* (tan x) (tan x)))
0.0ms	(log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))
24.0ms	(* (tan x) (tan x))
19.0ms	(* (tan x) (tan x))

series385.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- 1 (* (tan x) (tan x)))
224.0ms	(log1p (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))
44.0ms	(* (tan x) (tan x))
59.0ms	(* (tan x) (tan x))

simplify2.9s

Counts

161 → 161

Iterations

Iter	Nodes
done	5001
3	2555
2	1068
1	438
0	197

prune537.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(log (+ 1 (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.4b	(+ 1 (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))

rewrite411.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1`
18×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
9×	`add-exp-log`
8×	`add-cbrt-cube` `tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log-prod` `insert-posit16` `log1p-expm1-u`
3×	`fma-def`
2×	`pow2` `frac-times` `log-div` `flip3-+` `pow-plus` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `sum-log` `log1p-def` `div-sub` `rem-log-exp` `log-pow`

Counts

4 → 100

Calls

4 calls:

172.0ms	(log (+ 1 (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
32.0ms	(* (tan x) (tan x))
19.0ms	(* (tan x) (tan x))
183.0ms	(+ 1 (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))

series556.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(log (+ 1 (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))
60.0ms	(* (tan x) (tan x))
38.0ms	(* (tan x) (tan x))
174.0ms	(+ 1 (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))

simplify2.3s

Counts

112 → 112

Iterations

Iter	Nodes
done	5002
3	1721
2	698
1	281
0	114

prune621.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (tan x) (tan x) 1)
0.2b	(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
0.2b	(- 1 (tan x))
0.2b	(* (+ (tan x) 1) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt` `*-un-lft-identity`
39×	`add-cube-cbrt`
37×	`times-frac`
28×	`frac-times`
26×	`associate-/l*`
22×	`associate-r` `difference-of-squares`
15×	`flip3-+` `flip-+`
14×	`associate-*r/`
12×	`associate-/r*` `distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
8×	`associate-/l/`
6×	`pow1` `add-log-exp`
5×	`clear-num` `flip3--` `flip--`
4×	`expm1-log1p-u` `frac-2neg` `associate-l` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `un-div-inv`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`sub-neg` `diff-log` `div-sub` `pow-prod-down` `*-commutative` `fma-udef` `distribute-lft-out`

Counts

4 → 177

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1)
31.0ms	(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
13.0ms	(- 1 (tan x))
105.0ms	(* (+ (tan x) 1) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(fma (tan x) (tan x) 1)
99.0ms	(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
27.0ms	(- 1 (tan x))
142.0ms	(* (+ (tan x) 1) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))

simplify2.3s

Counts

189 → 189

Iterations

Iter	Nodes
done	5000
2	2321
1	700
0	260

prune865.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes315.0ms

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	14
1	14
0	10

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.4s	1443×	body	1280	valid
1.5s	4414×	body	80	valid
1.3s	1183×	body	640	valid
484.0ms	647×	body	320	valid
186.0ms	313×	body	160	valid