Details

sample296.0ms

Algorithm

intervals

Results

82.0ms	31×	body	640	valid
73.0ms	45×	body	1280	valid
35.0ms	144×	body	80	valid
20.0ms	26×	body	320	valid
6.0ms	10×	body	160	valid

simplify60.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan x)))
0.2b	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite107.0ms

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:

11.0ms	(- 1 (* (tan x) (tan x)))
29.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
29.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))

series264.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- 1 (* (tan x) (tan x)))
112.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
34.0ms	(* (tan x) (tan x))
70.0ms	(* (tan x) (tan x))

simplify1.5s

Counts

140 → 140

Iterations

Iter	Nodes
done	2004
3	2004
2	1114
1	399
0	157

prune786.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`add-cube-cbrt`
18×	`prod-diff`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`frac-times` `associate-r`
8×	`flip3-+` `flip-+` `associate-/l/`
7×	`associate-l`
6×	`flip3--` `flip--` `add-log-exp`
5×	`associate-l/` `associate-r/`
4×	`expm1-log1p-u` `tan-quot` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `fma-def` `times-frac` `swap-sqr` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `sub-neg` `div-exp` `pow-prod-down` `associate-/r/` `*-commutative` `distribute-lft-out` `difference-of-squares` `unswap-sqr`
1×	`pow2` `+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-plus` `pow-sqr` `pow-prod-up` `div-inv` `associate-/l*` `distribute-lft-out--`

Counts

4 → 138

Calls

4 calls:

22.0ms	(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
5.0ms	(+ 1 (tan x))
25.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
14.0ms	(* (tan x) (tan x))

series360.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
29.0ms	(+ 1 (tan x))
99.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
54.0ms	(* (tan x) (tan x))

simplify1.5s

Counts

150 → 150

Iterations

Iter	Nodes
done	2000
2	2000
1	716
0	233

prune622.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (/ (* (tan x) (sin x)) (cos x)))
0.2b	(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
0.2b	(/ (* (tan x) (sin x)) (cos x))
0.3b	(* (tan x) (tan x))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
35×	`add-cube-cbrt`
30×	`times-frac`
21×	`prod-diff`
13×	`add-cbrt-cube` `add-exp-log`
11×	`pow1`
10×	`difference-of-squares`
7×	`associate-/l*`
6×	`associate-/r*` `add-log-exp`
5×	`tan-quot` `div-inv` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-neg` `swap-sqr` `div-exp` `associate-r` `associate-l` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `flip--`
1×	`pow2` `frac-times` `sub-neg` `flip3-+` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `associate-r/` `pow-sqr` `-commutative` `pow-prod-up` `flip-+` `unswap-sqr`

Counts

4 → 145

Calls

4 calls:

20.0ms	(- 1 (/ (* (tan x) (sin x)) (cos x)))
59.0ms	(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
30.0ms	(/ (* (tan x) (sin x)) (cos x))
21.0ms	(* (tan x) (tan x))

series422.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- 1 (/ (* (tan x) (sin x)) (cos x)))
168.0ms	(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
110.0ms	(/ (* (tan x) (sin x)) (cos x))
56.0ms	(* (tan x) (tan x))

simplify1.7s

Counts

157 → 157

Iterations

Iter	Nodes
done	2006
3	2006
2	1870
1	637
0	245

prune906.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
135×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
73×	`add-cube-cbrt`
24×	`difference-of-squares`
19×	`associate-/r*`
16×	`associate-/l*`
15×	`add-cbrt-cube` `add-exp-log`
11×	`pow1`
7×	`div-inv`
5×	`cbrt-undiv` `div-exp` `tan-quot`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`clear-num` `frac-2neg` `swap-sqr` `associate-r` `associate-l` `associate-/r/` `associate-/l/`
1×	`pow2` `frac-times` `flip3-+` `pow-plus` `flip3--` `div-sub` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `flip--` `unswap-sqr`

Counts

4 → 198

Calls

4 calls:

95.0ms	(/ (- 1 (/ (tan x) (/ (cos x) (sin x)))) (+ 1 (* (tan x) (tan x))))
19.0ms	(/ (cos x) (sin x))
23.0ms	(/ (tan x) (/ (cos x) (sin x)))
21.0ms	(* (tan x) (tan x))

series680.0ms

Counts

4 → 12

Calls

4 calls:

510.0ms	(/ (- 1 (/ (tan x) (/ (cos x) (sin x)))) (+ 1 (* (tan x) (tan x))))
20.0ms	(/ (cos x) (sin x))
106.0ms	(/ (tan x) (/ (cos x) (sin x)))
44.0ms	(* (tan x) (tan x))

simplify1.3s

Counts

210 → 210

Iterations

Iter	Nodes
done	2003
2	2003
1	829
0	336

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes236.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	9

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.8s	1494×	body	1280	valid
1.5s	1266×	body	640	valid
1.1s	4292×	body	80	valid
454.0ms	654×	body	320	valid
165.0ms	294×	body	160	valid