Details

sample486.0ms

Algorithm

intervals

Results

261.0ms	45×	body	1280	valid
37.0ms	31×	body	640	valid
36.0ms	144×	body	80	valid
22.0ms	26×	body	320	valid
5.0ms	10×	body	160	valid

simplify56.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	38
5	38
4	36
3	28
2	23
1	15
0	7

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

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))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
22×	`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×	`insert-posit16`
3×	`associate-/r*`
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 → 114

Calls

4 calls:

14.0ms	(- 1 (* (tan x) (tan x)))
57.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
29.0ms	(* (tan x) (tan x))
51.0ms	(* (tan x) (tan x))

series446.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- 1 (* (tan x) (tan x)))
149.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
64.0ms	(* (tan x) (tan x))
175.0ms	(* (tan x) (tan x))

simplify1.4s

Counts

126 → 126

Iterations

Iter	Nodes
done	2000
3	2000
2	950
1	374
0	144

prune670.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

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))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`add-cube-cbrt`
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×	`tan-quot` `insert-posit16`
3×	`associate-/r*` `times-frac` `swap-sqr` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `cbrt-undiv` `sub-neg` `distribute-lft-in` `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 → 109

Calls

4 calls:

39.0ms	(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
9.0ms	(+ 1 (tan x))
45.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
27.0ms	(* (tan x) (tan x))

series368.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ (* (+ 1 (tan x)) (- 1 (tan x))) (+ 1 (* (tan x) (tan x))))
31.0ms	(+ 1 (tan x))
104.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
50.0ms	(* (tan x) (tan x))

simplify1.0s

Counts

121 → 121

Iterations

Iter	Nodes
done	2002
2	2002
1	529
0	181

prune531.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize47.0ms

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))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

136×	`pow1`
44×	`tan-quot`
39×	`pow-prod-up`
26×	`pow-prod-down`
25×	`pow-sqr`
22×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
21×	`pow-plus`
20×	`frac-times`
16×	`pow2` `*-un-lft-identity` `add-cube-cbrt`
14×	`associate-l/` `associate-r/`
11×	`prod-exp` `cbrt-unprod`
10×	`swap-sqr` `associate-r` `associate-l`
4×	`*-commutative` `insert-posit16` `add-log-exp` `unswap-sqr`

Counts

4 → 166

Calls

4 calls:

27.0ms	(* (tan x) (tan x))
27.0ms	(* (tan x) (tan x))
28.0ms	(* (tan x) (tan x))
126.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (tan x) (tan x))
65.0ms	(* (tan x) (tan x))
58.0ms	(* (tan x) (tan x))
81.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify1.7s

Counts

178 → 178

Iterations

Iter	Nodes
done	2009
4	2009
3	1922
2	954
1	318
0	108

prune711.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
21×	`times-frac` `add-cube-cbrt`
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` `distribute-lft-out--`
4×	`insert-posit16`
3×	`cbrt-undiv` `swap-sqr` `div-exp` `associate-r` `associate-l` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `prod-exp` `associate-*r/` `associate-/r/` `cbrt-unprod` `div-inv` `flip--`
1×	`pow2` `frac-times` `sub-neg` `flip3-+` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `pow-sqr` `-commutative` `pow-prod-up` `flip-+` `unswap-sqr`

Counts

4 → 113

Calls

4 calls:

8.0ms	(- 1 (/ (* (sin x) (tan x)) (cos x)))
26.0ms	(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (* (tan x) (tan x))))
14.0ms	(/ (* (sin x) (tan x)) (cos x))
20.0ms	(* (tan x) (tan x))

series382.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- 1 (/ (* (sin x) (tan x)) (cos x)))
146.0ms	(/ (- 1 (/ (* (sin x) (tan x)) (cos x))) (+ 1 (* (tan x) (tan x))))
98.0ms	(/ (* (sin x) (tan x)) (cos x))
61.0ms	(* (tan x) (tan x))

simplify1.5s

Counts

125 → 125

Iterations

Iter	Nodes
done	2066
3	2066
2	1491
1	495
0	187

prune744.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes271.0ms

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	9

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.8s	1494×	body	1280	valid
2.1s	1266×	body	640	valid
1.1s	4292×	body	80	valid
592.0ms	654×	body	320	valid
138.0ms	294×	body	160	valid