Details

sample275.0ms

Algorithm

intervals

Results

90.0ms	51×	body	640	valid
49.0ms	46×	body	1280	valid
21.0ms	133×	body	80	valid
10.0ms	20×	body	320	valid
2.0ms	6×	body	160	valid

simplify53.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	42
5	42
4	37
3	29
2	22
1	13
0	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize53.0ms

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))

rewrite94.0ms

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:

9.0ms	(- 1 (* (tan x) (tan x)))
26.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
26.0ms	(* (tan x) (tan x))
29.0ms	(* (tan x) (tan x))

series267.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- 1 (* (tan x) (tan x)))
103.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
38.0ms	(* (tan x) (tan x))
89.0ms	(* (tan x) (tan x))

simplify4.7s

Counts

140 → 140

Iterations

Iter	Nodes
3	2926
2	985
1	383
0	157

prune634.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
37×	`times-frac`
34×	`add-cube-cbrt`
22×	`associate-r`
16×	`difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
8×	`distribute-lft-out--` `add-log-exp`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `fma-def` `flip3-+` `fma-neg` `flip-+`
2×	`frac-times` `cbrt-undiv` `flip3--` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `flip--` `distribute-lft-out` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 142

Calls

4 calls:

14.0ms	(+ (tan x) 1)
10.0ms	(- 1 (tan x))
26.0ms	(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
45.0ms	(* (+ (tan x) 1) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (tan x) 1)
36.0ms	(- 1 (tan x))
107.0ms	(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
158.0ms	(* (+ (tan x) 1) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))

simplify10.1s

Counts

154 → 154

Iterations

Iter	Nodes
3	5364
2	1506
1	511
0	211

prune684.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

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)))))

rewrite119.0ms

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:

14.0ms	(* (tan x) (tan x))
19.0ms	(* (tan x) (tan x))
23.0ms	(* (tan x) (tan x))
57.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

series330.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (tan x) (tan x))
58.0ms	(* (tan x) (tan x))
61.0ms	(* (tan x) (tan x))
167.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

simplify48.7s

Counts

285 → 285

Iterations

Iter	Nodes
3	6505
2	1998
1	750
0	313

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(- 1 (/ (sin x) (cos x)))
0.2b	(- 1 (/ (sin x) (cos x)))
0.3b	(fma (- 1 (/ (sin x) (cos x))) (/ (sin x) (cos x)) (- 1 (/ (sin x) (cos x))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
90×	`*-un-lft-identity`
82×	`add-cube-cbrt`
78×	`prod-diff`
67×	`times-frac`
8×	`add-log-exp` `difference-of-squares`
7×	`div-inv`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`cbrt-undiv` `quot-tan` `clear-num` `frac-2neg` `div-exp` `fma-udef`

Counts

4 → 166

Calls

4 calls:

17.0ms	(/ (sin x) (cos x))
24.0ms	(- 1 (/ (sin x) (cos x)))
29.0ms	(- 1 (/ (sin x) (cos x)))
1.0ms	(fma (- 1 (/ (sin x) (cos x))) (/ (sin x) (cos x)) (- 1 (/ (sin x) (cos x))))

series200.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (sin x) (cos x))
22.0ms	(- 1 (/ (sin x) (cos x)))
33.0ms	(- 1 (/ (sin x) (cos x)))
124.0ms	(fma (- 1 (/ (sin x) (cos x))) (/ (sin x) (cos x)) (- 1 (/ (sin x) (cos x))))

simplify3.2s

Counts

178 → 178

Iterations

Iter	Nodes
3	3727
2	1318
1	496
0	212

prune492.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes195.0ms

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
2	9
1	9
0	8

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.7s	1521×	body	1280	valid
1.1s	1284×	body	640	valid
887.0ms	4276×	body	80	valid
403.0ms	631×	body	320	valid
112.0ms	288×	body	160	valid