Details

sample260.0ms

Algorithm

intervals

Results

90.0ms	41×	body	1280	valid
28.0ms	145×	body	80	valid
26.0ms	35×	body	640	valid
18.0ms	27×	body	320	valid
4.0ms	8×	body	160	valid

simplify59.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	47
6	47
5	45
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

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

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:

29.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
10.0ms	(- 1 (* (tan x) (tan x)))
28.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))

series294.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
52.0ms	(- 1 (* (tan x) (tan x)))
48.0ms	(* (tan x) (tan x))
59.0ms	(* (tan x) (tan x))

simplify3.3s

Counts

140 → 140

Iterations

Iter	Nodes
done	5000
2	2541
1	418
0	157

prune548.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

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:

13.0ms	(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
14.0ms	(- 1 (tan x))
9.0ms	(+ 1 (tan x))
32.0ms	(* (+ 1 (tan x)) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (- 1 (tan x)) (fma (tan x) (tan x) 1))
38.0ms	(- 1 (tan x))
30.0ms	(+ 1 (tan x))
153.0ms	(* (+ 1 (tan x)) (/ (- 1 (tan x)) (fma (tan x) (tan x) 1)))

simplify2.8s

Counts

154 → 154

Iterations

Iter	Nodes
done	5000
2	3330
1	546
0	208

prune677.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

rewrite163.0ms

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×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

4 → 174

Calls

4 calls:

28.0ms	(* (tan x) (tan x))
22.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))
94.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (tan x) (tan x))
58.0ms	(* (tan x) (tan x))
53.0ms	(* (tan x) (tan x))
64.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify1.4s

Counts

186 → 186

Iterations

Iter	Nodes
done	5000
2	1981
1	346
0	112

prune653.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

13.0ms	(* (tan x) (sin x))
11.0ms	(- 1 (/ (* (tan x) (sin x)) (cos x)))
24.0ms	(/ (* (tan x) (sin x)) (cos x))
18.0ms	(* (tan x) (tan x))

series266.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (tan x) (sin x))
57.0ms	(- 1 (/ (* (tan x) (sin x)) (cos x)))
87.0ms	(/ (* (tan x) (sin x)) (cos x))
57.0ms	(* (tan x) (tan x))

simplify2.4s

Counts

132 → 132

Iterations

Iter	Nodes
done	5000
2	2995
1	498
0	196

prune604.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes464.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	10

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.9s	1509×	body	1280	valid
1.4s	1338×	body	640	valid
962.0ms	4234×	body	80	valid
518.0ms	600×	body	320	valid
136.0ms	319×	body	160	valid