Details

sample337.0ms

Algorithm

intervals

Results

96.0ms	41×	body	640	valid
73.0ms	50×	body	1280	valid
34.0ms	140×	body	80	valid
11.0ms	17×	body	320	valid
4.0ms	8×	body	160	valid

simplify56.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 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))

rewrite81.0ms

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:

14.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
6.0ms	(- 1 (* (tan x) (tan x)))
24.0ms	(* (tan x) (tan x))
34.0ms	(* (tan x) (tan x))

series272.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
57.0ms	(- 1 (* (tan x) (tan x)))
37.0ms	(* (tan x) (tan x))
66.0ms	(* (tan x) (tan x))

simplify5.0s

Counts

140 → 140

Iterations

Iter	Nodes
3	2924
2	989
1	381
0	157

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 134

Calls

4 calls:

9.0ms	(+ 1 (tan x))
31.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
5.0ms	(- 1 (tan x))
26.0ms	(* (tan x) (tan x))

series188.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ 1 (tan x))
84.0ms	(* (+ 1 (tan x)) (- 1 (tan x)))
21.0ms	(- 1 (tan x))
56.0ms	(* (tan x) (tan x))

simplify8.2s

Counts

146 → 146

Iterations

Iter	Nodes
3	4399
2	1688
1	541
0	188

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 142

Calls

4 calls:

36.0ms	(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
24.0ms	(- 1 (/ (* (tan x) (sin x)) (cos x)))
18.0ms	(* (tan x) (sin x))
15.0ms	(* (tan x) (tan x))

series340.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (- 1 (/ (* (tan x) (sin x)) (cos x))) (+ 1 (* (tan x) (tan x))))
72.0ms	(- 1 (/ (* (tan x) (sin x)) (cos x)))
61.0ms	(* (tan x) (sin x))
59.0ms	(* (tan x) (tan x))

simplify31.0s

Counts

154 → 154

Iterations

Iter	Nodes
3	6567
2	1759
1	592
0	249

prune2.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
29×	`add-cube-cbrt`
27×	`prod-diff`
13×	`add-log-exp`
11×	`pow1` `associate-+l+` `flip3--` `flip--`
10×	`frac-add` `tan-quot`
6×	`fma-def` `add-cbrt-cube` `fma-neg` `add-exp-log` `difference-of-squares`
5×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `diff-log` `swap-sqr` `associate-r` `associate-l` `associate-*r/` `distribute-lft-out--`
2×	`sum-log`
1×	`pow2` `+-commutative` `flip3-+` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `associate-+l-` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 134

Calls

4 calls:

6.0ms	(- 1 (tan x))
5.0ms	(- 1 (tan x))
51.0ms	(+ (- 1 (tan x)) (* (- 1 (tan x)) (tan x)))
32.0ms	(* (tan x) (tan x))

series176.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- 1 (tan x))
37.0ms	(- 1 (tan x))
47.0ms	(+ (- 1 (tan x)) (* (- 1 (tan x)) (tan x)))
57.0ms	(* (tan x) (tan x))

simplify6.7s

Counts

146 → 146

Iterations

Iter	Nodes
3	7550
2	1818
1	495
0	185

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes372.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	10
1	10
0	8

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.7s	1520×	body	1280	valid
1.7s	1261×	body	640	valid
956.0ms	4317×	body	80	valid
470.0ms	600×	body	320	valid
232.0ms	302×	body	160	valid