Details

sample157.0ms

Algorithm

intervals

Results

33.0ms	37×	body	1280	valid
19.0ms	34×	body	640	valid
17.0ms	149×	body	80	valid
10.0ms	25×	body	320	valid
3.0ms	11×	body	160	valid

simplify107.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	45
6	45
5	43
4	37
3	29
2	22
1	13
0	7

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
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 → 119

Calls

4 calls:

18.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
14.0ms	(- 1.0 (* (tan x) (tan x)))
23.0ms	(* (tan x) (tan x))
29.0ms	(* (tan x) (tan x))

series340.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
41.0ms	(- 1.0 (* (tan x) (tan x)))
73.0ms	(* (tan x) (tan x))
82.0ms	(* (tan x) (tan x))

simplify1.4s

Counts

131 → 131

Iterations

Iter	Nodes
done	5001
2	1700
1	376
0	151

prune634.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (fma (tan x) (tan x) 1.0))
0.2b	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (fma (tan x) (tan x) 1.0)))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(* (tan x) (tan x))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
26×	`add-cube-cbrt`
20×	`times-frac`
19×	`add-exp-log`
16×	`associate-r`
14×	`pow1`
13×	`add-cbrt-cube`
7×	`associate-l`
6×	`add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `tan-quot` `log1p-expm1-u` `unswap-sqr`
3×	`frac-times` `associate-/r` `flip3--` `fma-neg` `swap-sqr` `prod-diff` `associate-l/` `cbrt-unprod` `flip--` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv` `difference-of-squares`
1×	`pow2` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `pow-sqr` `un-div-inv` `pow-prod-up` `pow-flip` `inv-pow`

Counts

4 → 127

Calls

4 calls:

13.0ms	(/ 1 (fma (tan x) (tan x) 1.0))
35.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (fma (tan x) (tan x) 1.0)))
5.0ms	(- 1.0 (* (tan x) (tan x)))
12.0ms	(* (tan x) (tan x))

series406.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ 1 (fma (tan x) (tan x) 1.0))
183.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (fma (tan x) (tan x) 1.0)))
60.0ms	(- 1.0 (* (tan x) (tan x)))
63.0ms	(* (tan x) (tan x))

simplify4.1s

Counts

139 → 139

Iterations

Iter	Nodes
done	5001
2	3348
1	453
0	189

prune646.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (tan x) (tan x) 1.0)
0.1b	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(* (tan x) (tan x))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

0.0ms	(fma (tan x) (tan x) 1.0)
24.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
9.0ms	(- 1.0 (* (tan x) (tan x)))
23.0ms	(* (tan x) (tan x))

series365.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(fma (tan x) (tan x) 1.0)
190.0ms	(/ (- 1.0 (* (tan x) (tan x))) (fma (tan x) (tan x) 1.0))
62.0ms	(- 1.0 (* (tan x) (tan x)))
63.0ms	(* (tan x) (tan x))

simplify1.2s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
2	1601
1	370
0	155

prune591.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
0.1b	(* (tan x) (sin x))
0.2b	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
0.2b	(* (tan x) (tan x))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
34×	`add-cube-cbrt`
24×	`times-frac`
21×	`prod-diff`
13×	`pow1`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`tan-quot` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `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 → 133

Calls

4 calls:

62.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
22.0ms	(* (tan x) (sin x))
19.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
30.0ms	(* (tan x) (tan x))

series442.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
66.0ms	(* (tan x) (sin x))
99.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
69.0ms	(* (tan x) (tan x))

simplify1.7s

Counts

145 → 145

Iterations

Iter	Nodes
done	5001
2	2916
1	606
0	242

prune631.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes179.0ms

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	9
0	9

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.6s	1524×	body	1280	valid
1.5s	4241×	body	80	valid
788.0ms	1272×	body	640	valid
270.0ms	632×	body	320	valid
90.0ms	331×	body	160	valid