Details

sample714.0ms

Algorithm

intervals

Results

261.0ms	52×	body	2560	valid
204.0ms	77×	body	1280	valid
74.0ms	59×	body	640	valid
26.0ms	30×	body	320	valid
11.0ms	22×	body	160	valid
5.0ms	16×	body	80	valid

simplify60.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
3	19
2	17
1	13
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.2b	(- x (tan x))
1.2b	(- x (sin x))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 113

Calls

3 calls:

37.0ms	(/ (- x (sin x)) (- x (tan x)))
10.0ms	(- x (tan x))
18.0ms	(- x (sin x))

series266.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(/ (- x (sin x)) (- x (tan x)))
93.0ms	(- x (tan x))
53.0ms	(- x (sin x))

simplify1.2s

Counts

122 → 122

Iterations

Iter	Nodes
done	2007
3	2007
2	1279
1	504
0	212

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) (* x x))
0.3b	(fma 27/2800 (* (* x x) (* x x)) 1/2)
15.1b	(fma 9/40 (* x x) (- (fma 27/2800 (* (* x x) (* x x)) 1/2)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

114×	`pow1`
36×	`pow-prod-up`
23×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus`
15×	`add-cbrt-cube` `add-exp-log`
13×	`pow2`
8×	`prod-exp` `cbrt-unprod`
3×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`swap-sqr` `associate-r` `associate-l` `*-commutative` `unswap-sqr`

Counts

3 → 88

Calls

3 calls:

39.0ms	(* (* x x) (* x x))
0.0ms	(fma 27/2800 (* (* x x) (* x x)) 1/2)
0.0ms	(fma 9/40 (* x x) (- (fma 27/2800 (* (* x x) (* x x)) 1/2)))

series266.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(* (* x x) (* x x))
133.0ms	(fma 27/2800 (* (* x x) (* x x)) 1/2)
74.0ms	(fma 9/40 (* x x) (- (fma 27/2800 (* (* x x) (* x x)) 1/2)))

simplify1.1s

Counts

97 → 97

Iterations

Iter	Nodes
done	2153
3	2153
2	665
1	202
0	79

prune918.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
1.0b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.2b	(- x (tan x))
1.2b	(- x (tan x))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 592

Calls

4 calls:

21.0ms	(/ (sin x) (- x (tan x)))
76.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
7.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series516.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (sin x) (- x (tan x)))
266.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
102.0ms	(- x (tan x))
64.0ms	(- x (tan x))

simplify1.7s

Counts

604 → 604

Iterations

Iter	Nodes
done	2001
2	2001
1	1405
0	620

prune7.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize72.0ms

Local error

Found 4 expressions with local error:

1.2b	(- x (tan x))
1.2b	(- x (tan x))
1.4b	(fma (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (/ x (cbrt (- x (tan x)))) (- (* (/ 1 (- x (tan x))) (sin x))))
30.8b	(fma (- (/ 1 (- x (tan x)))) (sin x) (* (/ 1 (- x (tan x))) (sin x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`prod-diff` `add-cube-cbrt`
8×	`add-log-exp`
6×	`fma-neg`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `fma-udef` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 80

Calls

4 calls:

5.0ms	(- x (tan x))
5.0ms	(- x (tan x))
0.0ms	(fma (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (/ x (cbrt (- x (tan x)))) (- (* (/ 1 (- x (tan x))) (sin x))))
0.0ms	(fma (- (/ 1 (- x (tan x)))) (sin x) (* (/ 1 (- x (tan x))) (sin x)))

series701.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- x (tan x))
72.0ms	(- x (tan x))
278.0ms	(fma (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (/ x (cbrt (- x (tan x)))) (- (* (/ 1 (- x (tan x))) (sin x))))
278.0ms	(fma (- (/ 1 (- x (tan x)))) (sin x) (* (/ 1 (- x (tan x))) (sin x)))

simplify1.4s

Counts

92 → 92

Iterations

Iter	Nodes
done	2009
4	2009
3	1968
2	691
1	289
0	138

prune1.3s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes73.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch183.0ms

Steps

Iters	Range		Point
8	0.0042870261776910435	186.95626557948964	0.029500701526914974
9	-0.35383103211093586	-9.60334830165094e-09	-0.029021700279035747

simplify7.0ms

Iterations

Iter	Nodes
done	24
1	24
0	21

end0.0ms

sample15.3s

Algorithm

intervals

Results

6.6s	1626×	body	2560	valid
5.1s	2728×	body	1280	valid
2.5s	1903×	body	640	valid
629.0ms	928×	body	320	valid
188.0ms	440×	body	160	valid
82.0ms	375×	body	80	valid