Details

sample1.7s

Algorithm

intervals

Results

1.1s	82×	body	1280	valid
353.0ms	54×	body	2560	valid
119.0ms	67×	body	640	valid
28.0ms	29×	body	320	valid
9.0ms	13×	body	160	valid
4.0ms	11×	body	80	valid

simplify30.0ms

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: 30.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite55.0ms

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:

24.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
8.0ms	(- x (sin x))

series307.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(/ (- x (sin x)) (- x (tan x)))
103.0ms	(- x (tan x))
81.0ms	(- x (sin x))

simplify1.0s

Counts

122 → 122

Iterations

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

prune993.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
1.8b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.9b	(- x (tan x))
1.9b	(- x (tan x))

rewrite139.0ms

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:

25.0ms	(/ (sin x) (- x (tan x)))
69.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
5.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series574.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (sin x) (- x (tan x)))
308.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
79.0ms	(- x (tan x))
98.0ms	(- x (tan x))

simplify1.6s

Counts

604 → 604

Iterations

Iter	Nodes
done	2001
2	2001
1	1405
0	620

prune7.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 27/2800 (* (* x x) (* x x)) 1/2)
0.1b	(* (* x x) (* x x))
0.4b	(* (* x x) 9/40)
17.1b	(- (* (* x x) 9/40) (fma 27/2800 (* (* x x) (* x x)) 1/2))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

120×	`pow1`
36×	`pow-prod-up`
26×	`pow-prod-down`
22×	`pow-sqr`
21×	`add-cbrt-cube` `add-exp-log`
18×	`pow-plus`
13×	`pow2`
11×	`prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u`
3×	`prod-diff`
2×	`associate-l` `*-commutative` `fma-udef` `unswap-sqr`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `swap-sqr` `flip--` `associate--r+`

Counts

4 → 119

Calls

4 calls:

0.0ms	(fma 27/2800 (* (* x x) (* x x)) 1/2)
26.0ms	(* (* x x) (* x x))
15.0ms	(* (* x x) 9/40)
38.0ms	(- (* (* x x) 9/40) (fma 27/2800 (* (* x x) (* x x)) 1/2))

series371.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(fma 27/2800 (* (* x x) (* x x)) 1/2)
62.0ms	(* (* x x) (* x x))
49.0ms	(* (* x x) 9/40)
88.0ms	(- (* (* x x) 9/40) (fma 27/2800 (* (* x x) (* x x)) 1/2))

simplify1.2s

Counts

131 → 131

Iterations

Iter	Nodes
done	2003
3	2003
2	958
1	334
0	129

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
1.9b	(- x (tan x))
19.1b	(/ (fma (pow x 5) -1/120 (fma 1/6 (* x (* x x)) (* 1/5040 (pow x 7)))) (- x (tan x)))
24.7b	(fma (pow x 5) -1/120 (fma 1/6 (* x (* x x)) (* 1/5040 (pow x 7))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`pow1`
15×	`times-frac`
11×	`add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
6×	`add-log-exp`
5×	`associate-/r*` `pow-prod-up` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`flip3--` `associate-/r/` `flip--`
1×	`pow2` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `cube-unmult` `div-exp` `associate-r` `pow-sqr` `*-commutative` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 107

Calls

4 calls:

32.0ms	(* x (* x x))
11.0ms	(- x (tan x))
18.0ms	(/ (fma (pow x 5) -1/120 (fma 1/6 (* x (* x x)) (* 1/5040 (pow x 7)))) (- x (tan x)))
1.0ms	(fma (pow x 5) -1/120 (fma 1/6 (* x (* x x)) (* 1/5040 (pow x 7))))

series432.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* x (* x x))
94.0ms	(- x (tan x))
157.0ms	(/ (fma (pow x 5) -1/120 (fma 1/6 (* x (* x x)) (* 1/5040 (pow x 7)))) (- x (tan x)))
115.0ms	(fma (pow x 5) -1/120 (fma 1/6 (* x (* x x)) (* 1/5040 (pow x 7))))

simplify1.3s

Counts

119 → 119

Iterations

Iter	Nodes
done	2007
3	2007
2	1105
1	424
0	198

prune856.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.8b

bsearch175.0ms

Steps

Iters	Range		Point
10	1.8230705747381016e-09	4364471.442644652	0.03210649578243009
9	-0.030639508246526274	-1.9696345359431407e-07	-0.025621427997812182

simplify4.0ms

Iterations

Iter	Nodes
done	25
1	25
0	21

end0.0ms

sample15.1s

Algorithm

intervals

Results

6.3s	1537×	body	2560	valid
5.0s	2771×	body	1280	valid
2.0s	1907×	body	640	valid
832.0ms	955×	body	320	valid
590.0ms	447×	body	160	valid
116.0ms	383×	body	80	valid