Details

sample588.0ms

Algorithm

intervals

Results

254.0ms	63×	body	2560	valid
192.0ms	91×	body	1280	valid
48.0ms	54×	body	640	valid
12.0ms	18×	body	320	valid
6.0ms	15×	body	160	valid
3.0ms	15×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize60.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.4b	(- x (sin x))
0.4b	(- x (tan x))

rewrite51.0ms

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:

21.0ms	(/ (- x (sin x)) (- x (tan x)))
12.0ms	(- x (sin x))
15.0ms	(- x (tan x))

series230.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(/ (- x (sin x)) (- x (tan x)))
36.0ms	(- x (sin x))
85.0ms	(- x (tan x))

simplify1.4s

Counts

122 → 122

Iterations

Iter	Nodes
done	5004
2	1394
1	504
0	212

prune463.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 27/2800 (* (* x x) (* x x)) 1/2)
0.1b	(* 9/40 (* x x))
0.1b	(* (* x x) (* x x))
15.3b	(- (* 9/40 (* x x)) (fma 27/2800 (* (* x x) (* x x)) 1/2))

rewrite115.0ms

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-l` `insert-posit16` `log1p-expm1-u`
3×	`prod-diff`
2×	`associate-r` `*-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)
24.0ms	(* 9/40 (* x x))
49.0ms	(* (* x x) (* x x))
39.0ms	(- (* 9/40 (* x x)) (fma 27/2800 (* (* x x) (* x x)) 1/2))

series343.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(fma 27/2800 (* (* x x) (* x x)) 1/2)
58.0ms	(* 9/40 (* x x))
44.0ms	(* (* x x) (* x x))
69.0ms	(- (* 9/40 (* x x)) (fma 27/2800 (* (* x x) (* x x)) 1/2))

simplify2.8s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
3	4019
2	995
1	353
0	127

prune274.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.3b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.4b	(- x (tan x))
0.4b	(- x (tan x))

rewrite179.0ms

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)))
102.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
10.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series479.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (sin x) (- x (tan x)))
255.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
83.0ms	(- x (tan x))
60.0ms	(- x (tan x))

simplify2.5s

Counts

604 → 604

Iterations

Iter	Nodes
done	5000
2	3423
1	1405
0	620

prune2.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.3b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.4b	(- x (tan x))
0.4b	(- x (tan x))

rewrite117.0ms

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:

13.0ms	(/ (sin x) (- x (tan x)))
66.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
5.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series499.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (sin x) (- x (tan x)))
283.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
79.0ms	(- x (tan x))
71.0ms	(- x (tan x))

simplify2.2s

Counts

604 → 604

Iterations

Iter	Nodes
done	5000
2	3423
1	1405
0	620

prune2.8s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes76.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.8b

bsearch210.0ms

Steps

Iters	Range		Point
11	4.21785760657603e-35	57.56933376468871	0.02825639784178301
9	-34.11472770615283	-3.67231414207575e-08	-0.027836888459983777

simplify6.0ms

Iterations

Iter	Nodes
done	26
1	26
0	25

end0.0ms

sample15.4s

Algorithm

intervals

Results

7.1s	1588×	body	2560	valid
5.1s	2730×	body	1280	valid
1.9s	1915×	body	640	valid
701.0ms	911×	body	320	valid
276.0ms	477×	body	160	valid
89.0ms	379×	body	80	valid