Details

sample502.0ms

Algorithm

intervals

Results

190.0ms	47×	body	2560	valid
126.0ms	90×	body	1280	valid
85.0ms	56×	body	640	valid
18.0ms	33×	body	320	valid
6.0ms	18×	body	160	valid
2.0ms	12×	body	80	valid

simplify545.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.2b	(- x (tan x))
1.3b	(- x (sin x))

rewrite92.0ms

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:

42.0ms	(/ (- x (sin x)) (- x (tan x)))
13.0ms	(- x (tan x))
20.0ms	(- x (sin x))

series281.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(/ (- x (sin x)) (- x (tan x)))
91.0ms	(- x (tan x))
56.0ms	(- x (sin x))

simplify2.9s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
3	4741
2	1279
1	504
0	212

prune399.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.0b	(log (exp (/ (- x (sin x)) (- x (tan x)))))
1.2b	(- x (tan x))
1.3b	(- x (sin x))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt` `*-un-lft-identity`
50×	`times-frac`
42×	`add-cube-cbrt`
32×	`log-pow`
31×	`exp-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`log-prod`
2×	`sub-neg` `diff-log` `div-sub` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp`

Counts

4 → 160

Calls

4 calls:

51.0ms	(/ (- x (sin x)) (- x (tan x)))
77.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
13.0ms	(- x (tan x))
17.0ms	(- x (sin x))

series370.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (- x (sin x)) (- x (tan x)))
124.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
70.0ms	(- x (tan x))
54.0ms	(- x (sin x))

simplify2.6s

Counts

172 → 172

Iterations

Iter	Nodes
done	5000
3	4804
2	1382
1	577
0	277

prune694.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

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))

rewrite216.0ms

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:

17.0ms	(/ (sin x) (- x (tan x)))
118.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
7.0ms	(- x (tan x))
8.0ms	(- x (tan x))

series514.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (sin x) (- x (tan x)))
286.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
82.0ms	(- x (tan x))
64.0ms	(- x (tan x))

simplify2.3s

Counts

604 → 604

Iterations

Iter	Nodes
done	5000
2	3356
1	1405
0	620

prune2.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

1.2b	(- x (tan x))
1.2b	(- x (tan x))
1.3b	(fma x (/ 1 (- x (tan x))) (- (* (/ (cbrt (sin x)) (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1))))
31.7b	(fma (- (/ (cbrt (sin x)) (- x (tan x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1) (* (/ (cbrt (sin x)) (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1)))

rewrite16.0ms

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:

7.0ms	(- x (tan x))
7.0ms	(- x (tan x))
0.0ms	(fma x (/ 1 (- x (tan x))) (- (* (/ (cbrt (sin x)) (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1))))
0.0ms	(fma (- (/ (cbrt (sin x)) (- x (tan x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1) (* (/ (cbrt (sin x)) (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1)))

series804.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- x (tan x))
74.0ms	(- x (tan x))
277.0ms	(fma x (/ 1 (- x (tan x))) (- (* (/ (cbrt (sin x)) (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1))))
370.0ms	(fma (- (/ (cbrt (sin x)) (- x (tan x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1) (* (/ (cbrt (sin x)) (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1)))

simplify2.0s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
3	2099
2	660
1	281
0	133

prune562.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes157.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.7b

bsearch96.0ms

Steps

Iters	Range		Point
9	1.7877411926250683e-07	0.113095154289168	0.06477336993094537
7	-1.1375194732999505	-0.018988436667384805	-0.029470951698575748

simplify5.0ms

Iterations

Iter	Nodes
done	28
1	28
0	27

end0.0ms

sample13.3s

Algorithm

intervals

Results

6.6s	1631×	body	2560	valid
3.8s	2720×	body	1280	valid
1.3s	1836×	body	640	valid
1.1s	953×	body	320	valid
205.0ms	515×	body	160	valid
61.0ms	345×	body	80	valid