Details

sample177.0ms

Algorithm

intervals

Results

84.0ms	71×	body	2560	valid
41.0ms	32×	body	1280	valid
21.0ms	41×	body	640	valid
10.0ms	28×	body	320	valid
9.0ms	72×	body	80	valid
3.0ms	12×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	28
4	28
3	26
2	21
1	13
0	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize11.0ms

Local error

Found 2 expressions with local error:

1.9b	(- 1 (cos x))
18.9b	(/ (- 1 (cos x)) (* x x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 63

Calls

2 calls:

6.0ms	(- 1 (cos x))
17.0ms	(/ (- 1 (cos x)) (* x x))

series74.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(- 1 (cos x))
53.0ms	(/ (- 1 (cos x)) (* x x))

simplify1.9s

Counts

69 → 69

Iterations

Iter	Nodes
3	3060
2	858
1	288
0	121

prune450.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.3b	(* (sin x) (sin x))
0.5b	(+ 1 (cos x))
19.1b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
25×	`*-un-lft-identity`
22×	`times-frac`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`cbrt-undiv` `div-exp`
11×	`pow1` `associate-/l*`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r/` `add-log-exp`
5×	`associate-/r*` `distribute-lft-out`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`fma-def` `div-sub` `swap-sqr` `associate-r` `associate-l` `sqr-sin`
2×	`clear-num` `frac-2neg` `sin-mult` `associate-/l/`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `unswap-sqr`

Counts

4 → 126

Calls

4 calls:

33.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
22.0ms	(* (sin x) (sin x))
10.0ms	(+ 1 (cos x))
46.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series167.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
24.0ms	(* (sin x) (sin x))
11.0ms	(+ 1 (cos x))
79.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify8.0s

Counts

138 → 138

Iterations

Iter	Nodes
3	9653
2	1861
1	512
0	190

prune896.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
0.1b	(/ (sin x) x)
0.1b	(/ (tan (/ x 2)) x)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
40×	`times-frac`
33×	`*-un-lft-identity` `add-cube-cbrt`
19×	`add-cbrt-cube` `add-exp-log`
13×	`associate-r` `associate-l`
6×	`cbrt-undiv` `associate-/r` `div-exp` `associate-/l`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `tan-quot` `associate-r/` `*-commutative` `associate-/l/`

Counts

3 → 114

Calls

3 calls:

18.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
8.0ms	(/ (sin x) x)
7.0ms	(/ (tan (/ x 2)) x)

series238.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
42.0ms	(/ (sin x) x)
76.0ms	(/ (tan (/ x 2)) x)

simplify9.9s

Counts

123 → 123

Iterations

Iter	Nodes
3	6069
2	1656
1	449
0	172

prune939.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (/ (sin x) x)) (cbrt (/ (sin x) x)))
0.3b	(cbrt (/ (sin x) x))
0.3b	(cbrt (/ (sin x) x))
0.3b	(cbrt (/ (sin x) x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`*-un-lft-identity` `add-cube-cbrt`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 156

Calls

4 calls:

18.0ms	(* (cbrt (/ (sin x) x)) (cbrt (/ (sin x) x)))
2.0ms	(cbrt (/ (sin x) x))
2.0ms	(cbrt (/ (sin x) x))
2.0ms	(cbrt (/ (sin x) x))

series834.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(* (cbrt (/ (sin x) x)) (cbrt (/ (sin x) x)))
187.0ms	(cbrt (/ (sin x) x))
217.0ms	(cbrt (/ (sin x) x))
215.0ms	(cbrt (/ (sin x) x))

simplify2.2s

Counts

168 → 168

Iterations

Iter	Nodes
4	3901
3	1663
2	753
1	327
0	173

prune1.6s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes38.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	9
1	9
0	8

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.7s	1655×	body	2560	valid
874.0ms	1216×	body	1280	valid
722.0ms	1458×	body	640	valid
648.0ms	2312×	body	80	valid
346.0ms	916×	body	320	valid
120.0ms	443×	body	160	valid