Details

sample122.0ms

Algorithm

intervals

Results

46.0ms	55×	body	2560	valid
20.0ms	42×	body	320	valid
19.0ms	45×	body	640	valid
19.0ms	34×	body	1280	valid
7.0ms	73×	body	80	valid
1.0ms	7×	body	160	valid

simplify27.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize11.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1 (cos x))
16.1b	(/ (- 1 (cos x)) (* x x))

rewrite422.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 47

Calls

2 calls:

14.0ms	(- 1 (cos x))
406.0ms	(/ (- 1 (cos x)) (* x x))

series134.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(- 1 (cos x))
98.0ms	(/ (- 1 (cos x)) (* x x))

simplify5.4s

Counts

53 → 53

Iterations

Iter	Nodes
4	5731
3	1877
2	652
1	223
0	93

prune449.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.3b	(* (sin x) (sin x))
0.3b	(+ 1 (cos x))
16.2b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
24×	`*-un-lft-identity`
22×	`times-frac`
16×	`add-sqr-sqrt`
14×	`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×	`flip3-+` `flip-+` `insert-posit16` `div-inv`
3×	`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 → 115

Calls

4 calls:

22.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
11.0ms	(* (sin x) (sin x))
5.0ms	(+ 1 (cos x))
19.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series205.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
33.0ms	(* (sin x) (sin x))
11.0ms	(+ 1 (cos x))
108.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify7.1s

Counts

127 → 127

Iterations

Iter	Nodes
3	9290
2	1817
1	494
0	182

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize32.0ms

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)

rewrite43.0ms

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×	`insert-posit16` `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 → 108

Calls

3 calls:

23.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
8.0ms	(/ (sin x) x)
10.0ms	(/ (tan (/ x 2)) x)

series278.0ms

Counts

3 → 9

Calls

3 calls:

153.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
52.0ms	(/ (sin x) x)
73.0ms	(/ (tan (/ x 2)) x)

simplify8.3s

Counts

117 → 117

Iterations

Iter	Nodes
3	5944
2	1645
1	444
0	166

prune857.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (sin x))
0.1b	(/ x (sin x))
0.3b	(/ 1 (* (+ (cos x) 1) (* (/ x (sin x)) (/ x (sin x)))))
0.3b	(+ (cos x) 1)

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-exp-log`
33×	`add-cbrt-cube`
27×	`prod-exp`
26×	`div-exp`
24×	`*-un-lft-identity`
22×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`times-frac`
12×	`cbrt-undiv`
11×	`associate-/r/`
10×	`pow1`
9×	`frac-times` `cbrt-unprod` `associate-/l*`
7×	`associate-/r*`
6×	`rec-exp` `1-exp` `associate-*r/` `add-log-exp`
5×	`flip3-+` `associate-*l/` `flip-+`
4×	`insert-posit16`
3×	`clear-num` `frac-2neg` `pow-prod-down` `div-inv` `pow-flip`
1×	`+-commutative` `sum-log` `distribute-lft-out` `inv-pow`

Counts

4 → 126

Calls

4 calls:

8.0ms	(/ x (sin x))
9.0ms	(/ x (sin x))
79.0ms	(/ 1 (* (+ (cos x) 1) (* (/ x (sin x)) (/ x (sin x)))))
10.0ms	(+ (cos x) 1)

series183.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ x (sin x))
33.0ms	(/ x (sin x))
92.0ms	(/ 1 (* (+ (cos x) 1) (* (/ x (sin x)) (/ x (sin x)))))
18.0ms	(+ (cos x) 1)

simplify5.3s

Counts

138 → 138

Iterations

Iter	Nodes
3	5768
2	1427
1	460
0	197

prune1.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes35.0ms

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

sample5.0s

Algorithm

intervals

Results

2.3s	1598×	body	2560	valid
899.0ms	1273×	body	1280	valid
865.0ms	1492×	body	640	valid
391.0ms	920×	body	320	valid
239.0ms	2276×	body	80	valid
99.0ms	441×	body	160	valid