Details

sample165.0ms

Algorithm

intervals

Results

85.0ms	71×	body	2560	valid
23.0ms	32×	body	1280	valid
22.0ms	41×	body	640	valid
11.0ms	28×	body	320	valid
10.0ms	72×	body	80	valid
3.0ms	12×	body	160	valid

simplify26.0ms

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

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:

5.0ms	(- 1 (cos x))
16.0ms	(/ (- 1 (cos x)) (* x x))

series86.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(- 1 (cos x))
57.0ms	(/ (- 1 (cos x)) (* x x))

simplify5.6s

Counts

53 → 53

Iterations

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

prune388.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

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))

rewrite78.0ms

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:

31.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
15.0ms	(* (sin x) (sin x))
5.0ms	(+ 1 (cos x))
26.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series186.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
31.0ms	(* (sin x) (sin x))
19.0ms	(+ 1 (cos x))
90.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify7.0s

Counts

127 → 127

Iterations

Iter	Nodes
3	9290
2	1817
1	494
0	182

prune679.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize18.0ms

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)

rewrite31.0ms

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:

15.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
8.0ms	(/ (sin x) x)
6.0ms	(/ (tan (/ x 2)) x)

series206.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
36.0ms	(/ (sin x) x)
74.0ms	(/ (tan (/ x 2)) x)

simplify10.3s

Counts

117 → 117

Iterations

Iter	Nodes
3	5944
2	1645
1	444
0	166

prune827.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
0.1b	(/ (sin x) x)
0.2b	(* (/ (sin x) x) (tan (/ x 2)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 90

Calls

3 calls:

36.0ms	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
8.0ms	(/ (sin x) x)
18.0ms	(* (/ (sin x) x) (tan (/ x 2)))

series311.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
47.0ms	(/ (sin x) x)
151.0ms	(* (/ (sin x) x) (tan (/ x 2)))

simplify9.4s

Counts

99 → 99

Iterations

Iter	Nodes
3	6327
2	1304
1	371
0	154

prune628.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes50.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	9
1	9
0	8

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.7s	1655×	body	2560	valid
774.0ms	1216×	body	1280	valid
753.0ms	1458×	body	640	valid
387.0ms	916×	body	320	valid
305.0ms	2312×	body	80	valid
99.0ms	443×	body	160	valid