Details

sample165.0ms

Algorithm

intervals

Results

61.0ms	52×	body	2560	valid
45.0ms	46×	body	1280	valid
26.0ms	48×	body	640	valid
9.0ms	24×	body	320	valid
9.0ms	71×	body	80	valid
4.0ms	15×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	30
4	30
3	28
2	23
1	15
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize11.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1 (cos x))
14.9b	(/ (- 1 (cos x)) (* x x))

rewrite47.0ms

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:

9.0ms	(- 1 (cos x))
27.0ms	(/ (- 1 (cos x)) (* x x))

series84.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(- 1 (cos x))
64.0ms	(/ (- 1 (cos x)) (* x x))

simplify3.4s

Counts

53 → 53

Iterations

Iter	Nodes
4	5574
3	1872
2	650
1	224
0	93

prune463.0ms

Pruning

8 alts after pruning (8 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)))
0.2b	(* (sin x) (sin x))
0.3b	(+ 1 (cos x))
15.0b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite74.0ms

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:

21.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
10.0ms	(* (sin x) (sin x))
5.0ms	(+ 1 (cos x))
35.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series224.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
33.0ms	(* (sin x) (sin x))
18.0ms	(+ 1 (cos x))
121.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify5.8s

Counts

127 → 127

Iterations

Iter	Nodes
3	9344
2	1809
1	493
0	182

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize22.0ms

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)

rewrite63.0ms

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:

34.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
14.0ms	(/ (sin x) x)
12.0ms	(/ (tan (/ x 2)) x)

series252.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
58.0ms	(/ (sin x) x)
72.0ms	(/ (tan (/ x 2)) x)

simplify2.8s

Counts

117 → 117

Iterations

Iter	Nodes
3	5853
2	1647
1	446
0	166

prune946.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize21.0ms

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)))

rewrite63.0ms

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:

24.0ms	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
11.0ms	(/ (sin x) x)
25.0ms	(* (/ (sin x) x) (tan (/ x 2)))

series275.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
44.0ms	(/ (sin x) x)
111.0ms	(* (/ (sin x) x) (tan (/ x 2)))

simplify2.3s

Counts

99 → 99

Iterations

Iter	Nodes
3	6422
2	1309
1	373
0	154

prune746.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes29.0ms

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

sample4.5s

Algorithm

intervals

Results

1.8s	1612×	body	2560	valid
1.1s	1199×	body	1280	valid
667.0ms	1519×	body	640	valid
397.0ms	949×	body	320	valid
250.0ms	2246×	body	80	valid
166.0ms	475×	body	160	valid