Details

sample138.0ms

Algorithm

intervals

Results

41.0ms	39×	body	2560	valid
30.0ms	87×	body	80	valid
23.0ms	40×	body	1280	valid
20.0ms	48×	body	640	valid
8.0ms	24×	body	320	valid
7.0ms	18×	body	160	valid

simplify17.0ms

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: 26.2b

localize11.0ms

Local error

Found 2 expressions with local error:

2.3b	(- 1 (cos x))
12.5b	(/ (- 1 (cos x)) (* x x))

rewrite23.0ms

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

series116.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(- 1 (cos x))
95.0ms	(/ (- 1 (cos x)) (* x x))

simplify3.7s

Counts

53 → 53

Iterations

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

prune396.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.3b	(* (sin x) (sin x))
0.4b	(+ 1 (cos x))
12.3b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite95.0ms

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:

36.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
20.0ms	(* (sin x) (sin x))
10.0ms	(+ 1 (cos x))
28.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series150.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
28.0ms	(* (sin x) (sin x))
12.0ms	(+ 1 (cos x))
70.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify5.5s

Counts

127 → 127

Iterations

Iter	Nodes
3	9344
2	1809
1	493
0	182

prune993.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize25.0ms

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)

rewrite30.0ms

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))
7.0ms	(/ (sin x) x)
6.0ms	(/ (tan (/ x 2)) x)

series264.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
48.0ms	(/ (sin x) x)
74.0ms	(/ (tan (/ x 2)) x)

simplify2.8s

Counts

117 → 117

Iterations

Iter	Nodes
3	5853
2	1647
1	446
0	166

prune886.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 3 expressions with local error:

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

rewrite33.0ms

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-r`
6×	`cbrt-undiv` `associate-/r*` `div-exp`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `associate-/l*`
3×	`associate-l` `insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-*r/` `unswap-sqr` `associate-/l/`
1×	`pow-prod-down` `tan-quot` `*-commutative`

Counts

3 → 87

Calls

3 calls:

14.0ms	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)
6.0ms	(/ (tan (/ x 2)) x)
12.0ms	(* (sin x) (/ (tan (/ x 2)) x))

series298.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)
61.0ms	(/ (tan (/ x 2)) x)
132.0ms	(* (sin x) (/ (tan (/ x 2)) x))

simplify3.2s

Counts

96 → 96

Iterations

Iter	Nodes
3	7143
2	1349
1	363
0	148

prune750.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes36.0ms

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

sample5.3s

Algorithm

intervals

Results

2.7s	1621×	body	2560	valid
922.0ms	1235×	body	1280	valid
824.0ms	1501×	body	640	valid
341.0ms	928×	body	320	valid
273.0ms	2287×	body	80	valid
94.0ms	428×	body	160	valid