Details

sample177.0ms

Algorithm

intervals

Results

89.0ms	58×	body	2560	valid
31.0ms	52×	body	640	valid
27.0ms	39×	body	1280	valid
8.0ms	66×	body	80	valid
7.0ms	21×	body	320	valid
5.0ms	20×	body	160	valid

simplify51.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	60
4	60
3	56
2	45
1	27
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize11.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1 (cos x))
17.7b	(/ (- 1 (cos x)) (* x x))

rewrite33.0ms

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))
26.0ms	(/ (- 1 (cos x)) (* x x))

series132.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(- 1 (cos x))
92.0ms	(/ (- 1 (cos x)) (* x x))

simplify2.2s

Counts

53 → 53

Iterations

Iter	Nodes
4	5175
3	1785
2	811
1	380
0	93

prune355.0ms

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))
0.4b	(+ 1 (cos x))
17.5b	(/ (/ (* (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:

22.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
11.0ms	(* (sin x) (sin x))
5.0ms	(+ 1 (cos x))
34.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series205.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
19.0ms	(* (sin x) (sin x))
12.0ms	(+ 1 (cos x))
103.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify634.0ms

Counts

127 → 127

Iterations

Iter	Nodes
2	2220
1	791
0	182

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite44.0ms

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:

9.0ms	(/ (tan (/ x 2)) x)
20.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
14.0ms	(/ (sin x) x)

series188.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ (tan (/ x 2)) x)
90.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
42.0ms	(/ (sin x) x)

simplify2.0s

Counts

117 → 117

Iterations

Iter	Nodes
3	4727
2	1867
1	730
0	166

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sin x) x) (/ (sin x) x))
0.4b	(+ 1 (cos x))
1.4b	(exp (log (/ (* (/ (sin x) x) (/ (sin x) x)) (+ 1 (cos x)))))
13.5b	(log (/ (* (/ (sin x) x) (/ (sin x) x)) (+ 1 (cos x))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
48×	`times-frac`
43×	`*-un-lft-identity`
37×	`add-cube-cbrt`
35×	`add-exp-log`
20×	`log-prod`
16×	`add-cbrt-cube`
13×	`pow1` `swap-sqr` `div-exp` `associate-r` `associate-l`
10×	`exp-sum`
8×	`prod-exp`
6×	`rem-log-exp` `div-inv` `add-log-exp`
4×	`cbrt-undiv` `exp-prod` `associate-/r/` `cbrt-unprod` `insert-posit16` `unswap-sqr`
3×	`flip3-+` `flip-+` `distribute-lft-out`
2×	`log-div` `log-pow`
1×	`pow2` `frac-times` `+-commutative` `sum-log` `pow-plus` `exp-diff` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `rem-exp-log`

Counts

4 → 131

Calls

4 calls:

29.0ms	(* (/ (sin x) x) (/ (sin x) x))
9.0ms	(+ 1 (cos x))
45.0ms	(exp (log (/ (* (/ (sin x) x) (/ (sin x) x)) (+ 1 (cos x)))))
10.0ms	(log (/ (* (/ (sin x) x) (/ (sin x) x)) (+ 1 (cos x))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (/ (sin x) x) (/ (sin x) x))
15.0ms	(+ 1 (cos x))
86.0ms	(exp (log (/ (* (/ (sin x) x) (/ (sin x) x)) (+ 1 (cos x)))))
159.0ms	(log (/ (* (/ (sin x) x) (/ (sin x) x)) (+ 1 (cos x))))

simplify580.0ms

Counts

143 → 143

Iterations

Iter	Nodes
2	2664
1	1001
0	233

prune1.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes44.0ms

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

1.9s	1656×	body	2560	valid
1.3s	1250×	body	1280	valid
699.0ms	1494×	body	640	valid
435.0ms	2185×	body	80	valid
426.0ms	950×	body	320	valid
105.0ms	465×	body	160	valid