Details

sample166.0ms

Algorithm

intervals

Results

59.0ms	52×	body	2560	valid
31.0ms	46×	body	1280	valid
27.0ms	71×	body	80	valid
26.0ms	48×	body	640	valid
9.0ms	24×	body	320	valid
4.0ms	15×	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: 32.0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-cbrt-cube` `add-exp-log`
6×	`times-frac` `associate-/l*` `difference-of-squares`
4×	`add-log-exp`
3×	`fma-neg` `distribute-lft-out--`
2×	`expm1-log1p-u` `pow1` `cbrt-undiv` `flip3--` `div-exp` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 63

Calls

2 calls:

11.0ms	(- 1 (cos x))
20.0ms	(/ (- 1 (cos x)) (* x x))

series112.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(- 1 (cos x))
89.0ms	(/ (- 1 (cos x)) (* x x))

simplify1.7s

Counts

69 → 69

Iterations

Iter	Nodes
3	2853
2	856
1	289
0	121

prune505.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
25×	`*-un-lft-identity`
22×	`times-frac`
17×	`add-sqr-sqrt`
15×	`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×	`expm1-log1p-u` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`fma-def` `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 → 126

Calls

4 calls:

18.0ms	(/ (* (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))

series185.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
29.0ms	(* (sin x) (sin x))
11.0ms	(+ 1 (cos x))
91.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify7.4s

Counts

138 → 138

Iterations

Iter	Nodes
3	9178
2	1856
1	511
0	190

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize34.0ms

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)

rewrite60.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 114

Calls

3 calls:

29.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
15.0ms	(/ (sin x) x)
13.0ms	(/ (tan (/ x 2)) x)

series233.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
34.0ms	(/ (sin x) x)
87.0ms	(/ (tan (/ x 2)) x)

simplify2.8s

Counts

123 → 123

Iterations

Iter	Nodes
3	5682
2	1662
1	451
0	172

prune873.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

153×	`times-frac`
98×	`add-sqr-sqrt`
89×	`*-un-lft-identity` `add-cube-cbrt`
43×	`associate-r`
19×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/l*`
10×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r*`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `associate-/l/`
1×	`pow-prod-down` `tan-quot` `associate-r/` `-commutative`

Counts

3 → 172

Calls

3 calls:

12.0ms	(/ (/ (tan (/ x 2)) x) x)
8.0ms	(/ (tan (/ x 2)) x)
32.0ms	(* (sin x) (/ (/ (tan (/ x 2)) x) x))

series199.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(/ (/ (tan (/ x 2)) x) x)
53.0ms	(/ (tan (/ x 2)) x)
88.0ms	(* (sin x) (/ (/ (tan (/ x 2)) x) x))

simplify3.0s

Counts

181 → 181

Iterations

Iter	Nodes
3	7864
2	1950
1	629
0	253

prune1.6s

Pruning

4 alts after pruning (3 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

sample5.0s

Algorithm

intervals

Results

2.3s	1612×	body	2560	valid
992.0ms	1199×	body	1280	valid
760.0ms	1519×	body	640	valid
378.0ms	949×	body	320	valid
261.0ms	2246×	body	80	valid
148.0ms	475×	body	160	valid