Details

sample165.0ms

Algorithm

intervals

Results

65.0ms	38×	body	2560	valid
31.0ms	50×	body	640	valid
27.0ms	35×	body	1280	valid
12.0ms	26×	body	320	valid
12.0ms	90×	body	80	valid
5.0ms	17×	body	160	valid

simplify31.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize19.0ms

Local error

Found 2 expressions with local error:

2.4b	(- 1 (cos x))
12.2b	(/ (- 1 (cos x)) (* x x))

rewrite35.0ms

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:

6.0ms	(- 1 (cos x))
18.0ms	(/ (- 1 (cos x)) (* x x))

series139.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(- 1 (cos x))
102.0ms	(/ (- 1 (cos x)) (* x x))

simplify1.5s

Counts

69 → 69

Iterations

Iter	Nodes
3	2853
2	856
1	289
0	121

prune513.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.3b	(* (sin x) (sin x))
0.4b	(+ 1 (cos x))
12.0b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite86.0ms

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:

28.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
21.0ms	(* (sin x) (sin x))
9.0ms	(+ 1 (cos x))
27.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series174.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
22.0ms	(* (sin x) (sin x))
11.0ms	(+ 1 (cos x))
91.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify7.1s

Counts

138 → 138

Iterations

Iter	Nodes
3	9178
2	1856
1	511
0	190

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite66.0ms

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:

30.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
18.0ms	(/ (tan (/ x 2)) x)
16.0ms	(/ (sin x) x)

series291.0ms

Counts

3 → 9

Calls

3 calls:

147.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
88.0ms	(/ (tan (/ x 2)) x)
55.0ms	(/ (sin x) x)

simplify3.5s

Counts

123 → 123

Iterations

Iter	Nodes
3	6590
2	1693
1	451
0	172

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 3 expressions with local error:

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

rewrite47.0ms

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×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u` `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 → 93

Calls

3 calls:

14.0ms	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)
7.0ms	(/ (tan (/ x 2)) x)
25.0ms	(* (sin x) (/ (tan (/ x 2)) x))

series311.0ms

Counts

3 → 9

Calls

3 calls:

130.0ms	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)
69.0ms	(/ (tan (/ x 2)) x)
112.0ms	(* (sin x) (/ (tan (/ x 2)) x))

simplify3.4s

Counts

102 → 102

Iterations

Iter	Nodes
3	7142
2	1363
1	372
0	154

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes34.0ms

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

sample5.1s

Algorithm

intervals

Results

1.9s	1656×	body	2560	valid
975.0ms	1189×	body	1280	valid
841.0ms	941×	body	320	valid
789.0ms	1468×	body	640	valid
279.0ms	2291×	body	80	valid
102.0ms	455×	body	160	valid