Details

sample153.0ms

Algorithm

intervals

Results

54.0ms	51×	body	2560	valid
35.0ms	43×	body	640	valid
25.0ms	39×	body	1280	valid
11.0ms	31×	body	320	valid
11.0ms	71×	body	80	valid
5.0ms	21×	body	160	valid

simplify37.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	28
4	28
3	26
2	21
1	13
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize24.0ms

Local error

Found 2 expressions with local error:

1.6b	(- 1 (cos x))
15.5b	(/ (- 1 (cos x)) (* x x))

rewrite67.0ms

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:

8.0ms	(- 1 (cos x))
57.0ms	(/ (- 1 (cos x)) (* x x))

series113.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(- 1 (cos x))
76.0ms	(/ (- 1 (cos x)) (* x x))

simplify2.0s

Counts

69 → 69

Iterations

Iter	Nodes
3	3060
2	858
1	288
0	121

prune675.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

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))
15.6b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite96.0ms

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:

33.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
25.0ms	(* (sin x) (sin x))
9.0ms	(+ 1 (cos x))
26.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series211.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
23.0ms	(* (sin x) (sin x))
18.0ms	(+ 1 (cos x))
126.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify7.5s

Counts

138 → 138

Iterations

Iter	Nodes
3	9653
2	1861
1	512
0	190

prune1.1s

Pruning

6 alts after pruning (6 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	(/ (sin x) x)
0.2b	(/ (tan (/ x 2)) x)

rewrite47.0ms

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:

22.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
13.0ms	(/ (sin x) x)
11.0ms	(/ (tan (/ x 2)) x)

series187.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
35.0ms	(/ (sin x) x)
64.0ms	(/ (tan (/ x 2)) x)

simplify8.9s

Counts

123 → 123

Iterations

Iter	Nodes
3	6069
2	1656
1	449
0	172

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize18.0ms

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)))

rewrite58.0ms

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×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u` `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 → 96

Calls

3 calls:

19.0ms	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
13.0ms	(/ (sin x) x)
25.0ms	(* (/ (sin x) x) (tan (/ x 2)))

series260.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
46.0ms	(/ (sin x) x)
104.0ms	(* (/ (sin x) x) (tan (/ x 2)))

simplify10.0s

Counts

105 → 105

Iterations

Iter	Nodes
3	6706
2	1329
1	379
0	160

prune922.0ms

Pruning

5 alts after pruning (3 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

simplify2.0ms

Iterations

Iter	Nodes
2	9
1	9
0	8

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.3s	1616×	body	2560	valid
1.3s	1241×	body	1280	valid
797.0ms	1476×	body	640	valid
498.0ms	936×	body	320	valid
242.0ms	2286×	body	80	valid
141.0ms	445×	body	160	valid