Details

sample111.0ms

Algorithm

intervals

Results

45.0ms	65×	body	2560	valid
29.0ms	39×	body	1280	valid
12.0ms	39×	body	640	valid
11.0ms	38×	body	320	valid
4.0ms	57×	body	80	valid
3.0ms	18×	body	160	valid

simplify37.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize11.0ms

Local error

Found 2 expressions with local error:

18.5b	(/ (- 1 (cos x)) (* x x))
1.9b	(- 1 (cos x))

rewrite54.0ms

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:

Slowest

45.0ms	(/ (- 1 (cos x)) (* x x))
6.0ms	(- 1 (cos x))

series97.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

63.0ms	(/ (- 1 (cos x)) (* x x))
34.0ms	(- 1 (cos x))

simplify967.0ms

Counts: 69 → 69

prune569.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

18.4b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
0.3b	(+ 1 (cos x))
0.2b	(* (sin x) (sin x))
0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))

rewrite82.0ms

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:

Slowest

28.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
21.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
20.0ms	(* (sin x) (sin x))
9.0ms	(+ 1 (cos x))

series195.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

93.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
64.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
27.0ms	(* (sin x) (sin x))
11.0ms	(+ 1 (cos x))

simplify697.0ms

Counts: 138 → 138

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ (sin x) x) (tan (/ x 2)))
0.1b	(/ (sin x) x)
0.0b	(/ (* (/ (sin x) x) (tan (/ x 2))) x)

rewrite68.0ms

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:

Slowest

31.0ms	(* (/ (sin x) x) (tan (/ x 2)))
27.0ms	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
8.0ms	(/ (sin x) x)

series353.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

163.0ms	(* (/ (sin x) x) (tan (/ x 2)))
153.0ms	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
37.0ms	(/ (sin x) x)

simplify2.3s

Counts: 105 → 105

prune904.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

461×	`times-frac`
222×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
32×	`div-inv`
20×	`associate-/r*`
19×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
16×	`associate-/r/`
15×	`tan-quot`
10×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`associate-/l/`

Counts

3 → 293

Calls

3 calls:

Slowest

16.0ms	(/ (/ (sin x) x) (/ x (tan (/ x 2))))
8.0ms	(/ (sin x) x)
5.0ms	(/ x (tan (/ x 2)))

series227.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

128.0ms	(/ (/ (sin x) x) (/ x (tan (/ x 2))))
66.0ms	(/ x (tan (/ x 2)))
33.0ms	(/ (sin x) x)

simplify571.0ms

Counts: 302 → 302

prune2.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes45.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch2.0ms

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.9s	1627×	body	2560	valid
783.0ms	1227×	body	1280	valid
664.0ms	1425×	body	640	valid
660.0ms	922×	body	320	valid
316.0ms	2321×	body	80	valid
92.0ms	478×	body	160	valid