Details

sample178.0ms

Algorithm

intervals

Results

94.0ms	63×	body	2560	valid
26.0ms	55×	body	640	valid
22.0ms	32×	body	1280	valid
11.0ms	27×	body	320	valid
8.0ms	66×	body	80	valid
5.0ms	13×	body	160	valid

simplify58.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize10.0ms

Local error

Found 2 expressions with local error:

17.8b	(/ (- 1 (cos x)) (* x x))
1.1b	(- 1 (cos x))

rewrite31.0ms

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

16.0ms	(/ (- 1 (cos x)) (* x x))
13.0ms	(- 1 (cos x))

series89.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

62.0ms	(/ (- 1 (cos x)) (* x x))
27.0ms	(- 1 (cos x))

simplify861.0ms

Counts: 69 → 69

prune593.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

17.5b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
0.4b	(+ 1 (cos x))
0.3b	(* (sin x) (sin x))
0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))

rewrite65.0ms

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

22.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
20.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
12.0ms	(* (sin x) (sin x))
9.0ms	(+ 1 (cos x))

series171.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

71.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
55.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
29.0ms	(* (sin x) (sin x))
15.0ms	(+ 1 (cos x))

simplify567.0ms

Counts: 138 → 138

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 3 expressions with local error:

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

Slowest

36.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
15.0ms	(/ (sin x) x)
12.0ms	(/ (tan (/ x 2)) x)

series272.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

132.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
82.0ms	(/ (tan (/ x 2)) x)
58.0ms	(/ (sin x) x)

simplify2.0s

Counts: 123 → 123

prune994.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x))
0.1b	(/ (sin x) x)
0.1b	(* (cos (* 1/2 x)) x)
0.1b	(* (/ (sin x) x) (/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-cbrt-cube` `add-exp-log`
32×	`add-sqr-sqrt`
25×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
16×	`associate-l`
10×	`cbrt-undiv` `div-exp` `associate-r` `prod-exp` `cbrt-unprod`
8×	`pow1`
6×	`associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`clear-num` `frac-2neg` `pow-prod-down` `*-commutative`
1×	`frac-times` `associate-l/` `associate-r/`

Counts

4 → 124

Calls

4 calls:

Slowest

41.0ms	(* (/ (sin x) x) (/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x)))
18.0ms	(/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x))
17.0ms	(* (cos (* 1/2 x)) x)
7.0ms	(/ (sin x) x)

series274.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

133.0ms	(* (/ (sin x) x) (/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x)))
61.0ms	(/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x))
42.0ms	(/ (sin x) x)
38.0ms	(* (cos (* 1/2 x)) x)

simplify747.0ms

Counts: 136 → 136

prune1.4s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes60.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.5s	1661×	body	2560	valid
1.1s	1436×	body	640	valid
718.0ms	1162×	body	1280	valid
300.0ms	2290×	body	80	valid
282.0ms	949×	body	320	valid
88.0ms	502×	body	160	valid