Details

sample175.0ms

Algorithm

intervals

Results

83.0ms	51×	body	2560	valid
28.0ms	38×	body	1280	valid
25.0ms	42×	body	640	valid
13.0ms	34×	body	320	valid
10.0ms	78×	body	80	valid
3.0ms	13×	body	160	valid

simplify60.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize17.0ms

Local error

Found 2 expressions with local error:

14.0b	(/ (- 1 (cos x)) (* x x))
1.5b	(- 1 (cos x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 47

Calls

2 calls:

Slowest

35.0ms	(/ (- 1 (cos x)) (* x x))
5.0ms	(- 1 (cos x))

series92.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

61.0ms	(/ (- 1 (cos x)) (* x x))
31.0ms	(- 1 (cos x))

simplify2.3s

Counts: 53 → 53

prune327.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

14.2b	(/ (/ (* (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)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
24×	`*-un-lft-identity`
22×	`times-frac`
16×	`add-sqr-sqrt`
14×	`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×	`flip3-+` `flip-+` `insert-posit16` `div-inv`
3×	`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 → 115

Calls

4 calls:

Slowest

34.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
24.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
22.0ms	(* (sin x) (sin x))
9.0ms	(+ 1 (cos x))

series173.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

93.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
47.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
20.0ms	(* (sin x) (sin x))
13.0ms	(+ 1 (cos x))

simplify474.0ms

Counts: 127 → 127

prune984.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 3 expressions with local error:

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

rewrite52.0ms

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×	`insert-posit16` `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 → 108

Calls

3 calls:

Slowest

23.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
13.0ms	(/ (sin x) x)
11.0ms	(/ (tan (/ x 2)) x)

series218.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

117.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
55.0ms	(/ (tan (/ x 2)) x)
45.0ms	(/ (sin x) x)

simplify1.8s

Counts: 117 → 117

prune818.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite70.0ms

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×	`associate-l` `insert-posit16` `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 → 87

Calls

3 calls:

Slowest

31.0ms	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)
24.0ms	(* (sin x) (/ (tan (/ x 2)) x))
12.0ms	(/ (tan (/ x 2)) x)

series258.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

104.0ms	(* (sin x) (/ (tan (/ x 2)) x))
85.0ms	(/ (* (sin x) (/ (tan (/ x 2)) x)) x)
70.0ms	(/ (tan (/ x 2)) x)

simplify2.2s

Counts: 96 → 96

prune682.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes62.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	1245×	body	1280	valid
1.4s	1533×	body	2560	valid
620.0ms	1503×	body	640	valid
256.0ms	898×	body	320	valid
247.0ms	2320×	body	80	valid
112.0ms	501×	body	160	valid