Details

sample122.0ms

Algorithm

intervals

Results

43.0ms	55×	body	2560	valid
36.0ms	46×	body	1280	valid
18.0ms	48×	body	640	valid
6.0ms	23×	body	320	valid
6.0ms	69×	body	80	valid
3.0ms	15×	body	160	valid

simplify37.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize11.0ms

Local error

Found 2 expressions with local error:

16.2b	(/ (- 1 (cos x)) (* x x))
1.7b	(- 1 (cos x))

rewrite27.0ms

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

21.0ms	(/ (- 1 (cos x)) (* x x))
5.0ms	(- 1 (cos x))

series73.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

49.0ms	(/ (- 1 (cos x)) (* x x))
24.0ms	(- 1 (cos x))

simplify593.0ms

Counts: 65 → 53

prune288.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

16.1b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
0.4b	(+ 1 (cos x))
0.2b	(* (sin x) (sin x))
0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))

rewrite53.0ms

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

19.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
15.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
10.0ms	(* (sin x) (sin x))
5.0ms	(+ 1 (cos x))

series138.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

64.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
42.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
21.0ms	(* (sin x) (sin x))
11.0ms	(+ 1 (cos x))

simplify774.0ms

Counts: 148 → 127

prune998.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite36.0ms

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

15.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
11.0ms	(/ (sin x) x)
9.0ms	(/ (tan (/ x 2)) x)

series202.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

89.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
72.0ms	(/ (tan (/ x 2)) x)
41.0ms	(/ (sin x) x)

simplify432.0ms

Counts: 141 → 117

prune930.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
33×	`add-sqr-sqrt`
31×	`add-cbrt-cube`
29×	`times-frac`
27×	`*-un-lft-identity`
26×	`associate-r` `add-cube-cbrt`
22×	`prod-exp`
12×	`div-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv`
4×	`associate-l` `pow-prod-down` `associate-*r/`
3×	`rec-exp` `associate-/r` `1-exp` `un-div-inv` `insert-posit16` `div-inv` `associate-/l` `add-log-exp` `unswap-sqr`
2×	`frac-times` `associate-l/` `-commutative`
1×	`clear-num` `frac-2neg` `tan-quot` `associate-/l/`

Counts

3 → 112

Calls

3 calls:

Slowest

31.0ms	(* (* (sin x) (/ 1 x)) (/ (tan (/ x 2)) x))
12.0ms	(* (sin x) (/ 1 x))
6.0ms	(/ (tan (/ x 2)) x)

series170.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

85.0ms	(* (* (sin x) (/ 1 x)) (/ (tan (/ x 2)) x))
54.0ms	(/ (tan (/ x 2)) x)
32.0ms	(* (sin x) (/ 1 x))

simplify595.0ms

Counts: 133 → 121

prune827.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes28.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.4s	1615×	body	2560	valid
928.0ms	1460×	body	640	valid
751.0ms	1314×	body	1280	valid
408.0ms	907×	body	320	valid
241.0ms	2202×	body	80	valid
88.0ms	502×	body	160	valid