Details

sample186.0ms

Algorithm

intervals

Results

66.0ms	54×	body	2560	valid
51.0ms	40×	body	1280	valid
26.0ms	45×	body	640	valid
12.0ms	75×	body	80	valid
9.0ms	22×	body	320	valid
6.0ms	20×	body	160	valid

simplify64.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize24.0ms

Local error

Found 2 expressions with local error:

16.2b	(/ (- 1 (cos x)) (* x x))
1.9b	(- 1 (cos x))

rewrite49.0ms

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

42.0ms	(/ (- 1 (cos x)) (* x x))
6.0ms	(- 1 (cos x))

series94.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

66.0ms	(/ (- 1 (cos x)) (* x x))
27.0ms	(- 1 (cos x))

simplify2.3s

Counts: 53 → 53

prune486.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

16.1b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
0.5b	(+ 1 (cos x))
0.3b	(* (sin x) (sin x))
0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))

rewrite69.0ms

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

28.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
17.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
15.0ms	(* (sin x) (sin x))
6.0ms	(+ 1 (cos x))

series208.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

90.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
66.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
33.0ms	(* (sin x) (sin x))
19.0ms	(+ 1 (cos x))

simplify969.0ms

Counts: 127 → 127

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize27.0ms

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))

rewrite45.0ms

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

19.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
13.0ms	(/ (tan (/ x 2)) x)
12.0ms	(/ (sin x) x)

series243.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

115.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
88.0ms	(/ (tan (/ x 2)) x)
40.0ms	(/ (sin x) x)

simplify2.2s

Counts: 117 → 117

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

185×	`times-frac`
137×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
104×	`add-cube-cbrt`
64×	`add-exp-log`
44×	`associate-l`
34×	`add-cbrt-cube`
30×	`div-exp`
19×	`associate-/r*`
14×	`cbrt-undiv` `prod-exp`
13×	`associate-r`
12×	`div-inv`
10×	`unswap-sqr`
9×	`associate-/l*`
7×	`pow1`
6×	`rec-exp` `1-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`associate-/r/`
1×	`frac-times` `pow-prod-down` `associate-l/` `tan-quot` `associate-r/` `*-commutative` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 234

Calls

4 calls:

Slowest

24.0ms	(* (/ 1 (/ x (sin x))) (/ (tan (/ x 2)) x))
20.0ms	(/ 1 (/ x (sin x)))
13.0ms	(/ (tan (/ x 2)) x)
9.0ms	(/ x (sin x))

series281.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

129.0ms	(* (/ 1 (/ x (sin x))) (/ (tan (/ x 2)) x))
59.0ms	(/ (tan (/ x 2)) x)
51.0ms	(/ x (sin x))
41.0ms	(/ 1 (/ x (sin x)))

simplify926.0ms

Counts: 246 → 246

prune2.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes67.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.8s	1632×	body	2560	valid
920.0ms	1263×	body	1280	valid
873.0ms	945×	body	320	valid
809.0ms	1462×	body	640	valid
337.0ms	2240×	body	80	valid
108.0ms	458×	body	160	valid