Details

sample197.0ms

Algorithm

intervals

Results

102.0ms	63×	body	2560	valid
31.0ms	55×	body	640	valid
27.0ms	32×	body	1280	valid
12.0ms	27×	body	320	valid
9.0ms	66×	body	80	valid
4.0ms	13×	body	160	valid

simplify45.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite37.0ms

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

28.0ms	(/ (- 1 (cos x)) (* x x))
6.0ms	(- 1 (cos x))

series119.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

93.0ms	(/ (- 1 (cos x)) (* x x))
25.0ms	(- 1 (cos x))

simplify2.2s

Counts: 53 → 53

prune431.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

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)))

rewrite64.0ms

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

22.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
22.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
13.0ms	(* (sin x) (sin x))
5.0ms	(+ 1 (cos x))

series204.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

82.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
65.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
39.0ms	(* (sin x) (sin x))
18.0ms	(+ 1 (cos x))

simplify702.0ms

Counts: 127 → 127

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize22.0ms

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))

rewrite34.0ms

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

18.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
9.0ms	(/ (sin x) x)
6.0ms	(/ (tan (/ x 2)) x)

series244.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

123.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
76.0ms	(/ (tan (/ x 2)) x)
45.0ms	(/ (sin x) x)

simplify2.0s

Counts: 117 → 117

prune953.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize28.0ms

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)))

rewrite82.0ms

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×	`associate-/r*` `insert-posit16` `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 → 116

Calls

4 calls:

Slowest

40.0ms	(* (/ (sin x) x) (/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x)))
17.0ms	(/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x))
16.0ms	(* (cos (* 1/2 x)) x)
7.0ms	(/ (sin x) x)

series606.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

379.0ms	(/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x))
108.0ms	(* (/ (sin x) x) (/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x)))
66.0ms	(* (cos (* 1/2 x)) x)
53.0ms	(/ (sin x) x)

simplify591.0ms

Counts: 128 → 128

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.9s	1661×	body	2560	valid
893.0ms	1162×	body	1280	valid
732.0ms	1436×	body	640	valid
585.0ms	502×	body	160	valid
363.0ms	949×	body	320	valid
288.0ms	2290×	body	80	valid