Details

sample99.0ms

Algorithm

intervals

Results

45.0ms	54×	body	2560	valid
17.0ms	40×	body	1280	valid
14.0ms	45×	body	640	valid
7.0ms	75×	body	80	valid
5.0ms	22×	body	320	valid
3.0ms	20×	body	160	valid

simplify37.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize47.0ms

Local error

Found 2 expressions with local error:

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

rewrite47.0ms

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

34.0ms	(/ (- 1 (cos x)) (* x x))
11.0ms	(- 1 (cos x))

series145.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

108.0ms	(/ (- 1 (cos x)) (* x x))
37.0ms	(- 1 (cos x))

simplify947.0ms

Counts: 69 → 69

prune642.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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)))

rewrite106.0ms

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

38.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
33.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
22.0ms	(* (sin x) (sin x))
10.0ms	(+ 1 (cos x))

series217.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

99.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
73.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
30.0ms	(* (sin x) (sin x))
16.0ms	(+ 1 (cos x))

simplify677.0ms

Counts: 138 → 138

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize19.0ms

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))

rewrite39.0ms

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

19.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
7.0ms	(/ (sin x) x)
6.0ms	(/ (tan (/ x 2)) x)

series226.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

123.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
68.0ms	(/ (tan (/ x 2)) x)
35.0ms	(/ (sin x) x)

simplify2.3s

Counts: 123 → 123

prune966.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ (/ (sin x) 1) (* (/ x (tan (/ x 2))) x))
0.1b	(/ x (tan (/ x 2)))
0.1b	(* (/ x (tan (/ x 2))) x)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
40×	`add-exp-log`
38×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `add-cube-cbrt`
31×	`add-cbrt-cube`
20×	`div-exp`
16×	`associate-/l*`
14×	`associate-l`
13×	`cbrt-undiv`
8×	`prod-exp`
6×	`cbrt-unprod`
5×	`pow1` `div-inv`
4×	`associate-/r*`
3×	`expm1-log1p-u` `1-exp` `associate-r` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-*l/` `tan-quot` `unswap-sqr`
1×	`pow-prod-down` `*-commutative` `associate-/l/`

Counts

3 → 124

Calls

3 calls:

Slowest

16.0ms	(/ (/ (sin x) 1) (* (/ x (tan (/ x 2))) x))
14.0ms	(* (/ x (tan (/ x 2))) x)
5.0ms	(/ x (tan (/ x 2)))

series329.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

131.0ms	(/ (/ (sin x) 1) (* (/ x (tan (/ x 2))) x))
102.0ms	(* (/ x (tan (/ x 2))) x)
95.0ms	(/ x (tan (/ x 2)))

simplify670.0ms

Counts: 133 → 133

prune1.1s

Pruning

5 alts after pruning (3 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

1.8s	1632×	body	2560	valid
813.0ms	1263×	body	1280	valid
573.0ms	1462×	body	640	valid
276.0ms	945×	body	320	valid
206.0ms	2240×	body	80	valid
159.0ms	458×	body	160	valid