Details

sample104.0ms

Algorithm

intervals

Results

50.0ms	60×	body	2560	valid
17.0ms	47×	body	640	valid
14.0ms	29×	body	1280	valid
7.0ms	87×	body	80	valid
6.0ms	24×	body	320	valid
2.0ms	9×	body	160	valid

simplify68.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize24.0ms

Local error

Found 2 expressions with local error:

17.8b	(/ (- 1 (cos x)) (* x x))
1.2b	(- 1 (cos x))

rewrite37.0ms

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

25.0ms	(/ (- 1 (cos x)) (* x x))
10.0ms	(- 1 (cos x))

series92.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

64.0ms	(/ (- 1 (cos x)) (* x x))
28.0ms	(- 1 (cos x))

simplify1.1s

Counts: 69 → 69

prune631.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

17.6b	(/ (/ (* (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)))

rewrite80.0ms

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

39.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
17.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
13.0ms	(* (sin x) (sin x))
10.0ms	(+ 1 (cos x))

series220.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

98.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
65.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
41.0ms	(* (sin x) (sin x))
16.0ms	(+ 1 (cos x))

simplify680.0ms

Counts: 138 → 138

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
31×	`add-sqr-sqrt` `add-cbrt-cube`
28×	`times-frac`
26×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
22×	`prod-exp`
12×	`div-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv`
6×	`frac-times` `tan-quot` `associate-*r/`
4×	`associate-r` `pow-prod-down` `associate-*l/`
3×	`expm1-log1p-u` `rec-exp` `associate-/r` `1-exp` `insert-posit16` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`*-commutative` `unswap-sqr`
1×	`clear-num` `frac-2neg`

Counts

3 → 119

Calls

3 calls:

Slowest

44.0ms	(* (/ 1 x) (* (/ (sin x) x) (tan (/ x 2))))
41.0ms	(* (/ (sin x) x) (tan (/ x 2)))
9.0ms	(/ (sin x) x)

series301.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

150.0ms	(* (/ (sin x) x) (tan (/ x 2)))
117.0ms	(* (/ 1 x) (* (/ (sin x) x) (tan (/ x 2))))
33.0ms	(/ (sin x) x)

simplify3.2s

Counts: 128 → 128

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ 1 (cos x))
0.3b	(/ 1 (* (* (/ x (sin x)) (/ x (sin x))) (+ 1 (cos x))))
0.1b	(* (/ x (sin x)) (/ x (sin x)))
0.1b	(/ x (sin x))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-exp-log`
55×	`add-sqr-sqrt`
52×	`times-frac`
45×	`*-un-lft-identity`
43×	`add-cbrt-cube` `add-cube-cbrt`
31×	`prod-exp`
29×	`div-exp`
17×	`pow1`
15×	`cbrt-undiv`
13×	`swap-sqr` `associate-r` `associate-l` `cbrt-unprod`
11×	`associate-/r/`
10×	`frac-times`
7×	`associate-*l/`
6×	`rec-exp` `1-exp` `associate-r/` `div-inv` `associate-/l` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `associate-/r*` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-flip`
2×	`clear-num` `frac-2neg`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `pow-sqr` `*-commutative` `pow-prod-up` `distribute-lft-out` `inv-pow`

Counts

4 → 177

Calls

4 calls:

Slowest

110.0ms	(/ 1 (* (* (/ x (sin x)) (/ x (sin x))) (+ 1 (cos x))))
33.0ms	(* (/ x (sin x)) (/ x (sin x)))
9.0ms	(/ x (sin x))
5.0ms	(+ 1 (cos x))

series262.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

109.0ms	(/ 1 (* (* (/ x (sin x)) (/ x (sin x))) (+ 1 (cos x))))
86.0ms	(* (/ x (sin x)) (/ x (sin x)))
50.0ms	(/ x (sin x))
17.0ms	(+ 1 (cos x))

simplify1.0s

Counts: 189 → 189

prune1.7s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes33.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.1s	1613×	body	2560	valid
916.0ms	1229×	body	1280	valid
782.0ms	1526×	body	640	valid
437.0ms	988×	body	320	valid
339.0ms	2184×	body	80	valid
103.0ms	460×	body	160	valid