Details

sample157.0ms

Algorithm

intervals

Results

75.0ms	60×	body	2560	valid
26.0ms	47×	body	640	valid
23.0ms	29×	body	1280	valid
11.0ms	87×	body	80	valid
10.0ms	24×	body	320	valid
3.0ms	9×	body	160	valid

simplify85.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite42.0ms

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

31.0ms	(/ (- 1 (cos x)) (* x x))
9.0ms	(- 1 (cos x))

series116.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

86.0ms	(/ (- 1 (cos x)) (* x x))
29.0ms	(- 1 (cos x))

simplify2.6s

Counts: 53 → 53

prune441.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

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)))

rewrite104.0ms

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

37.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
34.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
20.0ms	(* (sin x) (sin x))
9.0ms	(+ 1 (cos x))

series141.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

68.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
39.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
24.0ms	(* (sin x) (sin x))
11.0ms	(+ 1 (cos x))

simplify581.0ms

Counts: 127 → 127

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize20.0ms

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))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-exp-log`
54×	`add-sqr-sqrt`
52×	`times-frac`
44×	`*-un-lft-identity`
43×	`add-cbrt-cube`
42×	`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×	`associate-/r*` `pow-prod-down` `insert-posit16` `unswap-sqr`
3×	`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 → 166

Calls

4 calls:

Slowest

90.0ms	(/ 1 (* (* (/ x (sin x)) (/ x (sin x))) (+ 1 (cos x))))
33.0ms	(* (/ x (sin x)) (/ x (sin x)))
7.0ms	(+ 1 (cos x))
6.0ms	(/ x (sin x))

series193.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

87.0ms	(/ 1 (* (* (/ x (sin x)) (/ x (sin x))) (+ 1 (cos x))))
62.0ms	(* (/ x (sin x)) (/ x (sin x)))
33.0ms	(/ x (sin x))
11.0ms	(+ 1 (cos x))

simplify1.1s

Counts: 178 → 178

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-exp-log`
43×	`prod-exp`
40×	`add-cbrt-cube`
23×	`div-exp`
19×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`times-frac` `cbrt-unprod`
12×	`pow1` `associate-l`
11×	`cbrt-undiv`
10×	`associate-/r/`
9×	`associate-*l/`
8×	`rec-exp` `1-exp`
6×	`associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`frac-times` `associate-/r` `pow-prod-down` `associate-r/` `insert-posit16`
3×	`associate-r` `div-inv` `pow-flip`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log` `*-commutative` `distribute-lft-out` `inv-pow` `unswap-sqr`

Counts

4 → 129

Calls

4 calls:

Slowest

213.0ms	(* (/ 1 (* (* (/ x (sin x)) x) (+ 1 (cos x)))) (sin x))
61.0ms	(/ 1 (* (* (/ x (sin x)) x) (+ 1 (cos x))))
10.0ms	(+ 1 (cos x))
8.0ms	(/ x (sin x))

series189.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

77.0ms	(* (/ 1 (* (* (/ x (sin x)) x) (+ 1 (cos x)))) (sin x))
55.0ms	(/ 1 (* (* (/ x (sin x)) x) (+ 1 (cos x))))
43.0ms	(/ x (sin x))
15.0ms	(+ 1 (cos x))

simplify732.0ms

Counts: 141 → 141

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes71.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch2.0ms

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.6s	1613×	body	2560	valid
1.1s	1526×	body	640	valid
736.0ms	1229×	body	1280	valid
399.0ms	988×	body	320	valid
313.0ms	2184×	body	80	valid
90.0ms	460×	body	160	valid