Details

sample2.2s

Algorithm

intervals

Results

1.9s	269×	body	10240	exit
167.0ms	283×	body	80	valid
9.0ms	10×	body	160	valid

simplify357.0ms

Calls

1 calls:

Slowest

356.0ms

(- (* PI l) (* (/ 1 (* F F)) (tan (* PI l))))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.1b

localize40.0ms

Local error

Found 4 expressions with local error:

6.8b	(/ (tan (* PI l)) (* F F))
3.4b	(tan (* PI l))
0.3b	(* PI l)
0.3b	(* PI l)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-/l*`
2×	`tan-quot` `*-commutative`
1×	`cbrt-undiv` `clear-num` `associate-/r*` `frac-2neg` `div-exp` `div-inv` `associate-/l/`

Calls

4 calls:

Slowest

15.0ms	(/ (tan (* PI l)) (* F F))
4.0ms	(tan (* PI l))
0.0ms	(* PI l)
0.0ms	(* PI l)

series323.0ms

Calls

4 calls:

Slowest

167.0ms	(/ (tan (* PI l)) (* F F))
60.0ms	(tan (* PI l))
48.0ms	(* PI l)
47.0ms	(* PI l)

simplify1.2s

Calls

23 calls:

Slowest

427.0ms	(/ (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* (* F F) (* F F)) (* F F)))
261.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
213.0ms	(+ (/ (* PI l) (pow F 2)) (+ (* 2/15 (/ (* (pow PI 5) (pow l 5)) (pow F 2))) (* 1/3 (/ (* (pow PI 3) (pow l 3)) (pow F 2)))))
81.0ms	(- (log (tan (* PI l))) (log (* F F)))
52.0ms	(/ (sin (* PI l)) (* (pow F 2) (cos (* PI l))))

prune903.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

3.4b	(tan (* PI l))
0.3b	(* PI l)
0.3b	(* PI l)
0.2b	(/ (tan (* PI l)) F)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`tan-quot` `*-commutative`
1×	`clear-num` `frac-2neg` `div-inv` `associate-/l/`

Calls

4 calls:

Slowest

10.0ms	(/ (tan (* PI l)) F)
4.0ms	(tan (* PI l))
0.0ms	(* PI l)
0.0ms	(* PI l)

series243.0ms

Calls

4 calls:

Slowest

96.0ms	(/ (tan (* PI l)) F)
62.0ms	(tan (* PI l))
47.0ms	(* PI l)
37.0ms	(* PI l)

simplify737.0ms

Calls

15 calls:

Slowest

318.0ms	(+ (* 1/3 (/ (* (pow PI 3) (pow l 3)) F)) (+ (/ (* PI l) F) (* 2/15 (/ (* (pow PI 5) (pow l 5)) F))))
291.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
27.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
27.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
10.0ms	(/ (sin (* PI l)) (cos (* PI l)))

prune696.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

3.4b	(tan (* PI l))
0.3b	(* PI l)
0.3b	(* PI l)
0.2b	(/ (tan (* PI l)) F)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`tan-quot` `*-commutative`
1×	`clear-num` `frac-2neg` `div-inv` `associate-/l/`

Calls

4 calls:

Slowest

7.0ms	(/ (tan (* PI l)) F)
3.0ms	(tan (* PI l))
1.0ms	(* PI l)
0.0ms	(* PI l)

series267.0ms

Calls

4 calls:

Slowest

113.0ms	(/ (tan (* PI l)) F)
63.0ms	(tan (* PI l))
46.0ms	(* PI l)
45.0ms	(* PI l)

simplify835.0ms

Calls

15 calls:

Slowest

424.0ms	(+ (* 1/3 (/ (* (pow PI 3) (pow l 3)) F)) (+ (/ (* PI l) F) (* 2/15 (/ (* (pow PI 5) (pow l 5)) F))))
265.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
33.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
33.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
10.0ms	(/ (sin (* PI l)) (cos (* PI l)))

prune837.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 4 expressions with local error:

3.4b	(tan (* PI l))
0.4b	(/ 1 (/ F (tan (* PI l))))
0.3b	(* PI l)
0.3b	(* PI l)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `pow1` `associate-/r` `-un-lft-identity` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`tan-quot` `associate-/r/` `*-commutative` `div-inv`
1×	`rec-exp` `clear-num` `frac-2neg` `pow-flip` `inv-pow`

Calls

4 calls:

Slowest

3.0ms	(tan (* PI l))
3.0ms	(/ 1 (/ F (tan (* PI l))))
0.0ms	(* PI l)
0.0ms	(* PI l)

series299.0ms

Calls

4 calls:

Slowest

157.0ms	(/ 1 (/ F (tan (* PI l))))
55.0ms	(tan (* PI l))
44.0ms	(* PI l)
43.0ms	(* PI l)

simplify764.0ms

Calls

19 calls:

Slowest

311.0ms	(+ (* 1/3 (/ (* (pow PI 3) (pow l 3)) F)) (/ (* PI l) F))
260.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
33.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
33.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
18.0ms	(/ 1 (tan (* PI l)))

prune927.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.4b

regimes967.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.5b and baseline of 0.7b

bsearch8.0ms

end1.0ms

sample52.7s

Algorithm

intervals

Results

48.5s	7632×	body	10240	exit
3.4s	8887×	body	80	valid
229.0ms	266×	body	160	valid