Details

sample1.4s

Algorithm

intervals

Results

1.1s	249×	body	10240	exit
139.0ms	283×	body	80	valid
3.0ms	5×	body	160	valid

simplify227.0ms

Calls

1 calls:

Slowest

226.0ms

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.0b

localize29.0ms

Local error

Found 4 expressions with local error:

8.1b	(/ (tan (* PI l)) (* F F))
3.6b	(tan (* PI l))
0.2b	(* PI l)
0.2b	(* PI l)

rewrite20.0ms

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

14.0ms	(/ (tan (* PI l)) (* F F))
3.0ms	(tan (* PI l))
0.0ms	(* PI l)
0.0ms	(* PI l)

series391.0ms

Calls

4 calls:

Slowest

206.0ms	(/ (tan (* PI l)) (* F F))
109.0ms	(tan (* PI l))
38.0ms	(* PI l)
37.0ms	(* PI l)

simplify1.0s

Calls

23 calls:

Slowest

354.0ms	(/ (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* (* F F) (* F F)) (* F F)))
211.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
180.0ms	(+ (/ (* 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)))))
58.0ms	(- (log (tan (* PI l))) (log (* F F)))
45.0ms	(/ (sin (* PI l)) (* (pow F 2) (cos (* PI l))))

prune763.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

3.6b	(tan (* PI l))
0.2b	(/ (tan (* PI l)) F)
0.2b	(* PI l)
0.2b	(* PI l)

rewrite17.0ms

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)
5.0ms	(tan (* PI l))
0.0ms	(* PI l)
0.0ms	(* PI l)

series297.0ms

Calls

4 calls:

Slowest

153.0ms	(/ (tan (* PI l)) F)
89.0ms	(tan (* PI l))
34.0ms	(* PI l)
22.0ms	(* PI l)

simplify590.0ms

Calls

15 calls:

Slowest

283.0ms	(+ (* 1/3 (/ (* (pow PI 3) (pow l 3)) F)) (+ (/ (* PI l) F) (* 2/15 (/ (* (pow PI 5) (pow l 5)) F))))
224.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
21.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
16.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
7.0ms	(sqrt (tan (* PI l)))

prune574.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

3.6b	(tan (* PI l))
0.3b	(* (tan (* PI l)) (/ 1 F))
0.2b	(* PI l)
0.2b	(* PI l)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `tan-quot` `*-commutative`
1×	`frac-times` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `un-div-inv` `cbrt-unprod` `div-inv`

Calls

4 calls:

Slowest

9.0ms	(* (tan (* PI l)) (/ 1 F))
2.0ms	(tan (* PI l))
0.0ms	(* PI l)
0.0ms	(* PI l)

series287.0ms

Calls

4 calls:

Slowest

113.0ms	(* (tan (* PI l)) (/ 1 F))
95.0ms	(tan (* PI l))
42.0ms	(* PI l)
36.0ms	(* PI l)

simplify1.2s

Calls

24 calls:

Slowest

427.0ms	(* (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* (/ 1 F) (/ 1 F)) (/ 1 F)))
289.0ms	(+ (* 1/3 (/ (* (pow PI 3) (pow l 3)) F)) (+ (/ (* PI l) F) (* 2/15 (/ (* (pow PI 5) (pow l 5)) F))))
174.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
55.0ms	(+ (log (tan (* PI l))) (log (/ 1 F)))
50.0ms	(* (tan (* PI l)) (/ 1 F))

prune710.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

3.6b	(tan (* PI l))
0.2b	(/ (tan (* PI l)) F)
0.2b	(* PI l)
0.2b	(* PI l)

rewrite15.0ms

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)

series309.0ms

Calls

4 calls:

Slowest

155.0ms	(/ (tan (* PI l)) F)
86.0ms	(tan (* PI l))
37.0ms	(* PI l)
31.0ms	(* PI l)

simplify543.0ms

Calls

15 calls:

Slowest

266.0ms	(+ (* 1/3 (/ (* (pow PI 3) (pow l 3)) F)) (+ (/ (* PI l) F) (* 2/15 (/ (* (pow PI 5) (pow l 5)) F))))
185.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
30.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
16.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
7.0ms	(/ (sin (* PI l)) (cos (* PI l)))

prune633.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes361.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample20.1s

Algorithm

intervals

Results

17.3s	7840×	body	10240	exit
2.3s	8884×	body	80	valid
141.0ms	259×	body	160	valid