Details

sample1.4s

Algorithm

intervals

Results

1.2s	250×	body	10240	exit
72.0ms	290×	body	80	valid
4.0ms	7×	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: 8.2b

localize17.0ms

Local error

Found 4 expressions with local error:

7.8b	(/ (tan (* PI l)) (* F F))
3.2b	(tan (* PI l))
0.2b	(* PI l)
0.2b	(* PI l)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`pow1` `insert-posit16` `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

18.0ms	(/ (tan (* PI l)) (* F F))
3.0ms	(tan (* PI l))
0.0ms	(* PI l)
0.0ms	(* PI l)

series232.0ms

Calls

4 calls:

Slowest

118.0ms	(/ (tan (* PI l)) (* F F))
58.0ms	(tan (* PI l))
28.0ms	(* PI l)
27.0ms	(* PI l)

simplify956.0ms

Calls

23 calls:

Slowest

294.0ms	(/ (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* (* F F) (* F F)) (* F F)))
281.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
182.0ms	(+ (/ (* 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)))))
42.0ms	(- (log (tan (* PI l))) (log (* F F)))
23.0ms	(/ (sin (* PI l)) (* (pow F 2) (cos (* PI l))))

prune587.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

3.2b	(tan (* PI l))
0.2b	(* PI l)
0.2b	(* PI l)
0.2b	(/ (tan (* PI l)) F)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

9.0ms	(/ (tan (* PI l)) F)
4.0ms	(tan (* PI l))
0.0ms	(* PI l)
0.0ms	(* PI l)

series174.0ms

Calls

4 calls:

Slowest

77.0ms	(/ (tan (* PI l)) F)
43.0ms	(tan (* PI l))
29.0ms	(* PI l)
26.0ms	(* PI l)

simplify690.0ms

Calls

15 calls:

Slowest

301.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
254.0ms	(+ (* 1/3 (/ (* (pow PI 3) (pow l 3)) F)) (+ (/ (* PI l) F) (* 2/15 (/ (* (pow PI 5) (pow l 5)) F))))
34.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
31.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
9.0ms	(/ (sin (* PI l)) (cos (* PI l)))

prune567.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.4b

localize8.0ms

Local error

Found 4 expressions with local error:

3.2b	(tan (* PI l))
0.2b	(* PI l)
0.2b	(* PI l)
0.2b	(* (/ 1 F) (/ (tan (* PI l)) F))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

5.0ms	(* (/ 1 F) (/ (tan (* PI l)) F))
2.0ms	(tan (* PI l))
0.0ms	(* PI l)
0.0ms	(* PI l)

series281.0ms

Calls

4 calls:

Slowest

129.0ms	(* (/ 1 F) (/ (tan (* PI l)) F))
63.0ms	(tan (* PI l))
45.0ms	(* PI l)
44.0ms	(* PI l)

simplify1.3s

Calls

24 calls:

Slowest

485.0ms	(* (* (* (/ 1 F) (/ 1 F)) (/ 1 F)) (* (* (/ (tan (* PI l)) F) (/ (tan (* PI l)) F)) (/ (tan (* PI l)) F)))
309.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
128.0ms	(+ (log (/ 1 F)) (log (/ (tan (* PI l)) F)))
81.0ms	(* (/ 1 F) (/ (tan (* PI l)) F))
81.0ms	(+ (/ (* PI l) (pow F 2)) (* 1/3 (/ (* (pow PI 3) (pow l 3)) (pow F 2))))

prune654.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

3.2b	(tan (* PI l))
0.3b	(* (tan (* PI l)) (/ 1 F))
0.2b	(* PI l)
0.2b	(* PI l)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`associate-r` `insert-posit16` `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

16.0ms	(* (tan (* PI l)) (/ 1 F))
4.0ms	(tan (* PI l))
0.0ms	(* PI l)
0.0ms	(* PI l)

series214.0ms

Calls

4 calls:

Slowest

99.0ms	(* (tan (* PI l)) (/ 1 F))
48.0ms	(tan (* PI l))
39.0ms	(* PI l)
27.0ms	(* PI l)

simplify1.2s

Calls

24 calls:

Slowest

339.0ms	(* (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* (/ 1 F) (/ 1 F)) (/ 1 F)))
315.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
285.0ms	(+ (* 1/3 (/ (* (pow PI 3) (pow l 3)) F)) (+ (/ (* PI l) F) (* 2/15 (/ (* (pow PI 5) (pow l 5)) F))))
83.0ms	(+ (log (tan (* PI l))) (log (/ 1 F)))
31.0ms	(* (sin (* PI l)) (/ 1 F))

prune580.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.4b

regimes311.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample20.4s

Algorithm

intervals

Results

17.8s	7835×	body	10240	exit
2.0s	8961×	body	80	valid
147.0ms	254×	body	160	valid