Details

sample715.0ms

Algorithm

intervals

Results

475.0ms	231×	body	10240	exit
106.0ms	281×	body	80	valid
5.0ms	9×	body	160	valid

simplify179.0ms

Calls

1 calls:

Slowest

178.0ms

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.6b

localize15.0ms

Local error

Found 4 expressions with local error:

6.2b	(/ (tan (* PI l)) (* F F))
3.8b	(tan (* PI l))
0.2b	(* PI l)
0.2b	(* PI l)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

5.0ms	(/ (tan (* PI l)) (* F F))
1.0ms	(tan (* PI l))
0.0ms	(* PI l)
0.0ms	(* PI l)

series275.0ms

Calls

4 calls:

Slowest

137.0ms	(/ (tan (* PI l)) (* F F))
63.0ms	(tan (* PI l))
46.0ms	(* PI l)
28.0ms	(* PI l)

simplify986.0ms

Calls

23 calls:

Slowest

426.0ms	(+ (/ (* 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)))))
233.0ms	(/ (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* (* F F) (* F F)) (* F F)))
218.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
32.0ms	(- (log (tan (* PI l))) (log (* F F)))
16.0ms	(/ (* (cbrt (tan (* PI l))) (cbrt (tan (* PI l)))) F)

prune482.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

3.8b	(tan (* PI l))
0.2b	(* PI l)
0.2b	(* PI l)
0.2b	(/ (tan (* PI l)) F)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

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

series199.0ms

Calls

4 calls:

Slowest

69.0ms	(/ (tan (* PI l)) F)
64.0ms	(tan (* PI l))
34.0ms	(* PI l)
32.0ms	(* PI l)

simplify422.0ms

Calls

15 calls:

Slowest

210.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
182.0ms	(+ (* 1/3 (/ (* (pow PI 3) (pow l 3)) F)) (+ (/ (* PI l) F) (* 2/15 (/ (* (pow PI 5) (pow l 5)) F))))
6.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
6.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
2.0ms	(* (cbrt (tan (* PI l))) (cbrt (tan (* PI l))))

prune489.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

3.8b	(tan (* PI l))
0.3b	(* (tan (* PI l)) (/ 1 F))
0.2b	(* PI l)
0.2b	(* PI l)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

6.0ms	(* (tan (* PI l)) (/ 1 F))
2.0ms	(tan (* PI l))
0.0ms	(* PI l)
0.0ms	(* PI l)

series200.0ms

Calls

4 calls:

Slowest

88.0ms	(* (tan (* PI l)) (/ 1 F))
48.0ms	(tan (* PI l))
32.0ms	(* PI l)
32.0ms	(* PI l)

simplify986.0ms

Calls

24 calls:

Slowest

409.0ms	(* (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* (/ 1 F) (/ 1 F)) (/ 1 F)))
277.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
159.0ms	(+ (* 1/3 (/ (* (pow PI 3) (pow l 3)) F)) (+ (/ (* PI l) F) (* 2/15 (/ (* (pow PI 5) (pow l 5)) F))))
35.0ms	(+ (log (tan (* PI l))) (log (/ 1 F)))
23.0ms	(* (sin (* PI l)) (/ 1 F))

prune551.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize7.0ms

Local error

Found 4 expressions with local error:

3.8b	(tan (* PI l))
0.2b	(* PI l)
0.2b	(* PI l)
0.2b	(* (/ 1 F) (/ (tan (* PI l)) F))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

8.0ms	(* (/ 1 F) (/ (tan (* PI l)) F))
3.0ms	(tan (* PI l))
0.0ms	(* PI l)
0.0ms	(* PI l)

series255.0ms

Calls

4 calls:

Slowest

134.0ms	(* (/ 1 F) (/ (tan (* PI l)) F))
47.0ms	(tan (* PI l))
43.0ms	(* PI l)
31.0ms	(* PI l)

simplify1.2s

Calls

24 calls:

Slowest

469.0ms	(* (* (* (/ 1 F) (/ 1 F)) (/ 1 F)) (* (* (/ (tan (* PI l)) F) (/ (tan (* PI l)) F)) (/ (tan (* PI l)) F)))
267.0ms	(+ (/ (* PI l) (pow F 2)) (* 1/3 (/ (* (pow PI 3) (pow l 3)) (pow F 2))))
204.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
116.0ms	(+ (log (/ 1 F)) (log (/ (tan (* PI l)) F)))
74.0ms	(* (/ 1 F) (/ (tan (* PI l)) F))

prune559.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.4b

regimes362.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample19.9s

Algorithm

intervals

Results

16.7s	7600×	body	10240	exit
2.7s	8887×	body	80	valid
157.0ms	282×	body	160	valid