Details

sample922.0ms

Algorithm

intervals

Results

739.0ms	270×	body	10240	exit
99.0ms	277×	body	80	valid
2.0ms	4×	body	160	valid

simplify176.0ms

Calls

1 calls:

Slowest

175.0ms

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.9b

localize43.0ms

Local error

Found 4 expressions with local error:

7.6b	(* (/ 1 (* F F)) (tan (* PI l)))
2.1b	(tan (* PI l))
0.3b	(/ 1 (* F F))
0.2b	(* PI l)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log`
7×	`pow1`
6×	`add-cube-cbrt`
6×	`add-cbrt-cube`
6×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
4×	`add-log-exp`
4×	`log1p-expm1-u`
4×	`associate-l`
4×	`expm1-log1p-u`
3×	`tan-quot`
3×	`associate-r`
2×	`pow-flip`
2×	`div-inv`
2×	`*-commutative`
2×	`prod-exp`
2×	`rec-exp`
1×	`inv-pow`
1×	`cbrt-unprod`
1×	`associate-*r/`
1×	`associate-*l/`
1×	`pow-prod-down`
1×	`frac-2neg`
1×	`associate-/r*`
1×	`clear-num`
1×	`frac-times`
1×	`pow2`

Calls

4 calls:

Slowest

16.0ms	(* (/ 1 (* F F)) (tan (* PI l)))
3.0ms	(tan (* PI l))
1.0ms	(/ 1 (* F F))
0.0ms	(* PI l)

series244.0ms

Calls

4 calls:

Slowest

163.0ms	(* (/ 1 (* F F)) (tan (* PI l)))
39.0ms	(tan (* PI l))
34.0ms	(* PI l)
8.0ms	(/ 1 (* F F))

simplify977.0ms

Calls

27 calls:

Slowest

285.0ms	(+ (/ (* PI l) (pow F 2)) (* 1/3 (/ (* (pow PI 3) (pow l 3)) (pow F 2))))
251.0ms	(* (* (* (/ 1 (* F F)) (/ 1 (* F F))) (/ 1 (* F F))) (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))))
203.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
59.0ms	(+ (log (/ 1 (* F F))) (log (tan (* PI l))))
43.0ms	(* (/ 1 (* F F)) (tan (* PI l)))

prune715.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize14.0ms

Local error

Found 4 expressions with local error:

7.4b	(/ (tan (* l PI)) (* F F))
2.1b	(tan (* l PI))
0.2b	(* l PI)
0.2b	(* PI l)

rewrite13.0ms

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×	`log1p-expm1-u`
4×	`pow1`
4×	`expm1-log1p-u`
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

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

series244.0ms

Calls

4 calls:

Slowest

118.0ms	(/ (tan (* l PI)) (* F F))
48.0ms	(tan (* l PI))
42.0ms	(* PI l)
36.0ms	(* l PI)

simplify621.0ms

Calls

23 calls:

Slowest

253.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
171.0ms	(/ (* (* (tan (* l PI)) (tan (* l PI))) (tan (* l PI))) (* (* (* F F) (* F F)) (* F F)))
82.0ms	(+ (/ (* 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)))))
24.0ms	(- (log (tan (* l PI))) (log (* F F)))
20.0ms	(/ (sin (* PI l)) (* (pow F 2) (cos (* PI l))))

prune592.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

2.1b	(tan (* l PI))
0.2b	(* l PI)
0.2b	(* PI l)
0.2b	(/ (tan (* l PI)) 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×	`log1p-expm1-u`
4×	`add-exp-log`
4×	`add-cbrt-cube`
4×	`pow1`
4×	`expm1-log1p-u`
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 (* l PI)) F)
4.0ms	(tan (* l PI))
0.0ms	(* l PI)
0.0ms	(* PI l)

series171.0ms

Calls

4 calls:

Slowest

68.0ms	(/ (tan (* l PI)) F)
38.0ms	(tan (* l PI))
35.0ms	(* PI l)
29.0ms	(* l PI)

simplify555.0ms

Calls

15 calls:

Slowest

339.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
173.0ms	(+ (* 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))))
4.0ms	(/ (sin (* PI l)) (cos (* PI l)))

prune600.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

2.1b	(tan (* l PI))
0.2b	(* l PI)
0.2b	(* PI l)
0.2b	(/ (tan (* l PI)) F)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

4.0ms	(/ (tan (* l PI)) F)
2.0ms	(tan (* l PI))
0.0ms	(* l PI)
0.0ms	(* PI l)

series201.0ms

Calls

4 calls:

Slowest

69.0ms	(/ (tan (* l PI)) F)
45.0ms	(tan (* l PI))
44.0ms	(* PI l)
43.0ms	(* l PI)

simplify475.0ms

Calls

15 calls:

Slowest

296.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
136.0ms	(+ (* 1/3 (/ (* (pow PI 3) (pow l 3)) F)) (+ (/ (* PI l) F) (* 2/15 (/ (* (pow PI 5) (pow l 5)) F))))
7.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
6.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
4.0ms	(* (cbrt (tan (* l PI))) (cbrt (tan (* l PI))))

prune533.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.3b

regimes482.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample20.8s

Algorithm

intervals

Results

18.3s	7988×	body	10240	exit
2.0s	8863×	body	80	valid
124.0ms	269×	body	160	valid