Details

sample451.0ms

Algorithm

intervals

Results

331.0ms	231×	body	10240	exit
41.0ms	281×	body	80	valid
2.0ms	7×	body	160	valid

simplify241.0ms

Calls

1 calls:

Slowest

240.0ms

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.0b

localize38.0ms

Local error

Found 4 expressions with local error:

7.9b	(/ (tan (* PI l)) (* F F))
2.7b	(tan (* PI l))
0.3b	(* PI l)
0.3b	(* PI l)

rewrite21.0ms

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))
4.0ms	(tan (* PI l))
0.0ms	(* PI l)
0.0ms	(* PI l)

series336.0ms

Calls

4 calls:

Slowest

176.0ms	(/ (tan (* PI l)) (* F F))
104.0ms	(tan (* PI l))
29.0ms	(* PI l)
27.0ms	(* PI l)

simplify889.0ms

Calls

23 calls:

Slowest

318.0ms	(/ (* (* (tan (* PI l)) (tan (* PI l))) (tan (* PI l))) (* (* (* F F) (* F F)) (* F F)))
176.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
157.0ms	(+ (/ (* 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)))))
51.0ms	(- (log (tan (* PI l))) (log (* F F)))
45.0ms	(/ (sin (* PI l)) (* (pow F 2) (cos (* PI l))))

prune722.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

2.7b	(tan (* PI l))
0.3b	(* PI l)
0.3b	(* PI l)
0.2b	(/ (tan (* PI l)) F)

rewrite8.0ms

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

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

series244.0ms

Calls

4 calls:

Slowest

115.0ms	(/ (tan (* PI l)) F)
76.0ms	(tan (* PI l))
32.0ms	(* PI l)
21.0ms	(* PI l)

simplify642.0ms

Calls

15 calls:

Slowest

325.0ms	(+ (* 1/3 (/ (* (pow PI 3) (pow l 3)) F)) (+ (/ (* PI l) F) (* 2/15 (/ (* (pow PI 5) (pow l 5)) F))))
205.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
32.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
31.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
7.0ms	(* (cbrt (tan (* PI l))) (cbrt (tan (* PI l))))

prune595.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

2.7b	(tan (* PI l))
0.3b	(* PI l)
0.3b	(* PI l)
0.2b	(/ (tan (* PI l)) F)

rewrite11.0ms

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)
2.0ms	(tan (* PI l))
0.0ms	(* PI l)
0.0ms	(* PI l)

series234.0ms

Calls

4 calls:

Slowest

127.0ms	(/ (tan (* PI l)) F)
62.0ms	(tan (* PI l))
23.0ms	(* PI l)
21.0ms	(* PI l)

simplify608.0ms

Calls

15 calls:

Slowest

298.0ms	(+ (* 1/3 (/ (* (pow PI 3) (pow l 3)) F)) (+ (/ (* PI l) F) (* 2/15 (/ (* (pow PI 5) (pow l 5)) F))))
196.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
32.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
31.0ms	(/ (sin (* PI l)) (* F (cos (* PI l))))
9.0ms	(/ (sin (* PI l)) (cos (* PI l)))

prune673.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

2.7b	(tan (* PI l))
2.7b	(tan (* PI l))
2.7b	(tan (* PI l))
0.6b	(cbrt (tan (* PI l)))

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` `tan-quot` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`cbrt-div` `pow1/3`

Calls

4 calls:

Slowest

4.0ms	(tan (* PI l))
4.0ms	(tan (* PI l))
4.0ms	(tan (* PI l))
3.0ms	(cbrt (tan (* PI l)))

series561.0ms

Calls

4 calls:

Slowest

291.0ms	(cbrt (tan (* PI l)))
114.0ms	(tan (* PI l))
81.0ms	(tan (* PI l))
75.0ms	(tan (* PI l))

simplify1.0s

Calls

16 calls:

Slowest

273.0ms	(+ (* 1/9 (* (exp (* 1/3 (+ (log l) (log PI)))) (* (pow PI 2) (pow l 2)))) (+ (* 13/405 (* (exp (* 1/3 (+ (log l) (log PI)))) (* (pow PI 4) (pow l 4)))) (exp (* 1/3 (+ (log l) (log PI))))))
228.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
227.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
208.0ms	(+ (* 2/15 (* (pow PI 5) (pow l 5))) (+ (* 1/3 (* (pow PI 3) (pow l 3))) (* PI l)))
13.0ms	(pow (/ (sin (* PI l)) (cos (* PI l))) 1/3)

prune799.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

regimes321.0ms

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

18.0s	7836×	body	10240	exit
1.9s	8970×	body	80	valid
119.0ms	257×	body	160	valid