Details

sample325.0ms

Algorithm

intervals

Results

106.0ms	64×	body	1280	valid
90.0ms	21×	body	2560	valid
31.0ms	1×	body	10240	exit
17.0ms	147×	body	80	valid
13.0ms	23×	body	640	valid
5.0ms	13×	body	320	valid
2.0ms	8×	body	160	valid

simplify254.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	14
1	19	14
2	41	14
3	82	14
4	122	14
5	147	14
6	156	14
7	158	14
done	158	14

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.4b	(/ 1.0 (* F F))
4.9b	(* (/ 1.0 (* F F)) (tan (* PI l)))
30.3b	(tan (* PI l))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
17×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
8×	`pow1`
7×	`times-frac`
6×	`associate-r` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`tan-quot` `associate-/l*` `unswap-sqr`
2×	`pow-prod-down` `*-commutative` `div-inv`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/r*`

Counts

4 → 85

Calls

4 calls:

14.0ms	(* PI l)
16.0ms	(/ 1.0 (* F F))
102.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
18.0ms	(tan (* PI l))

series471.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* PI l)
52.0ms	(/ 1.0 (* F F))
242.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
148.0ms	(tan (* PI l))

simplify3.5s

Counts

97 → 97

Iterations

Useful iterations: 2 (279.0ms)

Iter	Nodes	Cost
0	143	924
1	316	903
2	1013	771
3	4042	771
done	5000	771

prune352.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* (/ 1 F) (* (/ 1.0 F) (tan (* PI l))))
0.3b	(* (/ 1.0 F) (tan (* PI l)))
30.3b	(tan (* PI l))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
32×	`add-cbrt-cube`
29×	`associate-l`
28×	`add-sqr-sqrt`
23×	`prod-exp`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`pow1` `cbrt-unprod`
11×	`div-exp`
7×	`tan-quot` `associate-r`
6×	`cbrt-undiv` `frac-times` `associate-*r/`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `*-commutative` `unswap-sqr`
2×	`div-inv`

Counts

4 → 117

Calls

4 calls:

7.0ms	(* PI l)
114.0ms	(* (/ 1 F) (* (/ 1.0 F) (tan (* PI l))))
53.0ms	(* (/ 1.0 F) (tan (* PI l)))
18.0ms	(tan (* PI l))

series513.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* PI l)
197.0ms	(* (/ 1 F) (* (/ 1.0 F) (tan (* PI l))))
191.0ms	(* (/ 1.0 F) (tan (* PI l)))
99.0ms	(tan (* PI l))

simplify2.1s

Counts

129 → 129

Iterations

Useful iterations: 2 (435.0ms)

Iter	Nodes	Cost
0	211	1572
1	504	1424
2	1690	1188
done	5000	1188

prune523.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* (/ 1 F) (* 1.0 (/ (tan (* PI l)) F)))
0.2b	(/ (tan (* PI l)) F)
30.3b	(tan (* PI l))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-exp-log`
29×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp`
18×	`times-frac`
16×	`associate-l`
11×	`pow1` `div-exp` `cbrt-unprod`
6×	`cbrt-undiv`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-r/` `associate-/r` `associate-/l*`
2×	`tan-quot` `*-commutative` `div-inv`
1×	`frac-times` `frac-2neg` `associate-*l/` `clear-num` `associate-/l/` `unswap-sqr`

Counts

4 → 107

Calls

4 calls:

9.0ms	(* PI l)
45.0ms	(* (/ 1 F) (* 1.0 (/ (tan (* PI l)) F)))
16.0ms	(/ (tan (* PI l)) F)
15.0ms	(tan (* PI l))

series466.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* PI l)
219.0ms	(* (/ 1 F) (* 1.0 (/ (tan (* PI l)) F)))
131.0ms	(/ (tan (* PI l)) F)
85.0ms	(tan (* PI l))

simplify2.6s

Counts

119 → 119

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	200	1445
1	452	1303
2	1550	1091
done	5000	1090

prune417.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.2b	(/ (tan (* PI l)) F)
30.3b	(tan (* PI l))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

14.0ms	(* PI l)
14.0ms	(* PI l)
26.0ms	(/ (tan (* PI l)) F)
17.0ms	(tan (* PI l))

series319.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* PI l)
30.0ms	(* PI l)
145.0ms	(/ (tan (* PI l)) F)
110.0ms	(tan (* PI l))

simplify1.9s

Counts

92 → 92

Iterations

Useful iterations: 3 (465.0ms)

Iter	Nodes	Cost
0	112	709
1	213	683
2	509	631
3	1433	630
done	5000	630

prune332.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.8b

regimes525.0ms

Accuracy

0% (0.4b remaining)

Error of 12.9b against oracle of 12.4b and baseline of 12.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	27
1	21	27
done	21	27

end0.0ms

sample10.3s

Algorithm

intervals

Results

5.1s	830×	body	2560	valid
2.5s	1701×	body	1280	valid
923.0ms	4480×	body	80	valid
853.0ms	975×	body	640	valid
254.0ms	7×	body	10240	exit
169.0ms	370×	body	320	valid
69.0ms	218×	body	160	valid