Details

sample87.0ms

Algorithm

intervals

Results

24.0ms	19×	body	2560	valid
23.0ms	41×	body	1280	valid
12.0ms	33×	body	640	valid
11.0ms	142×	body	80	valid
4.0ms	17×	body	320	valid
1.0ms	4×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	13
1	11	13
2	13	13
done	13	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize10.0ms

Local error

Found 3 expressions with local error:

7.1b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
25.8b	(sin (/ x (* y 2.0)))
26.3b	(tan (/ x (* y 2.0)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

4.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
2.0ms	(sin (/ x (* y 2.0)))
2.0ms	(tan (/ x (* y 2.0)))

series102.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
10.0ms	(sin (/ x (* y 2.0)))
51.0ms	(tan (/ x (* y 2.0)))

simplify1.3s

Counts

58 → 58

Iterations

Useful iterations: 3 (169.0ms)

Iter	Nodes	Cost
0	83	878
1	147	865
2	351	789
3	1205	785
done	5000	785

prune231.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 23.4b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune34.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 23.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
7.1b	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
25.8b	(sin (/ x (* y 2.0)))
26.3b	(tan (/ x (* y 2.0)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

0.0ms	(expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
5.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
2.0ms	(sin (/ x (* y 2.0)))
1.0ms	(tan (/ x (* y 2.0)))

series187.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(expm1 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
42.0ms	(/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))
10.0ms	(sin (/ x (* y 2.0)))
47.0ms	(tan (/ x (* y 2.0)))

simplify1.1s

Counts

72 → 72

Iterations

Useful iterations: 3 (219.0ms)

Iter	Nodes	Cost
0	100	1106
1	180	1089
2	436	983
3	1515	977
done	5001	977

prune298.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 23.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow x 2) E)
1.0b	(expm1 1)
14.3b	(/ (* (pow x 2) E) (pow y 2))
16.3b	(log1p (fma (/ (* (pow x 2) E) (pow y 2)) 0.125 (expm1 1)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
24×	`prod-exp`
21×	`div-exp`
17×	`add-sqr-sqrt`
15×	`pow-to-exp` `pow-exp`
12×	`e-exp-1`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
10×	`unpow-prod-down`
8×	`times-frac` `associate-l` `associate-/r*`
5×	`expm1-log1p-u` `log1p-expm1-u`
4×	`pow1` `unpow2` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`associate-r`
2×	`cbrt-undiv` `cbrt-unprod`
1×	`log1p-udef` `expm1-log1p` `frac-2neg` `log1p-expm1` `clear-num` `-commutative` `div-inv` `associate-/l` `expm1-udef`

Counts

4 → 106

Calls

4 calls:

6.0ms	(* (pow x 2) E)
0.0ms	(expm1 1)
6.0ms	(/ (* (pow x 2) E) (pow y 2))
0.0ms	(log1p (fma (/ (* (pow x 2) E) (pow y 2)) 0.125 (expm1 1)))

series197.0ms

Counts

4 → 10

Calls

4 calls:

29.0ms	(* (pow x 2) E)
0.0ms	(expm1 1)
49.0ms	(/ (* (pow x 2) E) (pow y 2))
118.0ms	(log1p (fma (/ (* (pow x 2) E) (pow y 2)) 0.125 (expm1 1)))

simplify901.0ms

Counts

116 → 116

Iterations

Useful iterations: 2 (245.0ms)

Iter	Nodes	Cost
0	163	1209
1	339	1110
2	1289	978
done	5000	978

prune310.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 23.4b

regimes336.0ms

Accuracy

0% (2.4b remaining)

Error of 28.7b against oracle of 26.3b and baseline of 28.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
done	1	1

end0.0ms

sample2.8s

Algorithm

intervals

Results

853.0ms	648×	body	2560	valid
837.0ms	1361×	body	1280	valid
387.0ms	1039×	body	640	valid
307.0ms	4071×	body	80	valid
143.0ms	582×	body	320	valid
63.0ms	299×	body	160	valid