Details

sample146.0ms

Algorithm

intervals

Results

47.0ms	86×	body	1280	valid
34.0ms	71×	body	640	valid
26.0ms	302×	body	80	valid
9.0ms	35×	body	320	valid
4.0ms	21×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	1888
6	631
5	245
4	128
3	65
2	30
1	15
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sinh y)
0.0b	(/ (sinh y) y)
0.2b	(* (sin x) (/ (sinh y) y))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `associate-l` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `sinh-def` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative` `associate-/l/`

Counts

3 → 74

Calls

3 calls:

2.0ms	(sinh y)
11.0ms	(/ (sinh y) y)
25.0ms	(* (sin x) (/ (sinh y) y))

series342.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(sinh y)
108.0ms	(/ (sinh y) y)
169.0ms	(* (sin x) (/ (sinh y) y))

simplify2.7s

Counts

83 → 83

Iterations

Iter	Nodes
done	5002
3	4027
2	1119
1	359
0	146

prune436.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/6 (* y y) (fma (* 1/120 (* y y)) (* y y) 1))
0.0b	(* (sin x) (fma 1/6 (* y y) (fma (* 1/120 (* y y)) (* y y) 1)))
0.1b	(* 1/120 (* y y))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

3 → 53

Calls

3 calls:

0.0ms	(fma 1/6 (* y y) (fma (* 1/120 (* y y)) (* y y) 1))
9.0ms	(* (sin x) (fma 1/6 (* y y) (fma (* 1/120 (* y y)) (* y y) 1)))
14.0ms	(* 1/120 (* y y))

series246.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(fma 1/6 (* y y) (fma (* 1/120 (* y y)) (* y y) 1))
153.0ms	(* (sin x) (fma 1/6 (* y y) (fma (* 1/120 (* y y)) (* y y) 1)))
28.0ms	(* 1/120 (* y y))

simplify2.6s

Counts

62 → 62

Iterations

Iter	Nodes
done	5007
3	2970
2	702
1	251
0	98

prune356.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (sin x) (* (* y y) (fma (* y y) 1/120 1/6)) (sin x))
0.0b	(fma (* y y) 1/120 1/6)
0.2b	(* (* y y) (fma (* y y) 1/120 1/6))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `add-cube-cbrt` `fma-udef`
3×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative` `unswap-sqr`

Counts

3 → 43

Calls

3 calls:

0.0ms	(fma (sin x) (* (* y y) (fma (* y y) 1/120 1/6)) (sin x))
0.0ms	(fma (* y y) 1/120 1/6)
17.0ms	(* (* y y) (fma (* y y) 1/120 1/6))

series355.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms	(fma (sin x) (* (* y y) (fma (* y y) 1/120 1/6)) (sin x))
74.0ms	(fma (* y y) 1/120 1/6)
140.0ms	(* (* y y) (fma (* y y) 1/120 1/6))

simplify2.8s

Counts

52 → 52

Iterations

Iter	Nodes
done	5002
3	2577
2	682
1	211
0	81

prune331.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* y y) (* (* (cbrt (fma (* y y) 1/120 1/6)) (cbrt (fma (* y y) 1/120 1/6))) (cbrt (fma (* y y) 1/120 1/6))))
1.0b	(cbrt (fma (* y y) 1/120 1/6))
1.0b	(cbrt (fma (* y y) 1/120 1/6))
1.0b	(cbrt (fma (* y y) 1/120 1/6))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1` `add-exp-log`
17×	`add-cbrt-cube`
15×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`associate-r` `associate-l` `*-commutative`

Counts

4 → 69

Calls

4 calls:

105.0ms	(* (* y y) (* (* (cbrt (fma (* y y) 1/120 1/6)) (cbrt (fma (* y y) 1/120 1/6))) (cbrt (fma (* y y) 1/120 1/6))))
1.0ms	(cbrt (fma (* y y) 1/120 1/6))
1.0ms	(cbrt (fma (* y y) 1/120 1/6))
2.0ms	(cbrt (fma (* y y) 1/120 1/6))

series672.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (* y y) (* (* (cbrt (fma (* y y) 1/120 1/6)) (cbrt (fma (* y y) 1/120 1/6))) (cbrt (fma (* y y) 1/120 1/6))))
150.0ms	(cbrt (fma (* y y) 1/120 1/6))
223.0ms	(cbrt (fma (* y y) 1/120 1/6))
163.0ms	(cbrt (fma (* y y) 1/120 1/6))

simplify3.6s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
3	4393
2	943
1	277
0	108

prune544.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

regimes128.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.3s	3028×	body	1280	valid
1.3s	2479×	body	640	valid
1.1s	8608×	body	80	valid
299.0ms	1295×	body	320	valid
95.0ms	593×	body	160	valid