Details

sample126.0ms

Algorithm

intervals

Results

54.0ms	57×	body	1280	valid
26.0ms	44×	body	640	valid
16.0ms	123×	body	80	valid
10.0ms	23×	body	320	valid
3.0ms	9×	body	160	valid

simplify410.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	16
1	20	16
2	43	16
3	89	16
4	168	16
5	257	16
6	273	16
done	273	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize25.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
12.6b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 85

Calls

3 calls:

125.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
53.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
96.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series259.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
74.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
110.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.7s

Counts

94 → 94

Iterations

Useful iterations: 2 (386.0ms)

Iter	Nodes	Cost
0	169	1554
1	405	1349
2	1480	1080
done	5000	1080

prune441.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin (* x 0.5)) (sin x))
0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
28×	`times-frac`
26×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r`
14×	`associate-l`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
4×	`pow-prod-down` `associate-*l/`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`*-commutative` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-*r/` `clear-num`

Counts

3 → 104

Calls

3 calls:

27.0ms	(/ (sin (* x 0.5)) (sin x))
136.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
56.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series273.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(/ (sin (* x 0.5)) (sin x))
144.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
71.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify2.0s

Counts

113 → 113

Iterations

Useful iterations: 2 (381.0ms)

Iter	Nodes	Cost
0	189	1786
1	447	1612
2	1605	1349
done	5001	1349

prune485.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
0.2b	(/ (sin (* x 0.5)) (sin x))
0.2b	(* (/ (* (sin (* 0.5 x)) 8.0) 3.0) (/ (sin (* x 0.5)) (sin x)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
27×	`add-sqr-sqrt`
25×	`times-frac`
22×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/r*`
5×	`pow1`
4×	`div-inv` `associate-/l*`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `unswap-sqr`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

3 → 100

Calls

3 calls:

36.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
24.0ms	(/ (sin (* x 0.5)) (sin x))
64.0ms	(* (/ (* (sin (* 0.5 x)) 8.0) 3.0) (/ (sin (* x 0.5)) (sin x)))

series289.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
59.0ms	(/ (sin (* x 0.5)) (sin x))
169.0ms	(* (/ (* (sin (* 0.5 x)) 8.0) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify1.6s

Counts

109 → 109

Iterations

Useful iterations: 2 (395.0ms)

Iter	Nodes	Cost
0	184	1811
1	450	1731
2	1654	1375
done	5001	1375

prune557.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin (* x 0.5)) (sin x))
0.2b	(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
0.2b	(* (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin (* x 0.5)) (sin x)))
0.3b	(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

rewrite459.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
37×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
34×	`add-exp-log` `add-cbrt-cube`
33×	`associate-l`
28×	`sqrt-prod`
20×	`pow1`
17×	`associate-r`
16×	`prod-exp` `cbrt-unprod`
13×	`sqrt-div` `associate-*l/`
10×	`pow-prod-down`
6×	`frac-times`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-*r/` `div-exp` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-/r` `-commutative` `associate-/l*` `unswap-sqr`
1×	`frac-2neg` `clear-num`

Counts

4 → 147

Calls

4 calls:

14.0ms	(/ (sin (* x 0.5)) (sin x))
54.0ms	(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
278.0ms	(* (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin (* x 0.5)) (sin x)))
106.0ms	(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

series569.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (sin (* x 0.5)) (sin x))
104.0ms	(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
231.0ms	(* (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin (* x 0.5)) (sin x)))
170.0ms	(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

simplify1.9s

Counts

159 → 159

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	240	2970
1	575	2348
2	2088	1952
done	5000	1945

prune726.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes75.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	15	18
1	19	16
done	19	16

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.7s	1569×	body	1280	valid
1.2s	1216×	body	640	valid
737.0ms	643×	body	320	valid
684.0ms	4238×	body	80	valid
85.0ms	334×	body	160	valid