Details

sample740.0ms

Algorithm

intervals

Results

147.0ms	44×	body	640	valid
119.0ms	57×	body	1280	valid
46.0ms	145×	body	80	valid
35.0ms	29×	body	320	valid
19.0ms	60×	body	80	nan
8.0ms	8×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5020
7	4228
6	1403
5	705
4	360
3	169
2	91
1	46
0	20

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.2b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (tan B))
0.2b	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
15.4b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`add-exp-log`
19×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`times-frac`
7×	`unpow-prod-down` `associate-l`
6×	`associate-/r*` `prod-exp`
5×	`pow1` `div-exp`
4×	`insert-posit16` `associate-/l*` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `associate-r` `pow-exp` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg` `cbrt-unprod` `div-inv`
1×	`pow-pow` `tan-quot` `associate-/r/` `*-commutative`

Counts

4 → 97

Calls

4 calls:

5.0ms	(/ x (tan B))
55.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
146.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
43.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series647.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ x (tan B))
223.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
130.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
136.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.5s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
2	1400
1	458
0	199

prune719.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2)) F)
0.6b	(* (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2))
15.4b	(sqrt (+ (+ 2 (* F F)) (* x 2)))
15.4b	(sqrt (+ (+ 2 (* F F)) (* x 2)))

rewrite427.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`unpow-prod-down`
39×	`add-exp-log`
28×	`prod-exp` `sqrt-prod`
19×	`*-un-lft-identity` `add-cube-cbrt`
17×	`unswap-sqr`
13×	`associate-r`
12×	`pow-to-exp` `swap-sqr` `pow-exp` `sqr-pow`
11×	`add-cbrt-cube` `associate-l`
8×	`pow1`
4×	`sqrt-div` `cbrt-unprod` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `*-commutative` `flip-+`
1×	`pow2` `pow-sqr` `pow-prod-up`

Counts

4 → 130

Calls

4 calls:

202.0ms	(* (* (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2)) F)
178.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2))
24.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))
19.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (* (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2)) F)
90.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2))
55.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))
87.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))

simplify3.4s

Counts

142 → 142

Iterations

Iter	Nodes
done	5003
3	4852
2	1224
1	412
0	167

prune898.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
0.3b	(/ (* x (cos B)) (sin B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
15.4b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
18×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
13×	`*-un-lft-identity` `add-cube-cbrt`
7×	`unpow-prod-down` `associate-l` `prod-exp`
6×	`associate-/r*` `times-frac` `div-exp`
5×	`pow1`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `associate-r` `pow-exp` `cbrt-unprod` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg` `div-inv` `associate-/l*`
1×	`pow-pow` `*-commutative`

Counts

4 → 90

Calls

4 calls:

67.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
12.0ms	(/ (* x (cos B)) (sin B))
82.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
49.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series611.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
159.0ms	(/ (* x (cos B)) (sin B))
122.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
131.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.3s

Counts

102 → 102

Iterations

Iter	Nodes
done	5003
2	1556
1	469
0	185

prune768.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
0.3b	(* (* x (cos B)) (/ 1 (sin B)))
15.4b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-exp-log`
23×	`add-sqr-sqrt` `add-cbrt-cube`
18×	`*-un-lft-identity` `prod-exp` `add-cube-cbrt`
16×	`associate-r`
12×	`times-frac`
10×	`pow1`
8×	`div-exp` `associate-l` `cbrt-unprod`
7×	`unpow-prod-down`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `associate-/r*` `pow-prod-down` `pow-exp` `unswap-sqr` `sqr-pow`
2×	`rec-exp` `1-exp` `*-commutative` `div-inv`
1×	`clear-num` `pow-pow` `frac-2neg` `associate-r/` `un-div-inv` `associate-/l`

Counts

4 → 107

Calls

4 calls:

35.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
110.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
24.0ms	(* (* x (cos B)) (/ 1 (sin B)))
45.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series600.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
109.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
145.0ms	(* (* x (cos B)) (/ 1 (sin B)))
98.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.8s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
2	1790
1	590
0	221

prune756.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes558.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.5b

bsearch921.0ms

Steps

Iters	Range		Point
11	5.329679411286879e-06	4836007051726157.0	11813.229538844102
4	-2.11910976054219e+64	-1.1307817522197012e+64	-1.1491247194378224e+64

simplify37.0ms

Iterations

Iter	Nodes
done	40
1	40
0	33

end0.0ms

sample13.6s

Algorithm

intervals

Results

5.4s	1633×	body	1280	valid
2.9s	1364×	body	640	valid
2.8s	4807×	body	80	valid
953.0ms	686×	body	320	valid
896.0ms	1747×	body	80	nan
300.0ms	349×	body	160	valid