Details

sample555.0ms

Algorithm

intervals

Results

120.0ms	42×	body	1280	valid
117.0ms	159×	body	80	valid
104.0ms	47×	body	640	valid
43.0ms	29×	body	320	valid
24.0ms	57×	body	80	nan
6.0ms	7×	body	160	valid

simplify381.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

381.0ms

(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.9b

localize73.0ms

Local error

Found 4 expressions with local error:

21.2b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.7b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.1b	(/ x (tan B))

rewrite623.0ms

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:

Slowest

489.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
106.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
19.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
5.0ms	(/ x (tan B))

series585.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

190.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
181.0ms	(/ x (tan B))
113.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
100.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify10.1s

Counts

79 → 109

Calls

79 calls:

Slowest

564.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
541.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
507.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)
491.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
464.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

21.2b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.7b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.1b	(/ (* x (cos B)) (sin B))

rewrite169.0ms

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:

Slowest

100.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
31.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
23.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
14.0ms	(/ (* x (cos B)) (sin B))

series573.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

227.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
130.0ms	(/ (* x (cos B)) (sin B))
119.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
96.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify10.0s

Counts

66 → 102

Calls

66 calls:

Slowest

606.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
604.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
581.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
563.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
473.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

21.2b	(sqrt (+ (+ 2 (* F F)) (* 2 x)))
21.2b	(sqrt (+ (+ 2 (* F F)) (* 2 x)))
0.7b	(/ (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F) (sin B))
0.7b	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))

rewrite413.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-exp-log`
50×	`add-sqr-sqrt`
44×	`unpow-prod-down`
28×	`prod-exp` `sqrt-prod`
20×	`*-un-lft-identity` `add-cube-cbrt`
16×	`unswap-sqr`
15×	`add-cbrt-cube`
12×	`pow-to-exp` `swap-sqr` `pow-exp` `sqr-pow`
11×	`div-exp`
10×	`associate-r` `associate-l`
6×	`pow1`
4×	`sqrt-div` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `associate-/r*` `times-frac`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow2` `clear-num` `frac-2neg` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `div-inv` `associate-/l`

Counts

4 → 135

Calls

4 calls:

Slowest

178.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))
167.0ms	(/ (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F) (sin B))
35.0ms	(sqrt (+ (+ 2 (* F F)) (* 2 x)))
28.0ms	(sqrt (+ (+ 2 (* F F)) (* 2 x)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

191.0ms	(/ (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F) (sin B))
94.0ms	(sqrt (+ (+ 2 (* F F)) (* 2 x)))
83.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))
76.0ms	(sqrt (+ (+ 2 (* F F)) (* 2 x)))

simplify29.6s

Counts

140 → 147

Calls

140 calls:

Slowest

641.0ms	(/ (* (* (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F) (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F)) (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F)) (* (* (sin B) (sin B)) (sin B)))
567.0ms	(/ (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) 1)
561.0ms	(- (+ (log (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))) (log F)) (log (sin B)))
532.0ms	(/ (* (* (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))) (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))) (* (* F F) F)) (* (* (sin B) (sin B)) (sin B)))
516.0ms	(/ (* (* (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))) (* (* F F) F)) (* (* (sin B) (sin B)) (sin B)))

prune2.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

21.2b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.7b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.3b	(* x (/ (cos B) (sin B)))
0.3b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

Slowest

93.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
39.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
35.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
12.0ms	(* x (/ (cos B) (sin B)))

series530.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

212.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
136.0ms	(* x (/ (cos B) (sin B)))
92.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
90.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify10.4s

Counts

78 → 113

Calls

78 calls:

Slowest

838.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)
556.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
531.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
473.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
432.0ms	(* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (* (* F F) F))

prune1.5s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.0b

regimes497.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.8b

bsearch640.0ms

end0.0ms

sample15.0s

Algorithm

intervals

Results

5.9s	1686×	body	1280	valid
3.7s	1414×	body	640	valid
2.3s	4670×	body	80	valid
1.6s	714×	body	320	valid
805.0ms	1611×	body	80	nan
355.0ms	349×	body	160	valid