Details

sample604.0ms

Algorithm

intervals

Results

160.0ms	51×	body	640	valid
117.0ms	34×	body	1280	valid
94.0ms	175×	body	80	valid
67.0ms	16×	body	320	valid
21.0ms	42×	body	80	nan
10.0ms	9×	body	160	valid

simplify344.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

343.0ms

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.8b

localize74.0ms

Local error

Found 4 expressions with local error:

14.6b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.1b	(/ x (tan B))

rewrite193.0ms

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

107.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
39.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
38.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
5.0ms	(/ x (tan B))

series553.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

217.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
130.0ms	(/ x (tan B))
111.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
95.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify10.5s

Counts

79 → 109

Calls

79 calls:

Slowest

708.0ms	(pow (* (cbrt (+ (+ 2 (* F F)) (* 2 x))) (cbrt (+ (+ 2 (* F F)) (* 2 x)))) -1/2)
550.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
547.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
539.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
493.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

14.6b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.1b	(* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (/ 1 (sin B)))
0.1b	(/ x (tan B))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-exp-log`
31×	`prod-exp`
29×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube`
18×	`times-frac`
16×	`associate-r`
9×	`div-exp`
8×	`associate-l`
7×	`pow1` `unpow-prod-down` `cbrt-unprod`
6×	`pow-to-exp` `pow-exp`
4×	`rec-exp` `1-exp` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-/r` `associate-/l` `unswap-sqr` `sqr-pow`
2×	`*-commutative` `div-inv`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `tan-quot` `associate-*r/` `associate-/r/` `un-div-inv`

Counts

4 → 119

Calls

4 calls:

Slowest

113.0ms	(* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (/ 1 (sin B)))
83.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
27.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
10.0ms	(/ x (tan B))

series600.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

226.0ms	(* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (/ 1 (sin B)))
159.0ms	(/ x (tan B))
121.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
94.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify14.0s

Counts

100 → 131

Calls

100 calls:

Slowest

590.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
544.0ms	(+ (+ (log (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (log F)) (- (log (sin B))))
532.0ms	(* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (/ 1 (sin B)))
525.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
523.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

14.6b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.2b	(/ (* x (cos B)) (sin B))

rewrite209.0ms

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

106.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
52.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
38.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
12.0ms	(/ (* x (cos B)) (sin B))

series555.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

246.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
129.0ms	(/ (* x (cos B)) (sin B))
92.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
88.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify10.2s

Counts

66 → 102

Calls

66 calls:

Slowest

874.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)
602.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
597.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
546.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
498.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

14.6b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b	(/ 1 (/ (sin B) (* x (cos B))))
0.3b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log`
36×	`times-frac`
32×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube`
16×	`div-exp`
10×	`associate-/r*`
9×	`prod-exp`
7×	`cbrt-undiv` `unpow-prod-down` `associate-l`
6×	`pow1` `div-inv`
4×	`insert-posit16` `associate-/l*` `add-log-exp`
3×	`pow-to-exp` `rec-exp` `pow-unpow` `1-exp` `associate-r` `pow-exp` `cbrt-unprod` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg`
1×	`pow-pow` `associate-/r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 125

Calls

4 calls:

Slowest

103.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
56.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
28.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
13.0ms	(/ 1 (/ (sin B) (* x (cos B))))

series520.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

208.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
123.0ms	(/ 1 (/ (sin B) (* x (cos B))))
97.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
91.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify12.9s

Counts

115 → 137

Calls

115 calls:

Slowest

567.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
541.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
521.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
503.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
470.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)

prune2.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes225.0ms

Accuracy

98.6% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.6b

bsearch555.0ms

end27.0ms

sample13.5s

Algorithm

intervals

Results

4.9s	1612×	body	1280	valid
3.3s	4908×	body	80	valid
2.7s	1355×	body	640	valid
992.0ms	1618×	body	80	nan
956.0ms	681×	body	320	valid
286.0ms	349×	body	160	valid