Details

sample676.0ms

Algorithm

intervals

Results

119.0ms	47×	body	1280	valid
98.0ms	169×	body	80	valid
94.0ms	42×	body	640	valid
26.0ms	19×	body	320	valid
21.0ms	54×	body	80	nan
8.0ms	11×	body	160	valid

simplify594.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

593.0ms

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

prune81.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.8b

localize134.0ms

Local error

Found 4 expressions with local error:

19.6b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.9b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.2b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.1b	(/ x (tan B))

rewrite761.0ms

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

566.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
143.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
37.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
10.0ms	(/ x (tan B))

series633.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

227.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
157.0ms	(/ x (tan B))
153.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
96.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify10.5s

Counts

79 → 109

Calls

79 calls:

Slowest

628.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
588.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
561.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
555.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
453.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

19.6b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.8b	(/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
0.2b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b	(/ 1 (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

Slowest

116.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
62.0ms	(/ 1 (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)))
41.0ms	(/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
35.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

series663.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

238.0ms	(/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
216.0ms	(/ 1 (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)))
114.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
94.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify27.1s

Counts

117 → 143

Calls

117 calls:

Slowest

942.0ms	(/ 1 (/ 1 (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)))
857.0ms	(/ (sqrt 1) (/ 1 (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)))
624.0ms	(/ (sqrt 1) (/ (* (cbrt (sin B)) (cbrt (sin B))) (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)))
620.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
566.0ms	(/ (cbrt 1) (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)))

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

19.6b	(pow (+ (* x 2) (+ 2 (* F F))) -1/2)
0.9b	(* (/ 1 (sin B)) (* F (pow (+ (* x 2) (+ 2 (* F F))) -1/2)))
0.2b	(* F (pow (+ (* x 2) (+ 2 (* F F))) -1/2))
0.1b	(/ 1 (sin B))

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

58×	`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-l`
10×	`div-exp`
8×	`pow1` `associate-r`
7×	`unpow-prod-down` `cbrt-unprod`
6×	`pow-to-exp` `pow-exp`
5×	`rec-exp` `1-exp`
4×	`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` `associate-*l/` `pow-flip` `inv-pow`

Counts

4 → 121

Calls

4 calls:

Slowest

144.0ms	(* (/ 1 (sin B)) (* F (pow (+ (* x 2) (+ 2 (* F F))) -1/2)))
124.0ms	(* F (pow (+ (* x 2) (+ 2 (* F F))) -1/2))
20.0ms	(pow (+ (* x 2) (+ 2 (* F F))) -1/2)
10.0ms	(/ 1 (sin B))

series618.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

262.0ms	(pow (+ (* x 2) (+ 2 (* F F))) -1/2)
209.0ms	(* (/ 1 (sin B)) (* F (pow (+ (* x 2) (+ 2 (* F F))) -1/2)))
122.0ms	(* F (pow (+ (* x 2) (+ 2 (* F F))) -1/2))
25.0ms	(/ 1 (sin B))

simplify16.3s

Counts

99 → 133

Calls

99 calls:

Slowest

623.0ms	(* (sqrt F) (pow (sqrt (+ (* x 2) (+ 2 (* F F)))) -1/2))
612.0ms	(* (/ 1 (sin B)) (* F (pow (+ (* x 2) (+ 2 (* F F))) -1/2)))
556.0ms	(* (sqrt F) (pow (+ (* x 2) (+ 2 (* F F))) (/ -1/2 2)))
522.0ms	(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
514.0ms	(+ (- 0 (log (sin B))) (log (* F (pow (+ (* x 2) (+ 2 (* F F))) -1/2))))

prune2.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

19.6b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.9b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.2b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b	(/ (* x (cos B)) (sin B))

rewrite210.0ms

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

104.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
48.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
32.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
23.0ms	(/ (* x (cos B)) (sin B))

series537.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

222.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
118.0ms	(/ (* x (cos B)) (sin B))
106.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
91.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify10.8s

Counts

66 → 102

Calls

66 calls:

Slowest

1.0s	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
575.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
559.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
533.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
477.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes496.0ms

Accuracy

97.2% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.2b

bsearch630.0ms

end0.0ms

sample14.1s

Algorithm

intervals

Results

6.2s	1688×	body	1280	valid
2.8s	1411×	body	640	valid
2.3s	4800×	body	80	valid
1.3s	696×	body	320	valid
788.0ms	1657×	body	80	nan
329.0ms	346×	body	160	valid