Details

sample655.0ms

Algorithm

intervals

Results

162.0ms	158×	body	80	valid
158.0ms	45×	body	1280	valid
127.0ms	56×	body	640	valid
40.0ms	23×	body	320	valid
26.0ms	60×	body	80	nan
12.0ms	11×	body	160	valid

simplify517.0ms

Calls

1 calls:

Slowest

516.0ms

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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.3b

localize84.0ms

Local error

Found 4 expressions with local error:

16.7b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.4b	(/ (* (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))

rewrite206.0ms

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`

Calls

4 calls:

Slowest

133.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
32.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
31.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
7.0ms	(/ x (tan B))

series583.0ms

Calls

4 calls:

Slowest

203.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
150.0ms	(/ x (tan B))
124.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
106.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify11.0s

Calls

79 calls:

Slowest

799.0ms	(* (* (* (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))
603.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
589.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
536.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
529.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

16.7b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.4b	(/ (* (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))

rewrite175.0ms

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`

Calls

4 calls:

Slowest

93.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
32.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
24.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
23.0ms	(/ (* x (cos B)) (sin B))

series562.0ms

Calls

4 calls:

Slowest

214.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
144.0ms	(/ (* x (cos B)) (sin B))
106.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
97.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify10.3s

Calls

66 calls:

Slowest

597.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
596.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
540.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
532.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
480.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

16.7b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.4b	(/ (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)))

rewrite247.0ms

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`

Calls

4 calls:

Slowest

126.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
48.0ms	(/ 1 (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)))
45.0ms	(/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
25.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

series609.0ms

Calls

4 calls:

Slowest

196.0ms	(/ 1 (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)))
184.0ms	(/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
125.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
104.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify26.4s

Calls

117 calls:

Slowest

905.0ms	(/ 1 (/ 1 (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)))
792.0ms	(/ (* (* 1 1) 1) (/ (* (* (sin B) (sin B)) (sin B)) (* (* (* (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))))
641.0ms	(/ (sqrt 1) (/ (* (cbrt (sin B)) (cbrt (sin B))) (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)))
625.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
602.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))

prune2.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

16.7b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.9b	(/ (/ 1 (sin B)) (/ 1 (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)))
0.2b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b	(/ (* x (cos B)) (sin B))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

208×	`times-frac`
172×	`add-exp-log`
112×	`div-exp`
100×	`add-sqr-sqrt`
95×	`*-un-lft-identity` `add-cube-cbrt`
40×	`prod-exp`
32×	`add-cbrt-cube`
29×	`rec-exp` `1-exp`
24×	`div-inv`
15×	`cbrt-undiv`
14×	`pow-to-exp` `pow-exp` `associate-/l*`
10×	`associate-/r*`
7×	`unpow-prod-down` `associate-l`
5×	`pow1`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `associate-r` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg`
1×	`pow-pow` `associate-/r/` `*-commutative` `associate-/l/`

Calls

4 calls:

Slowest

78.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
54.0ms	(/ (/ 1 (sin B)) (/ 1 (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)))
19.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
12.0ms	(/ (* x (cos B)) (sin B))

series430.0ms

Calls

4 calls:

Slowest

149.0ms	(/ (/ 1 (sin B)) (/ 1 (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)))
121.0ms	(/ (* x (cos B)) (sin B))
85.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
75.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify1.1m

Calls

309 calls:

Slowest

1.3s	(/ (/ (sqrt 1) 1) (/ 1 (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)))
944.0ms	(/ (/ (* (cbrt 1) (cbrt 1)) 1) (/ 1 (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)))
923.0ms	(/ 1 (/ 1 (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)))
783.0ms	(/ 1 (/ 1 (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)))
766.0ms	(/ (/ (sqrt 1) 1) (/ (sqrt 1) (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)))

prune4.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes472.0ms

Accuracy

98% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.7b

bsearch897.0ms

end0.0ms

sample13.1s

Algorithm

intervals

Results

4.8s	1675×	body	1280	valid
3.3s	4754×	body	80	valid
2.6s	1421×	body	640	valid
1.0s	684×	body	320	valid
706.0ms	1679×	body	80	nan
377.0ms	352×	body	160	valid